diff --git a/.env.example b/.env.example
index 33807b2..761e765 100644
--- a/.env.example
+++ b/.env.example
@@ -5,3 +5,4 @@ DJANGO_ALLOWED_HOSTS=localhost,127.0.0.1
 DATABASE_URL=mysql://hulumath:hulumath@127.0.0.1:3307/hulumath
 REDIS_URL=redis://localhost:6379/0
 CORS_ALLOWED_ORIGINS=http://localhost:3000
+CALCULATOR_RATE=30/minute
diff --git a/.env.production.example b/.env.production.example
index 5f98d53..08183a6 100644
--- a/.env.production.example
+++ b/.env.production.example
@@ -14,6 +14,7 @@ CORS_ALLOWED_ORIGINS=https://math.example.com
 CSRF_TRUSTED_ORIGINS=https://math.example.com
 API_ANON_RATE=120/minute
 API_USER_RATE=600/minute
+CALCULATOR_RATE=30/minute
 SECURE_HSTS_SECONDS=31536000
 
 # 仅供部署脚本直接访问 127.0.0.1:8000 时设置 Host 头。
diff --git a/Makefile b/Makefile
index 10d126d..d8ed05c 100644
--- a/Makefile
+++ b/Makefile
@@ -18,5 +18,6 @@ test:
 	.venv/bin/python -m pytest -q
 
 check:
+	.venv/bin/ruff check backend scripts
 	cd backend && ../.venv/bin/python manage.py check
 	cd backend && ../.venv/bin/python manage.py makemigrations --check --dry-run
diff --git a/README.md b/README.md
index 4c49c0b..997acec 100644
--- a/README.md
+++ b/README.md
@@ -14,13 +14,13 @@
 - 12 题 MathBTI、16 种数学人格、人物卡与数学精灵初始化
 - 统一版本化剧情引擎、85 节点信仰者主线、2 个人物 Skill 样板
 - 剧情服务端存档、嵌套资源效果、结局与幂等选择
-- 入门、标准、进阶三赛道的实时 1v1、今日挑战和单人闯关
+- 入门、标准、进阶三赛道的实时 1v1、今日挑战、单人闯关、24 点和数独
 - 题目版本、服务端计时判分、Elo Rating、排行榜和基础反作弊
 - Channels WebSocket 比赛进度通道，Redis Channel Layer
 - LaTeX 文档与版本、六级零基础课程、练习判定
 - 54 条旧版志愿者视频、五维能力地图、专业筛选与融合视频流
 - 视频观看进度、幂等奖励、收藏、五维能力、数学精灵和人物卡册
-- 多工具工具箱：口算入口、科学计算器、符号查询、函数绘图和 LaTeX Lab
+- 多工具工具箱：强计算器、增强函数绘图、数学白板、几何画板、符号查询和 LaTeX Lab
 - Django Admin、健康检查、请求 ID、限流与统一 API 错误结构
 - MySQL 8.0/Redis Docker Compose、Gitea CI 和自动化测试
 
@@ -88,6 +88,7 @@ backend/
 ├── progression/    # 五维能力、精灵、卡牌、奖励
 ├── content/        # 视频、知识卡片、人物内容
 ├── engagement/     # 签到与通知
+├── toolbox/        # 受限数学计算内核与工具 API
 ├── common/         # 健康检查、错误、日志
 └── config/         # Django/ASGI 配置
 ```
diff --git a/backend/common/test_frontend_assets.py b/backend/common/test_frontend_assets.py
index fd44998..b5719ea 100644
--- a/backend/common/test_frontend_assets.py
+++ b/backend/common/test_frontend_assets.py
@@ -34,3 +34,24 @@ def test_admin_css_深色系统下仍保持完整浅色主题():
     assert "background-color: #ffffff !important" in source
     assert ".theme-toggle" in source
     assert "display: none" in source
+
+
+def test_toolbox_and_games_资源入口与移动端触控样式存在():
+    template = (settings.BASE_DIR / "templates" / "index.html").read_text(encoding="utf-8")
+    toolbox = (STATIC_ROOT / "js" / "toolbox.js").read_text(encoding="utf-8")
+    games = (STATIC_ROOT / "js" / "games.js").read_text(encoding="utf-8")
+    styles = (STATIC_ROOT / "css" / "app.css").read_text(encoding="utf-8")
+
+    assert "js/toolbox.js" in template
+    assert "js/games.js" in template
+    assert 'id="whiteboard-canvas"' in template
+    assert 'id="geometry-canvas"' in template
+    assert 'id="math-game-list"' in template
+    assert "window.HuluToolbox" in toolbox
+    assert "pointerdown" in toolbox
+    assert "window.HuluGames" in games
+    assert "sudoku-board" in games
+    assert "touch-action: none" in styles
+    assert ".calculator-controls [hidden]" in styles
+    assert ".sudoku-board" in styles
+    assert "@media (max-width: 700px)" in styles
diff --git a/backend/config/settings.py b/backend/config/settings.py
index 509f7b3..725243a 100644
--- a/backend/config/settings.py
+++ b/backend/config/settings.py
@@ -38,6 +38,7 @@ INSTALLED_APPS = [
     "latex_lab",
     "content",
     "engagement",
+    "toolbox",
     "common",
 ]
 
@@ -142,6 +143,7 @@ REST_FRAMEWORK = {
     "DEFAULT_THROTTLE_RATES": {
         "anon": os.getenv("API_ANON_RATE", "120/minute"),
         "user": os.getenv("API_USER_RATE", "600/minute"),
+        "calculator": os.getenv("CALCULATOR_RATE", "30/minute"),
     },
 }
 
diff --git a/backend/config/urls.py b/backend/config/urls.py
index 3a6c2e1..e4dccb6 100644
--- a/backend/config/urls.py
+++ b/backend/config/urls.py
@@ -17,4 +17,5 @@ urlpatterns = [
     path("api/v1/latex/", include("latex_lab.urls")),
     path("api/v1/content/", include("content.urls")),
     path("api/v1/progression/", include("progression.urls")),
+    path("api/v1/toolbox/", include("toolbox.urls")),
 ]
diff --git a/backend/contest/admin.py b/backend/contest/admin.py
index 9ba5564..140d575 100644
--- a/backend/contest/admin.py
+++ b/backend/contest/admin.py
@@ -7,6 +7,7 @@ from .models import (
     ContestAttempt,
     ContestQuestion,
     LeaderboardSnapshot,
+    MathGameAttempt,
     Question,
     QuestionVersion,
     RatingHistory,
@@ -64,3 +65,21 @@ admin.site.register(ContestAnswer)
 admin.site.register(RealtimeMatch)
 admin.site.register(RatingHistory)
 admin.site.register(LeaderboardSnapshot)
+
+
+@admin.register(MathGameAttempt)
+class MathGameAttemptAdmin(admin.ModelAdmin):
+    list_display = (
+        "id",
+        "user",
+        "kind",
+        "difficulty",
+        "status",
+        "score",
+        "hints_used",
+        "started_at",
+    )
+    list_filter = ("kind", "difficulty", "status")
+    search_fields = ("user__username", "user__nickname")
+    readonly_fields = ("puzzle", "solution", "submission", "started_at", "submitted_at")
+    ordering = ("-started_at",)
diff --git a/backend/contest/game_services.py b/backend/contest/game_services.py
new file mode 100644
index 0000000..aaa2549
--- /dev/null
+++ b/backend/contest/game_services.py
@@ -0,0 +1,220 @@
+import ast
+import secrets
+from collections import Counter
+from fractions import Fraction
+
+from django.db import transaction
+from django.utils import timezone
+from rest_framework.exceptions import ValidationError
+
+from .models import MathGameAttempt
+
+SUDOKU_PUZZLES = {
+    MathGameAttempt.Difficulty.EASY: [
+        (
+            "530070000600195000098000060800060003400803001700020006060000280000419005000080079",
+            "534678912672195348198342567859761423426853791713924856961537284287419635345286179",
+        ),
+    ],
+    MathGameAttempt.Difficulty.STANDARD: [
+        (
+            "000260701680070090190004500820100040004602900050003028009300074040050036703018000",
+            "435269781682571493197834562826195347374682915951743628519326874248957136763418259",
+        ),
+    ],
+    MathGameAttempt.Difficulty.HARD: [
+        (
+            "000000010400000000020000000000050407008000300001090000300400200050100000000806000",
+            "693784512487512936125963874932651487568247391741398625319475268856129743274836159",
+        ),
+    ],
+}
+
+TWENTY_FOUR_PUZZLES = {
+    MathGameAttempt.Difficulty.EASY: [(3, 3, 8, 8), (1, 3, 4, 6), (4, 4, 10, 10)],
+    MathGameAttempt.Difficulty.STANDARD: [(2, 3, 4, 9), (3, 5, 7, 13), (4, 7, 8, 8)],
+    MathGameAttempt.Difficulty.HARD: [(1, 5, 5, 5), (3, 3, 7, 7), (5, 5, 7, 11)],
+}
+
+
+def _grid_from_text(value):
+    return [[int(value[row * 9 + column]) for column in range(9)] for row in range(9)]
+
+
+def game_payload(attempt):
+    return {
+        "attempt_id": attempt.id,
+        "kind": attempt.kind,
+        "difficulty": attempt.difficulty,
+        "status": attempt.status,
+        "puzzle": attempt.puzzle,
+        "score": attempt.score,
+        "duration_ms": attempt.duration_ms,
+        "hints_used": attempt.hints_used,
+        "started_at": attempt.started_at,
+    }
+
+
+def start_game(user, kind, difficulty):
+    if kind not in MathGameAttempt.Kind.values:
+        raise ValidationError({"kind": "不支持的数学玩法"})
+    if difficulty not in MathGameAttempt.Difficulty.values:
+        raise ValidationError({"difficulty": "不支持的难度"})
+    if kind == MathGameAttempt.Kind.SUDOKU:
+        puzzle_text, solution_text = secrets.choice(SUDOKU_PUZZLES[difficulty])
+        puzzle = {"grid": _grid_from_text(puzzle_text), "hints": []}
+        solution = {"grid": _grid_from_text(solution_text)}
+    else:
+        numbers = list(secrets.choice(TWENTY_FOUR_PUZZLES[difficulty]))
+        secrets.SystemRandom().shuffle(numbers)
+        puzzle = {"numbers": numbers}
+        solution = {"target": 24}
+    attempt = MathGameAttempt.objects.create(
+        user=user,
+        kind=kind,
+        difficulty=difficulty,
+        puzzle=puzzle,
+        solution=solution,
+    )
+    return game_payload(attempt)
+
+
+def _validate_twenty_four_expression(source, numbers):
+    source = str(source or "").strip()
+    if not source or len(source) > 120:
+        raise ValidationError({"expression": "请输入不超过 120 个字符的表达式"})
+    try:
+        tree = ast.parse(source, mode="eval")
+    except SyntaxError as exc:
+        raise ValidationError({"expression": "表达式语法无效"}) from exc
+    used = []
+
+    def evaluate(node):
+        if isinstance(node, ast.Constant) and isinstance(node.value, int):
+            used.append(node.value)
+            return Fraction(node.value)
+        if isinstance(node, ast.BinOp) and isinstance(
+            node.op,
+            (ast.Add, ast.Sub, ast.Mult, ast.Div),
+        ):
+            left = evaluate(node.left)
+            right = evaluate(node.right)
+            if isinstance(node.op, ast.Add):
+                return left + right
+            if isinstance(node.op, ast.Sub):
+                return left - right
+            if isinstance(node.op, ast.Mult):
+                return left * right
+            if right == 0:
+                raise ValidationError({"expression": "不能除以零"})
+            return left / right
+        raise ValidationError({"expression": "只允许题目数字、括号和 + - * /"})
+
+    result = evaluate(tree.body)
+    if Counter(used) != Counter(numbers):
+        raise ValidationError({"expression": "必须且只能使用题目给出的四个数字各一次"})
+    if result != 24:
+        raise ValidationError({"expression": f"当前结果是 {result}，还没有得到 24"})
+    return source
+
+
+def _validate_sudoku_grid(raw_grid, puzzle, solution):
+    if (
+        not isinstance(raw_grid, list)
+        or len(raw_grid) != 9
+        or any(not isinstance(row, list) or len(row) != 9 for row in raw_grid)
+    ):
+        raise ValidationError({"grid": "数独答案必须是 9×9 网格"})
+    try:
+        grid = [[int(value) for value in row] for row in raw_grid]
+    except (TypeError, ValueError) as exc:
+        raise ValidationError({"grid": "每个格子必须填写 1 到 9"}) from exc
+    if any(value < 1 or value > 9 for row in grid for value in row):
+        raise ValidationError({"grid": "每个格子必须填写 1 到 9"})
+    givens = puzzle["grid"]
+    for row in range(9):
+        for column in range(9):
+            if givens[row][column] and grid[row][column] != givens[row][column]:
+                raise ValidationError({"grid": "不能修改题目给出的数字"})
+    if grid != solution["grid"]:
+        raise ValidationError({"grid": "答案尚未满足全部行、列和九宫格"})
+    return grid
+
+
+@transaction.atomic
+def submit_game(user, attempt_id, submission, submission_key):
+    attempt = MathGameAttempt.objects.select_for_update().get(id=attempt_id, user=user)
+    if attempt.status == MathGameAttempt.Status.COMPLETED:
+        if submission_key and attempt.submission_key == submission_key:
+            return game_payload(attempt)
+        raise ValidationError("这局游戏已经完成")
+    if not submission_key:
+        raise ValidationError({"Idempotency-Key": "提交必须提供幂等键"})
+
+    if attempt.kind == MathGameAttempt.Kind.SUDOKU:
+        normalized = {
+            "grid": _validate_sudoku_grid(
+                submission.get("grid"),
+                attempt.puzzle,
+                attempt.solution,
+            )
+        }
+    else:
+        normalized = {
+            "expression": _validate_twenty_four_expression(
+                submission.get("expression"),
+                attempt.puzzle["numbers"],
+            )
+        }
+
+    now = timezone.now()
+    duration_ms = max(0, int((now - attempt.started_at).total_seconds() * 1000))
+    base_score = 1800 if attempt.kind == MathGameAttempt.Kind.SUDOKU else 1000
+    time_penalty = duration_ms // (2000 if attempt.kind == MathGameAttempt.Kind.SUDOKU else 1000)
+    attempt.submission = normalized
+    attempt.status = MathGameAttempt.Status.COMPLETED
+    attempt.duration_ms = duration_ms
+    attempt.score = max(100, base_score - time_penalty - attempt.hints_used * 150)
+    attempt.submission_key = submission_key
+    attempt.submitted_at = now
+    attempt.save(
+        update_fields=[
+            "submission",
+            "status",
+            "duration_ms",
+            "score",
+            "submission_key",
+            "submitted_at",
+        ]
+    )
+    return game_payload(attempt)
+
+
+@transaction.atomic
+def request_sudoku_hint(user, attempt_id):
+    attempt = MathGameAttempt.objects.select_for_update().get(id=attempt_id, user=user)
+    if attempt.kind != MathGameAttempt.Kind.SUDOKU:
+        raise ValidationError("只有数独支持提示")
+    if attempt.status != MathGameAttempt.Status.ACTIVE:
+        raise ValidationError("这局游戏已经结束")
+    hints = list(attempt.puzzle.get("hints", []))
+    if len(hints) >= 3:
+        raise ValidationError("每局最多使用 3 次提示")
+    candidates = [
+        (row, column)
+        for row in range(9)
+        for column in range(9)
+        if attempt.puzzle["grid"][row][column] == 0
+        and not any(item["row"] == row and item["column"] == column for item in hints)
+    ]
+    row, column = secrets.choice(candidates)
+    hint = {
+        "row": row,
+        "column": column,
+        "value": attempt.solution["grid"][row][column],
+    }
+    hints.append(hint)
+    attempt.puzzle = {**attempt.puzzle, "hints": hints}
+    attempt.hints_used = len(hints)
+    attempt.save(update_fields=["puzzle", "hints_used"])
+    return {**hint, "hints_used": attempt.hints_used}
diff --git a/backend/contest/migrations/0003_mathgameattempt_and_more.py b/backend/contest/migrations/0003_mathgameattempt_and_more.py
new file mode 100644
index 0000000..ed9b817
--- /dev/null
+++ b/backend/contest/migrations/0003_mathgameattempt_and_more.py
@@ -0,0 +1,44 @@
+# Generated by Django 4.2.23 on 2026-08-08 17:26
+
+from django.conf import settings
+from django.db import migrations, models
+import django.db.models.deletion
+import uuid
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        migrations.swappable_dependency(settings.AUTH_USER_MODEL),
+        ('contest', '0002_realtimematch_matchmaking_lookup_idx'),
+    ]
+
+    operations = [
+        migrations.CreateModel(
+            name='MathGameAttempt',
+            fields=[
+                ('id', models.UUIDField(default=uuid.uuid4, editable=False, primary_key=True, serialize=False)),
+                ('kind', models.CharField(choices=[('sudoku', '数独'), ('twenty_four', '24 点')], max_length=20)),
+                ('difficulty', models.CharField(choices=[('easy', '入门'), ('standard', '标准'), ('hard', '进阶')], default='standard', max_length=16)),
+                ('puzzle', models.JSONField(default=dict)),
+                ('solution', models.JSONField(default=dict)),
+                ('submission', models.JSONField(blank=True, default=dict)),
+                ('status', models.CharField(choices=[('active', '进行中'), ('completed', '已完成'), ('failed', '未通过')], default='active', max_length=16)),
+                ('score', models.PositiveIntegerField(default=0)),
+                ('duration_ms', models.PositiveIntegerField(default=0)),
+                ('hints_used', models.PositiveSmallIntegerField(default=0)),
+                ('submission_key', models.CharField(blank=True, max_length=80, null=True)),
+                ('started_at', models.DateTimeField(auto_now_add=True)),
+                ('submitted_at', models.DateTimeField(blank=True, null=True)),
+                ('user', models.ForeignKey(on_delete=django.db.models.deletion.CASCADE, related_name='math_game_attempts', to=settings.AUTH_USER_MODEL)),
+            ],
+            options={
+                'ordering': ['-started_at'],
+                'indexes': [models.Index(fields=['kind', 'status', '-score', 'duration_ms'], name='math_game_ranking_idx')],
+            },
+        ),
+        migrations.AddConstraint(
+            model_name='mathgameattempt',
+            constraint=models.UniqueConstraint(fields=('user', 'submission_key'), name='unique_user_math_game_submission'),
+        ),
+    ]
diff --git a/backend/contest/models.py b/backend/contest/models.py
index 670e967..9ac860e 100644
--- a/backend/contest/models.py
+++ b/backend/contest/models.py
@@ -192,3 +192,57 @@ class CheatFlag(models.Model):
     evidence = models.JSONField(default=dict)
     status = models.CharField(max_length=16, choices=Status.choices, default=Status.OPEN)
     created_at = models.DateTimeField(auto_now_add=True)
+
+
+class MathGameAttempt(models.Model):
+    class Kind(models.TextChoices):
+        SUDOKU = "sudoku", "数独"
+        TWENTY_FOUR = "twenty_four", "24 点"
+
+    class Difficulty(models.TextChoices):
+        EASY = "easy", "入门"
+        STANDARD = "standard", "标准"
+        HARD = "hard", "进阶"
+
+    class Status(models.TextChoices):
+        ACTIVE = "active", "进行中"
+        COMPLETED = "completed", "已完成"
+        FAILED = "failed", "未通过"
+
+    id = models.UUIDField(primary_key=True, default=uuid.uuid4, editable=False)
+    user = models.ForeignKey(
+        settings.AUTH_USER_MODEL,
+        on_delete=models.CASCADE,
+        related_name="math_game_attempts",
+    )
+    kind = models.CharField(max_length=20, choices=Kind.choices)
+    difficulty = models.CharField(
+        max_length=16,
+        choices=Difficulty.choices,
+        default=Difficulty.STANDARD,
+    )
+    puzzle = models.JSONField(default=dict)
+    solution = models.JSONField(default=dict)
+    submission = models.JSONField(default=dict, blank=True)
+    status = models.CharField(max_length=16, choices=Status.choices, default=Status.ACTIVE)
+    score = models.PositiveIntegerField(default=0)
+    duration_ms = models.PositiveIntegerField(default=0)
+    hints_used = models.PositiveSmallIntegerField(default=0)
+    submission_key = models.CharField(max_length=80, null=True, blank=True)
+    started_at = models.DateTimeField(auto_now_add=True)
+    submitted_at = models.DateTimeField(null=True, blank=True)
+
+    class Meta:
+        constraints = [
+            models.UniqueConstraint(
+                fields=("user", "submission_key"),
+                name="unique_user_math_game_submission",
+            )
+        ]
+        indexes = [
+            models.Index(
+                fields=("kind", "status", "-score", "duration_ms"),
+                name="math_game_ranking_idx",
+            )
+        ]
+        ordering = ["-started_at"]
diff --git a/backend/contest/test_game_services.py b/backend/contest/test_game_services.py
new file mode 100644
index 0000000..588e768
--- /dev/null
+++ b/backend/contest/test_game_services.py
@@ -0,0 +1,121 @@
+import pytest
+from rest_framework.exceptions import ValidationError
+
+from accounts.models import User
+from contest.game_services import (
+    SUDOKU_PUZZLES,
+    request_sudoku_hint,
+    start_game,
+    submit_game,
+)
+from contest.models import MathGameAttempt
+
+
+@pytest.fixture
+def game_user(db):
+    return User.objects.create_user(
+        username="game_user",
+        password="StrongPass_2026",
+        nickname="游戏玩家",
+    )
+
+
+@pytest.mark.django_db
+def test_twenty_four_服务端校验数字使用与幂等提交(game_user):
+    attempt = MathGameAttempt.objects.create(
+        user=game_user,
+        kind=MathGameAttempt.Kind.TWENTY_FOUR,
+        puzzle={"numbers": [1, 3, 4, 6]},
+        solution={"target": 24},
+    )
+
+    result = submit_game(
+        game_user,
+        attempt.id,
+        {"expression": "6 / (1 - 3 / 4)"},
+        "game-submit-1",
+    )
+    replay = submit_game(
+        game_user,
+        attempt.id,
+        {"expression": "1 + 3 + 4 + 6"},
+        "game-submit-1",
+    )
+
+    assert result["status"] == MathGameAttempt.Status.COMPLETED
+    assert result["score"] >= 100
+    assert replay["score"] == result["score"]
+
+
+@pytest.mark.django_db
+def test_twenty_four_拒绝额外数字和非四则表达式(game_user):
+    attempt = MathGameAttempt.objects.create(
+        user=game_user,
+        kind=MathGameAttempt.Kind.TWENTY_FOUR,
+        puzzle={"numbers": [1, 3, 4, 6]},
+        solution={"target": 24},
+    )
+
+    with pytest.raises(ValidationError, match="四个数字"):
+        submit_game(
+            game_user,
+            attempt.id,
+            {"expression": "6 / (1 - 3 / 4) + 24 - 24"},
+            "invalid-extra-number",
+        )
+    with pytest.raises(ValidationError, match="只允许"):
+        submit_game(
+            game_user,
+            attempt.id,
+            {"expression": "pow(2, 3) * 3"},
+            "invalid-function",
+        )
+
+
+@pytest.mark.django_db
+def test_sudoku_提示受限并由服务端校验完整答案(game_user):
+    payload = start_game(
+        game_user,
+        MathGameAttempt.Kind.SUDOKU,
+        MathGameAttempt.Difficulty.EASY,
+    )
+    attempt = MathGameAttempt.objects.get(id=payload["attempt_id"])
+    hint = request_sudoku_hint(game_user, attempt.id)
+    solution_text = SUDOKU_PUZZLES[MathGameAttempt.Difficulty.EASY][0][1]
+    solution = [
+        [int(solution_text[row * 9 + column]) for column in range(9)]
+        for row in range(9)
+    ]
+
+    result = submit_game(
+        game_user,
+        attempt.id,
+        {"grid": solution},
+        "sudoku-submit-1",
+    )
+
+    assert hint["value"] == solution[hint["row"]][hint["column"]]
+    assert result["status"] == MathGameAttempt.Status.COMPLETED
+    assert result["hints_used"] == 1
+
+
+@pytest.mark.django_db
+def test_math_game_api_目录公开但开局需要登录(client, game_user):
+    catalog = client.get("/api/v1/contests/games/")
+    anonymous_start = client.post(
+        "/api/v1/contests/games/twenty_four/start/",
+        {"difficulty": "easy"},
+        content_type="application/json",
+    )
+    client.force_login(game_user)
+    authenticated_start = client.post(
+        "/api/v1/contests/games/twenty_four/start/",
+        {"difficulty": "easy"},
+        content_type="application/json",
+    )
+
+    assert catalog.status_code == 200
+    assert {item["kind"] for item in catalog.json()} == {"sudoku", "twenty_four"}
+    assert anonymous_start.status_code in {401, 403}
+    assert authenticated_start.status_code == 201
+    assert "solution" not in authenticated_start.json()
diff --git a/backend/contest/urls.py b/backend/contest/urls.py
index dcf9ae5..a9f664d 100644
--- a/backend/contest/urls.py
+++ b/backend/contest/urls.py
@@ -7,6 +7,11 @@ from .views import (
     LeaderboardView,
     MatchmakingView,
     MatchStateView,
+    MathGameCatalogView,
+    MathGameHistoryView,
+    MathGameStartView,
+    MathGameSubmitView,
+    SudokuHintView,
 )
 
 urlpatterns = [
@@ -16,4 +21,17 @@ urlpatterns = [
     path("<slug:slug>/leaderboard/", LeaderboardView.as_view(), name="leaderboard"),
     path("attempts/<uuid:attempt_id>/submit/", AttemptSubmitView.as_view(), name="attempt-submit"),
     path("matches/<uuid:match_id>/", MatchStateView.as_view(), name="match-state"),
+    path("games/", MathGameCatalogView.as_view(), name="math-game-catalog"),
+    path("games/history/", MathGameHistoryView.as_view(), name="math-game-history"),
+    path("games/<str:kind>/start/", MathGameStartView.as_view(), name="math-game-start"),
+    path(
+        "games/attempts/<uuid:attempt_id>/submit/",
+        MathGameSubmitView.as_view(),
+        name="math-game-submit",
+    ),
+    path(
+        "games/attempts/<uuid:attempt_id>/hint/",
+        SudokuHintView.as_view(),
+        name="sudoku-hint",
+    ),
 ]
diff --git a/backend/contest/views.py b/backend/contest/views.py
index 04ef6de..f9ab9cb 100644
--- a/backend/contest/views.py
+++ b/backend/contest/views.py
@@ -3,7 +3,8 @@ from rest_framework import permissions, status
 from rest_framework.response import Response
 from rest_framework.views import APIView
 
-from .models import Contest, ContestAttempt, RealtimeMatch
+from .game_services import game_payload, request_sudoku_hint, start_game, submit_game
+from .models import Contest, ContestAttempt, MathGameAttempt, RealtimeMatch
 from .services import (
     find_match,
     match_payload,
@@ -98,3 +99,59 @@ class LeaderboardView(APIView):
                 for index, attempt in enumerate(attempts, start=1)
             ]
         )
+
+
+class MathGameCatalogView(APIView):
+    permission_classes = [permissions.AllowAny]
+
+    def get(self, request):
+        return Response(
+            [
+                {
+                    "kind": MathGameAttempt.Kind.TWENTY_FOUR,
+                    "title": "24 点",
+                    "summary": "四个数字各用一次，只用四则运算得到 24。",
+                    "ability": "connection",
+                    "estimated_minutes": 3,
+                },
+                {
+                    "kind": MathGameAttempt.Kind.SUDOKU,
+                    "title": "数独",
+                    "summary": "在行、列和九宫格约束中完成 9×9 数字推理。",
+                    "ability": "detection",
+                    "estimated_minutes": 8,
+                },
+            ]
+        )
+
+
+class MathGameStartView(APIView):
+    def post(self, request, kind):
+        payload = start_game(
+            request.user,
+            kind,
+            request.data.get("difficulty", MathGameAttempt.Difficulty.STANDARD),
+        )
+        return Response(payload, status=status.HTTP_201_CREATED)
+
+
+class MathGameSubmitView(APIView):
+    def post(self, request, attempt_id):
+        payload = submit_game(
+            request.user,
+            attempt_id,
+            request.data,
+            request.headers.get("Idempotency-Key"),
+        )
+        return Response(payload)
+
+
+class SudokuHintView(APIView):
+    def post(self, request, attempt_id):
+        return Response(request_sudoku_hint(request.user, attempt_id))
+
+
+class MathGameHistoryView(APIView):
+    def get(self, request):
+        attempts = MathGameAttempt.objects.filter(user=request.user)[:20]
+        return Response([game_payload(attempt) for attempt in attempts])
diff --git a/backend/progression/views.py b/backend/progression/views.py
index 3d20205..b33b81e 100644
--- a/backend/progression/views.py
+++ b/backend/progression/views.py
@@ -40,5 +40,17 @@ class ProgressionProfileView(APIView):
                     }
                     for item in request.user.cards.select_related("card")
                 ],
+                "recent_games": [
+                    {
+                        "kind": attempt.kind,
+                        "label": attempt.get_kind_display(),
+                        "difficulty": attempt.get_difficulty_display(),
+                        "status": attempt.status,
+                        "score": attempt.score,
+                        "duration_ms": attempt.duration_ms,
+                        "started_at": attempt.started_at,
+                    }
+                    for attempt in request.user.math_game_attempts.all()[:10]
+                ],
             }
         )
diff --git a/backend/static/css/app.css b/backend/static/css/app.css
index a4108c7..c729308 100644
--- a/backend/static/css/app.css
+++ b/backend/static/css/app.css
@@ -132,6 +132,21 @@ button { color: inherit; }
 .track-switch { display: flex; gap: 5px; margin-bottom: 22px; }
 .track-switch button { border: 1px solid var(--line); padding: 9px 18px; border-radius: 99px; background: transparent; cursor: pointer; }
 .track-switch button.active { background: var(--ink); color: white; }
+.math-games-section { margin-top: 60px; }
+.game-card-grid { display: grid; grid-template-columns: repeat(2, minmax(0, 1fr)); gap: 16px; }
+.game-card { min-height: 285px; padding: 26px; border: 1px solid var(--line); border-radius: 20px; background: var(--panel); display: flex; flex-direction: column; overflow: hidden; position: relative; }
+.game-card::after { content: ""; position: absolute; width: 140px; height: 140px; right: -65px; top: -65px; border-radius: 50%; background: rgba(204,232,91,.18); }
+.game-sudoku::after { background: rgba(93,115,232,.13); }
+.game-card-top { display: flex; justify-content: space-between; align-items: start; }.game-card-top > span { display: grid; place-items: center; width: 58px; height: 58px; border-radius: 16px; background: var(--ink); color: var(--lime); font: 700 20px Georgia, serif; }.game-card-top small { color: var(--muted); }
+.game-card > b { margin-top: 24px; color: var(--green); font-size: 9px; letter-spacing: .18em; }.game-card h3 { margin: 8px 0; font: 28px Georgia, serif; }.game-card p { margin: 0; color: var(--muted); line-height: 1.7; }
+.game-card-controls { display: flex; gap: 10px; margin-top: auto; }.game-card-controls select { min-width: 100px; border: 1px solid var(--line); border-radius: 10px; padding: 11px; background: white; }.game-card-controls .primary-button { margin-left: auto; }
+.twenty-four-numbers { display: grid; grid-template-columns: repeat(4, 1fr); gap: 12px; margin: 24px 0; }.twenty-four-numbers button { aspect-ratio: 1; border: 1px solid var(--line); border-radius: 18px; background: var(--ink); color: var(--lime); font: 36px Georgia, serif; cursor: pointer; }
+.twenty-four-form { display: grid; gap: 12px; }.game-keypad { display: grid; grid-template-columns: repeat(6, 1fr); gap: 8px; }.game-keypad button { border: 1px solid var(--line); border-radius: 9px; padding: 10px; background: white; cursor: pointer; }
+.sudoku-board { width: min(100%, 540px); margin: 22px auto; display: grid; grid-template-columns: repeat(9, 1fr); border: 3px solid var(--ink); background: var(--ink); gap: 1px; }
+.sudoku-board input { width: 100%; min-width: 0; aspect-ratio: 1; border: 0; border-radius: 0; background: white; color: var(--green); text-align: center; font: 600 21px Georgia, serif; outline: 2px solid transparent; outline-offset: -2px; }
+.sudoku-board input:nth-child(3n) { border-right: 2px solid var(--ink); }.sudoku-board input:nth-child(9n) { border-right: 0; }.sudoku-board input:nth-child(n+19):nth-child(-n+27), .sudoku-board input:nth-child(n+46):nth-child(-n+54) { border-bottom: 2px solid var(--ink); }
+.sudoku-board input:focus { outline-color: var(--green); }.sudoku-board input.given { background: #ecece5; color: var(--ink); font-weight: 800; }.sudoku-board input.hint { background: #fff2ca; color: #9a5b22; }
+.sudoku-actions { display: flex; justify-content: flex-end; gap: 10px; }.game-result-panel { margin-top: 30px; padding: 30px; border-radius: 18px; background: var(--ink); color: white; text-align: center; }.game-result-panel strong { color: var(--lime); font: 48px Georgia, serif; }.game-result-panel p { color: #b9c2bc; }
 .editor-shell { display: grid; grid-template-columns: 1fr 1fr; overflow: hidden; min-height: 430px; }
 .editor-pane, .preview-pane { padding: 28px; }
 .editor-pane { background: #1d2721; color: white; }
@@ -144,7 +159,8 @@ button { color: inherit; }
 .metric-grid { display: grid; grid-template-columns: repeat(5, 1fr); gap: 10px; }
 .metric { background: rgba(25,101,72,.06); border-radius: 14px; padding: 17px; }
 .metric b, .metric span { display: block; }.metric b { font: 28px Georgia, serif; }.metric span { margin-top: 5px; color: var(--muted); font-size: 11px; }
-.tool-grid { display: grid; grid-template-columns: repeat(5, minmax(0, 1fr)); gap: 12px; margin-bottom: 22px; }
+.profile-subtitle { margin: 30px 0 12px; font: 24px Georgia, serif; }.profile-game-list { display: grid; grid-template-columns: repeat(auto-fit, minmax(180px, 1fr)); gap: 9px; }.profile-game-list > div { padding: 13px; border-radius: 11px; background: #eef1eb; }.profile-game-list b, .profile-game-list span { display: block; }.profile-game-list span { margin-top: 5px; color: var(--muted); font-size: 11px; }
+.tool-grid { display: grid; grid-template-columns: repeat(auto-fit, minmax(170px, 1fr)); gap: 12px; margin-bottom: 22px; }
 .tool-card {
   min-height: 165px; border: 1px solid var(--line); border-radius: 18px; padding: 22px;
   background: rgba(255,255,252,.7); text-align: left; cursor: pointer; transition: .2s ease;
@@ -159,19 +175,29 @@ button { color: inherit; }
 .tool-workspace.active { display: block; animation: rise .3s ease; }
 .workspace-heading { display: flex; justify-content: space-between; gap: 30px; align-items: end; margin-bottom: 25px; }
 .workspace-heading h2 { margin: 7px 0 0; font: 31px Georgia, serif; }.workspace-heading p { max-width: 480px; color: var(--muted); font-size: 13px; }
-.calculator-shell { max-width: 800px; margin: auto; }
+.calculator-shell { max-width: 980px; margin: auto; }
 .calculator-display { min-height: 145px; border-radius: 18px; padding: 25px; background: var(--ink); color: white; display: flex; flex-direction: column; justify-content: space-between; text-align: right; }
 .calculator-display small { color: #9eaaa2; }.calculator-display output { color: var(--lime); font: 48px/1 Georgia, serif; overflow-wrap: anywhere; }
 .formula-input, .search-input { width: 100%; border: 1px solid var(--line); border-radius: 12px; padding: 14px 16px; background: white; outline-color: var(--green); }
 .calculator-shell > .formula-input { margin: 14px 0; font: 18px "SFMono-Regular", Consolas, monospace; }
 .calculator-actions { display: flex; flex-wrap: wrap; gap: 8px; }.calculator-actions button { border: 1px solid var(--line); border-radius: 10px; padding: 11px 15px; background: white; cursor: pointer; }.calculator-actions .primary-button { margin-left: auto; color: white; background: var(--green); border: 0; }
+.calculator-controls { display: grid; grid-template-columns: repeat(4, minmax(120px, 1fr)); gap: 10px; margin-bottom: 14px; }.calculator-controls label, .calculator-expression-label { display: grid; gap: 7px; color: var(--muted); font-size: 11px; }.calculator-controls select, .calculator-controls input { width: 100%; border: 1px solid var(--line); border-radius: 10px; padding: 11px; background: white; }
+.calculator-controls [hidden] { display: none !important; }
+.calculator-expression-label textarea { min-height: 92px; margin: 0 0 12px; resize: vertical; font: 17px/1.6 "SFMono-Regular", Consolas, monospace; }
+.calculator-result { margin-top: 17px; }.calc-result-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 10px; margin-top: 10px; }.calc-result-grid > div { min-width: 0; padding: 14px; border: 1px solid var(--line); border-radius: 12px; background: white; }.calc-result-grid span { display: block; color: var(--muted); font-size: 10px; text-transform: uppercase; letter-spacing: .12em; }.calc-result-grid code { display: block; margin-top: 8px; overflow-wrap: anywhere; color: var(--green); }
+.calc-steps { margin: 13px 0 0; padding: 14px 14px 14px 34px; border-radius: 12px; background: #eef1eb; color: var(--muted); font-size: 12px; line-height: 1.8; }.calc-steps:empty { display: none; }
 .search-input { width: min(370px, 100%); }
 .symbol-grid { display: grid; grid-template-columns: repeat(4, 1fr); gap: 10px; }
 .symbol-card { border: 1px solid var(--line); border-radius: 15px; padding: 18px; background: white; cursor: pointer; text-align: left; }
 .symbol-card strong { display: block; color: var(--green); font: 29px Georgia, serif; }.symbol-card b { display: block; margin-top: 10px; }.symbol-card small { display: block; margin-top: 5px; color: var(--muted); }.symbol-card code { display: inline-block; margin-top: 12px; padding: 4px 7px; border-radius: 6px; background: #f0f1eb; color: #405048; }
 .graph-shell { display: grid; grid-template-columns: 245px minmax(0, 1fr); gap: 20px; }
-.graph-controls { display: flex; flex-direction: column; gap: 17px; }.graph-controls label { display: grid; gap: 8px; color: var(--muted); font-size: 12px; }.graph-controls p { color: #b84136; font-size: 12px; }
+.graph-controls { display: flex; flex-direction: column; gap: 17px; }.graph-controls label { display: grid; gap: 8px; color: var(--muted); font-size: 12px; }.graph-controls p { color: #b84136; font-size: 12px; }.graph-controls textarea { min-height: 100px; resize: vertical; font: 13px/1.6 "SFMono-Regular", Consolas, monospace; }
+.check-row { display: flex !important; grid-template-columns: auto 1fr; align-items: center; gap: 8px !important; }.check-row input { margin: 0; }
+.graph-analysis { padding: 11px; border-radius: 10px; background: #eef1eb; color: var(--muted); font-size: 11px; line-height: 1.6; }
 #graph-canvas { width: 100%; height: auto; border: 1px solid var(--line); border-radius: 17px; background: #fbfbf7; }
+.drawing-toolbar { display: flex; flex-wrap: wrap; align-items: center; gap: 8px; margin-bottom: 14px; }.drawing-toolbar button, .drawing-toolbar label { border: 1px solid var(--line); border-radius: 9px; padding: 9px 12px; background: white; color: var(--muted); cursor: pointer; }.drawing-toolbar button.active { border-color: var(--ink); background: var(--ink); color: white; }.drawing-toolbar .primary-button { margin-left: auto; border: 0; background: var(--green); color: white; }.drawing-toolbar label { display: flex; align-items: center; gap: 7px; font-size: 11px; }.drawing-toolbar input[type=color] { width: 28px; height: 24px; padding: 0; border: 0; background: transparent; }
+.toolbar-text-input { flex: 1 1 190px; min-width: 150px; border: 1px solid var(--line); border-radius: 9px; padding: 10px 12px; background: white; }.drawing-toolbar .file-tool input { display: none; }
+.canvas-stage { width: 100%; overflow: hidden; border: 1px solid var(--line); border-radius: 16px; background: white; box-shadow: inset 0 0 0 1px rgba(255,255,255,.6); }.canvas-stage canvas { display: block; width: 100%; height: auto; touch-action: none; cursor: crosshair; }.geometry-stage { background: #fbfbf7; }.canvas-hint { color: var(--muted); font-size: 11px; text-align: center; }
 .discover-title { padding-bottom: 24px; }
 .ability-map { border: 1px solid var(--line); border-radius: var(--radius); padding: 28px; background: rgba(255,255,252,.64); overflow: hidden; }
 .map-heading { display: flex; align-items: start; justify-content: space-between; gap: 20px; }.map-heading h2 { margin: 0 0 6px; font: 30px Georgia, serif; }.map-heading p { margin: 0; color: var(--muted); font-size: 13px; }
@@ -225,16 +251,17 @@ dialog::backdrop { background: rgba(17,25,20,.55); backdrop-filter: blur(5px); }
   .app-shell { grid-template-columns: 80px 1fr; }.sidebar { padding: 25px 13px; }.brand span:last-child, .nav-item:not(.active) span, .nav-item { font-size: 0; }
   .nav-item { text-align: center; }.nav-item span { width: auto; font-size: 11px !important; }.sidebar-foot { display: none; }
   .hero-grid { grid-template-columns: 1fr; }.daily-card { min-height: 350px; }.spirit-grid { grid-template-columns: 1fr 1fr; }.content-grid { grid-template-columns: 1fr 1fr; }
-  .tool-grid { grid-template-columns: repeat(3, 1fr); }.symbol-grid { grid-template-columns: repeat(3, 1fr); }.video-grid { grid-template-columns: 1fr 1fr; }
+  .tool-grid { grid-template-columns: repeat(3, 1fr); }.symbol-grid { grid-template-columns: repeat(3, 1fr); }.video-grid { grid-template-columns: 1fr 1fr; }.calculator-controls { grid-template-columns: repeat(2, 1fr); }
 }
 @media (max-width: 700px) {
   .app-shell { display: block; }.sidebar { position: fixed; top: auto; bottom: 0; width: 100%; height: 68px; z-index: 10; border: 0; border-top: 1px solid var(--line); padding: 8px; }
   .brand, .sidebar-foot { display: none; }.nav { margin: 0; grid-template-columns: repeat(6, 1fr); gap: 2px; }.nav-item { padding: 11px 2px; font-size: 0; }.nav-item span { display: block; margin: auto; }
   .main { padding: 0 18px 90px; }.topbar { height: 66px; }.topbar p { max-width: 55%; white-space: nowrap; overflow: hidden; text-overflow: ellipsis; }
   .hero { min-height: 500px; padding: 35px 25px; }.hero h1 { font-size: 44px; }.hero-actions { align-items: stretch; flex-direction: column; }
-  .section-heading { display: block; }.section-heading p { margin-top: 12px; }.spirit-grid, .content-grid, .editor-shell, .metric-grid, .tool-grid, .symbol-grid, .video-grid, .graph-shell { grid-template-columns: 1fr; }
+  .section-heading { display: block; }.section-heading p { margin-top: 12px; }.spirit-grid, .content-grid, .editor-shell, .metric-grid, .tool-grid, .symbol-grid, .video-grid, .graph-shell, .game-card-grid, .calc-result-grid { grid-template-columns: 1fr; }
   .content-grid { gap: 11px; }.editor-shell { min-height: 700px; }.page-title { padding-top: 42px; }.page-title h1 { font-size: 45px; }
-  .tool-card { min-height: 125px; }.workspace-heading, .map-heading { display: block; }.workspace-heading p { margin-top: 12px; }.tool-workspace { padding: 20px; }
+  .tool-card { min-height: 125px; }.workspace-heading, .map-heading { display: block; }.workspace-heading p { margin-top: 12px; }.tool-workspace { padding: 16px; }.calculator-controls { grid-template-columns: 1fr 1fr; }.calculator-display { min-height: 120px; padding: 18px; }.calculator-display output { font-size: 34px; }.calc-examples .primary-button { width: 100%; margin-left: 0; }.drawing-toolbar { align-items: stretch; }.drawing-toolbar .primary-button { width: 100%; margin-left: 0; }.canvas-stage canvas { width: 100%; min-width: 0; }
+  .math-games-section { margin-top: 45px; }.game-card { min-height: 260px; padding: 21px; }.game-card-controls { align-items: stretch; }.game-card-controls .primary-button { flex: 1; }.twenty-four-numbers { gap: 7px; }.twenty-four-numbers button { border-radius: 13px; font-size: 28px; }.sudoku-board input { font-size: clamp(13px, 4.5vw, 20px); }.sudoku-actions { display: grid; grid-template-columns: 1fr 1fr; }.game-keypad { gap: 5px; }
   .map-stage { height: 480px; transform: scale(.92); }.ability-node { width: 108px; height: 94px; }.node-vision { left: calc(50% - 54px); }.node-humanities { left: 0; top: 100px; }.node-connection { right: 0; top: 100px; }.node-detection { left: 2%; bottom: 30px; }.node-modeling { right: 2%; bottom: 30px; }.pet-node { top: 190px; }
   .map-lines { display: none; }.ability-legend { margin-top: 14px; justify-content: start; }.video-cover { height: 150px; }
 }
diff --git a/backend/static/js/app.js b/backend/static/js/app.js
index 18c20a4..09cfbe3 100644
--- a/backend/static/js/app.js
+++ b/backend/static/js/app.js
@@ -638,6 +638,26 @@ async function loadProfile() {
       metrics.append(item);
     });
     root.append(heading, pet, metrics);
+    if (profile.recent_games?.length) {
+      const gameTitle = document.createElement("h3");
+      gameTitle.className = "profile-subtitle";
+      gameTitle.textContent = "最近数学玩法";
+      const gameList = document.createElement("div");
+      gameList.className = "profile-game-list";
+      profile.recent_games.forEach((game) => {
+        const item = document.createElement("div");
+        const name = document.createElement("b");
+        name.textContent = `${game.label} · ${game.difficulty}`;
+        const detail = document.createElement("span");
+        detail.textContent =
+          game.status === "completed"
+            ? `${game.score} 分 · ${(game.duration_ms / 1000).toFixed(1)} 秒`
+            : "进行中";
+        item.append(name, detail);
+        gameList.append(item);
+      });
+      root.append(gameTitle, gameList);
+    }
   } catch (error) {
     root.textContent = error.message;
   }
@@ -673,10 +693,20 @@ function evaluateExpression(source, variables = {}) {
     sin: Math.sin,
     cos: Math.cos,
     tan: Math.tan,
+    asin: Math.asin,
+    acos: Math.acos,
+    atan: Math.atan,
+    sinh: Math.sinh,
+    cosh: Math.cosh,
+    tanh: Math.tanh,
     sqrt: Math.sqrt,
     log: Math.log10,
     ln: Math.log,
+    exp: Math.exp,
     abs: Math.abs,
+    floor: Math.floor,
+    ceil: Math.ceil,
+    round: Math.round,
   };
 
   const skip = () => {
@@ -880,7 +910,7 @@ function switchTool(tool) {
   $$(".tool-workspace").forEach((workspace) => {
     workspace.classList.toggle("active", workspace.id === `tool-${tool}`);
   });
-  if (tool === "graph") window.setTimeout(drawGraph, 30);
+  window.HuluToolbox?.activate(tool);
 }
 
 async function saveFormula() {
@@ -906,24 +936,9 @@ function bindUI() {
   $$(".tool-card").forEach((button) => {
     button.addEventListener("click", () => switchTool(button.dataset.tool));
   });
-  $("#calc-run").addEventListener("click", runCalculator);
-  $("#calc-input").addEventListener("keydown", (event) => {
-    if (event.key === "Enter") runCalculator();
-  });
-  $$("[data-calc-example]").forEach((button) => {
-    button.addEventListener("click", () => {
-      $("#calc-input").value = button.dataset.calcExample;
-      runCalculator();
-    });
-  });
   $("#symbol-search").addEventListener("input", (event) => {
     renderSymbols(event.target.value);
   });
-  $("#graph-run").addEventListener("click", drawGraph);
-  $("#graph-range").addEventListener("input", drawGraph);
-  $("#graph-expression").addEventListener("keydown", (event) => {
-    if (event.key === "Enter") drawGraph();
-  });
   $$(".ability-node").forEach((button) => {
     button.addEventListener("click", () => {
       state.videoAbility =
@@ -980,9 +995,15 @@ function bindUI() {
 
 async function boot() {
   bindUI();
+  window.HuluToolbox?.init();
   renderSymbols();
-  runCalculator();
-  await Promise.all([loadUser(), loadStories(), loadContests(), loadContent()]);
+  await Promise.all([
+    loadUser(),
+    loadStories(),
+    loadContests(),
+    loadContent(),
+    window.HuluGames?.load(),
+  ]);
 }
 
 boot();
diff --git a/backend/static/js/games.js b/backend/static/js/games.js
new file mode 100644
index 0000000..ee153b2
--- /dev/null
+++ b/backend/static/js/games.js
@@ -0,0 +1,295 @@
+(function () {
+  const $game = (selector, root = document) => root.querySelector(selector);
+
+  const GAME_META = {
+    twenty_four: {
+      title: "24 点",
+      kicker: "ARITHMETIC PUZZLE",
+      action: "开始组式",
+    },
+    sudoku: {
+      title: "数独",
+      kicker: "LOGIC GRID",
+      action: "开始推理",
+    },
+  };
+
+  function difficultySelect() {
+    const select = document.createElement("select");
+    select.className = "game-difficulty";
+    [
+      ["easy", "入门"],
+      ["standard", "标准"],
+      ["hard", "进阶"],
+    ].forEach(([value, label]) => {
+      const option = document.createElement("option");
+      option.value = value;
+      option.textContent = label;
+      if (value === "standard") option.selected = true;
+      select.append(option);
+    });
+    return select;
+  }
+
+  function gameCard(game) {
+    const meta = GAME_META[game.kind];
+    const article = document.createElement("article");
+    article.className = `game-card game-${game.kind}`;
+    const top = document.createElement("div");
+    top.className = "game-card-top";
+    const icon = document.createElement("span");
+    icon.textContent = game.kind === "sudoku" ? "9×9" : "24";
+    const time = document.createElement("small");
+    time.textContent = `约 ${game.estimated_minutes} 分钟`;
+    top.append(icon, time);
+    const kicker = document.createElement("b");
+    kicker.textContent = meta.kicker;
+    const title = document.createElement("h3");
+    title.textContent = game.title;
+    const summary = document.createElement("p");
+    summary.textContent = game.summary;
+    const controls = document.createElement("div");
+    controls.className = "game-card-controls";
+    const difficulty = difficultySelect();
+    const start = document.createElement("button");
+    start.className = "primary-button";
+    start.textContent = meta.action;
+    start.addEventListener("click", () => startGame(game.kind, difficulty.value));
+    controls.append(difficulty, start);
+    article.append(top, kicker, title, summary, controls);
+    return article;
+  }
+
+  async function loadGames() {
+    const root = $game("#math-game-list");
+    try {
+      const games = await api("contests/games/");
+      root.replaceChildren(...games.map(gameCard));
+    } catch (error) {
+      root.textContent = error.message;
+    }
+  }
+
+  async function startGame(kind, difficulty) {
+    if (!requireAuth()) return;
+    try {
+      const attempt = await api(`contests/games/${kind}/start/`, {
+        method: "POST",
+        body: { difficulty },
+      });
+      renderGame(attempt);
+      $game("#experience-dialog").showModal();
+    } catch (error) {
+      showToast(error.message);
+    }
+  }
+
+  function gameHeading(attempt) {
+    const fragment = document.createDocumentFragment();
+    const label = document.createElement("span");
+    label.className = "kicker";
+    label.textContent =
+      `${GAME_META[attempt.kind].kicker} · ${attempt.difficulty.toUpperCase()}`;
+    const title = document.createElement("h2");
+    title.textContent = GAME_META[attempt.kind].title;
+    fragment.append(label, title);
+    return fragment;
+  }
+
+  function resultPanel(attempt) {
+    const panel = document.createElement("div");
+    panel.className = "game-result-panel";
+    const score = document.createElement("strong");
+    score.textContent = `${attempt.score} 分`;
+    const details = document.createElement("p");
+    details.textContent =
+      `用时 ${(attempt.duration_ms / 1000).toFixed(1)} 秒 · 提示 ${attempt.hints_used} 次`;
+    panel.append(score, details);
+    return panel;
+  }
+
+  function renderGame(attempt) {
+    if (attempt.kind === "sudoku") renderSudoku(attempt);
+    else renderTwentyFour(attempt);
+  }
+
+  function renderTwentyFour(attempt) {
+    const root = $game("#experience-content");
+    root.replaceChildren();
+    root.append(gameHeading(attempt));
+    if (attempt.status === "completed") {
+      root.append(resultPanel(attempt));
+      return;
+    }
+    const instruction = document.createElement("p");
+    instruction.className = "scene";
+    instruction.textContent = "四个数字必须各使用一次，只允许 +、−、×、÷ 和括号。";
+    const numbers = document.createElement("div");
+    numbers.className = "twenty-four-numbers";
+    attempt.puzzle.numbers.forEach((number) => {
+      const tile = document.createElement("button");
+      tile.type = "button";
+      tile.textContent = number;
+      tile.addEventListener("click", () => {
+        input.value += String(number);
+        input.focus();
+      });
+      numbers.append(tile);
+    });
+    const form = document.createElement("form");
+    form.className = "twenty-four-form";
+    const input = document.createElement("input");
+    input.className = "formula-input";
+    input.placeholder = "例如：6 / (1 - 3 / 4)";
+    input.autocomplete = "off";
+    input.inputMode = "text";
+    const keypad = document.createElement("div");
+    keypad.className = "game-keypad";
+    ["+", "-", "*", "/", "(", ")"].forEach((operator) => {
+      const button = document.createElement("button");
+      button.type = "button";
+      button.textContent = operator;
+      button.addEventListener("click", () => {
+        input.value += operator;
+        input.focus();
+      });
+      keypad.append(button);
+    });
+    const submit = document.createElement("button");
+    submit.className = "primary-button";
+    submit.type = "submit";
+    submit.textContent = "验证并计分";
+    form.append(input, keypad, submit);
+    form.addEventListener("submit", async (event) => {
+      event.preventDefault();
+      submit.disabled = true;
+      try {
+        const result = await api(
+          `contests/games/attempts/${attempt.attempt_id}/submit/`,
+          {
+            method: "POST",
+            headers: { "Idempotency-Key": createIdempotencyKey() },
+            body: { expression: input.value },
+          },
+        );
+        renderTwentyFour(result);
+        showToast("得到 24，成绩已记录");
+      } catch (error) {
+        showToast(error.message);
+        submit.disabled = false;
+      }
+    });
+    root.append(instruction, numbers, form);
+    window.setTimeout(() => input.focus(), 50);
+  }
+
+  function sudokuCell(given, value, row, column) {
+    const input = document.createElement("input");
+    input.inputMode = "numeric";
+    input.pattern = "[1-9]";
+    input.maxLength = 1;
+    input.dataset.row = row;
+    input.dataset.column = column;
+    input.value = value || "";
+    input.className = given ? "given" : "";
+    input.readOnly = given;
+    input.setAttribute("aria-label", `第 ${row + 1} 行第 ${column + 1} 列`);
+    input.addEventListener("input", () => {
+      input.value = input.value.replace(/[^1-9]/g, "").slice(0, 1);
+    });
+    return input;
+  }
+
+  function renderSudoku(attempt) {
+    const root = $game("#experience-content");
+    root.replaceChildren();
+    root.append(gameHeading(attempt));
+    if (attempt.status === "completed") {
+      root.append(resultPanel(attempt));
+      return;
+    }
+    const instruction = document.createElement("p");
+    instruction.className = "scene";
+    instruction.textContent = "每一行、每一列和每个 3×3 九宫格都要包含 1 到 9。";
+    const board = document.createElement("div");
+    board.className = "sudoku-board";
+    const hints = new Map(
+      (attempt.puzzle.hints || []).map((item) => [`${item.row}-${item.column}`, item.value])
+    );
+    attempt.puzzle.grid.forEach((rowValues, row) => {
+      rowValues.forEach((givenValue, column) => {
+        const hintValue = hints.get(`${row}-${column}`) || 0;
+        const input = sudokuCell(Boolean(givenValue), givenValue || hintValue, row, column);
+        if (hintValue) {
+          input.readOnly = true;
+          input.classList.add("hint");
+        }
+        board.append(input);
+      });
+    });
+    const actions = document.createElement("div");
+    actions.className = "sudoku-actions";
+    const hint = document.createElement("button");
+    hint.type = "button";
+    hint.className = "ghost-button";
+    hint.textContent = `提示（已用 ${attempt.hints_used}/3）`;
+    hint.disabled = attempt.hints_used >= 3;
+    const submit = document.createElement("button");
+    submit.type = "button";
+    submit.className = "primary-button";
+    submit.textContent = "检查并完成";
+    hint.addEventListener("click", async () => {
+      hint.disabled = true;
+      try {
+        const result = await api(
+          `contests/games/attempts/${attempt.attempt_id}/hint/`,
+          { method: "POST", body: {} },
+        );
+        const input = $game(
+          `[data-row="${result.row}"][data-column="${result.column}"]`,
+          board,
+        );
+        input.value = result.value;
+        input.readOnly = true;
+        input.classList.add("hint");
+        attempt.hints_used = result.hints_used;
+        hint.textContent = `提示（已用 ${result.hints_used}/3）`;
+        hint.disabled = result.hints_used >= 3;
+      } catch (error) {
+        showToast(error.message);
+        hint.disabled = false;
+      }
+    });
+    submit.addEventListener("click", async () => {
+      submit.disabled = true;
+      const grid = Array.from({ length: 9 }, () => Array(9).fill(0));
+      $gameAll("input", board).forEach((input) => {
+        grid[Number(input.dataset.row)][Number(input.dataset.column)] =
+          Number(input.value || 0);
+      });
+      try {
+        const result = await api(
+          `contests/games/attempts/${attempt.attempt_id}/submit/`,
+          {
+            method: "POST",
+            headers: { "Idempotency-Key": createIdempotencyKey() },
+            body: { grid },
+          },
+        );
+        renderSudoku(result);
+        showToast("数独完成，成绩已记录");
+      } catch (error) {
+        showToast(error.message);
+        submit.disabled = false;
+      }
+    });
+    actions.append(hint, submit);
+    root.append(instruction, board, actions);
+  }
+
+  function $gameAll(selector, root = document) {
+    return [...root.querySelectorAll(selector)];
+  }
+
+  window.HuluGames = { load: loadGames };
+})();
diff --git a/backend/static/js/toolbox.js b/backend/static/js/toolbox.js
new file mode 100644
index 0000000..05c511f
--- /dev/null
+++ b/backend/static/js/toolbox.js
@@ -0,0 +1,710 @@
+(function () {
+  const $tool = (selector, root = document) => root.querySelector(selector);
+  const $$tool = (selector, root = document) => [...root.querySelectorAll(selector)];
+
+  const CALC_FIELDS = {
+    derivative: ["order"],
+    integral: ["bounds"],
+    limit: ["point"],
+    base: ["base"],
+    unit: ["unit"],
+  };
+
+  function formatCalculatorResult(result) {
+    if (Array.isArray(result)) {
+      return {
+        exact: result.map((item) => item.exact).join(", "),
+        decimal: result.map((item) => item.decimal).join(", "),
+        latex: result.map((item) => item.latex).join(", "),
+      };
+    }
+    if (result && typeof result === "object" && "exact" in result) return result;
+    const entries = Object.entries(result || {});
+    return {
+      exact: entries.map(([key, value]) => `${key}: ${value}`).join(" · "),
+      decimal: entries.map(([key, value]) => `${key}: ${value}`).join(" · "),
+      latex: entries.map(([key, value]) => `${key}=${value}`).join(", "),
+    };
+  }
+
+  function updateCalculatorFields() {
+    const operation = $tool("#calc-operation").value;
+    const visible = new Set(CALC_FIELDS[operation] || []);
+    $$tool("[data-calc-field]").forEach((field) => {
+      field.hidden = !visible.has(field.dataset.calcField);
+    });
+    const input = $tool("#calc-input");
+    const placeholders = {
+      statistics: "12, 15, 18, 21, 24",
+      base: "FF",
+      matrix_det: "1,2;3,4",
+      matrix_inverse: "1,2;3,4",
+      matrix_rref: "1,2,3;2,4,6",
+      matrix_transpose: "1,2,3;4,5,6",
+      solve: "x^2 - 5*x + 6 = 0",
+    };
+    input.placeholder = placeholders[operation] || "例如：sqrt(2) + 1/3";
+  }
+
+  async function runCalculator() {
+    const button = $tool("#calc-run");
+    const operation = $tool("#calc-operation").value;
+    const expression = $tool("#calc-input").value.trim();
+    button.disabled = true;
+    $tool("#calc-history").textContent = "数学内核正在计算…";
+    try {
+      const payload = await api("toolbox/calculate/", {
+        method: "POST",
+        body: {
+          operation,
+          expression,
+          variable: $tool("#calc-variable").value,
+          order: $tool("#calc-order").value,
+          lower: $tool("#calc-lower").value,
+          upper: $tool("#calc-upper").value,
+          point: $tool("#calc-point").value,
+          from_base: $tool("#calc-from-base").value,
+          to_base: $tool("#calc-to-base").value,
+          from_unit: $tool("#calc-from-unit").value,
+          to_unit: $tool("#calc-to-unit").value,
+        },
+      });
+      const result = formatCalculatorResult(payload.result);
+      $tool("#calc-history").textContent = `${operation} · ${expression}`;
+      $tool("#calc-output").textContent = result.exact || "完成";
+      $tool("#calc-decimal").textContent = result.decimal || result.exact || "—";
+      $tool("#calc-latex").textContent = result.latex || result.exact || "—";
+      $tool("#calc-steps").replaceChildren(
+        ...(payload.steps || []).map((step) => {
+          const item = document.createElement("li");
+          item.textContent = step;
+          return item;
+        })
+      );
+    } catch (error) {
+      $tool("#calc-history").textContent = error.message;
+      $tool("#calc-output").textContent = "计算失败";
+      $tool("#calc-decimal").textContent = "—";
+      $tool("#calc-latex").textContent = "—";
+      $tool("#calc-steps").replaceChildren();
+    } finally {
+      button.disabled = false;
+    }
+  }
+
+  const GRAPH_COLORS = ["#196548", "#d86f45", "#5d73e8", "#8667b5"];
+
+  function drawFunctionPath(context, expression, variables, range, width, height, color) {
+    const toY = (value) => height / 2 - (value / range) * (height / 2);
+    context.strokeStyle = color;
+    context.lineWidth = 3;
+    context.beginPath();
+    let drawing = false;
+    const samples = [];
+    for (let pixel = 0; pixel <= width; pixel += 2) {
+      const x = (pixel / width) * range * 2 - range;
+      let y;
+      try {
+        y = evaluateExpression(expression, { ...variables, x });
+      } catch (error) {
+        if (pixel === 0) throw error;
+        drawing = false;
+        continue;
+      }
+      samples.push({ x, y });
+      const screenY = toY(y);
+      if (!Number.isFinite(screenY) || screenY < -height * 2 || screenY > height * 3) {
+        drawing = false;
+        continue;
+      }
+      if (!drawing) context.moveTo(pixel, screenY);
+      else context.lineTo(pixel, screenY);
+      drawing = true;
+    }
+    context.stroke();
+    return samples;
+  }
+
+  function graphAnalysis(samples) {
+    const roots = [];
+    let extrema = 0;
+    for (let index = 1; index < samples.length; index += 1) {
+      const before = samples[index - 1];
+      const current = samples[index];
+      if (before.y === 0 || before.y * current.y < 0) {
+        const root = (before.x + current.x) / 2;
+        if (!roots.length || Math.abs(root - roots.at(-1)) > 0.15) roots.push(root);
+      }
+      if (index > 1) {
+        const previousSlope = before.y - samples[index - 2].y;
+        const currentSlope = current.y - before.y;
+        if (previousSlope * currentSlope < 0) extrema += 1;
+      }
+    }
+    return { roots: roots.slice(0, 8), extrema };
+  }
+
+  function drawGraph() {
+    const canvas = $tool("#graph-canvas");
+    const context = canvas.getContext("2d");
+    const expressions = $tool("#graph-expression").value
+      .split("\n")
+      .map((item) => item.trim())
+      .filter(Boolean)
+      .slice(0, 4);
+    const range = Number($tool("#graph-range").value);
+    const parameter = Number($tool("#graph-parameter").value);
+    const width = canvas.width;
+    const height = canvas.height;
+    $tool("#graph-range-label").textContent = `−${range} 到 ${range}`;
+    $tool("#graph-parameter-label").textContent = `a = ${parameter}`;
+    $tool("#graph-error").textContent = "";
+    context.clearRect(0, 0, width, height);
+    context.fillStyle = "#fbfbf7";
+    context.fillRect(0, 0, width, height);
+    const toX = (x) => ((x + range) / (range * 2)) * width;
+    const toY = (y) => height / 2 - (y / range) * (height / 2);
+
+    context.strokeStyle = "#e4e5df";
+    context.lineWidth = 1;
+    for (let value = -range; value <= range; value += 1) {
+      context.beginPath();
+      context.moveTo(toX(value), 0);
+      context.lineTo(toX(value), height);
+      context.moveTo(0, toY(value));
+      context.lineTo(width, toY(value));
+      context.stroke();
+    }
+    context.strokeStyle = "#718078";
+    context.lineWidth = 2;
+    context.beginPath();
+    context.moveTo(0, height / 2);
+    context.lineTo(width, height / 2);
+    context.moveTo(width / 2, 0);
+    context.lineTo(width / 2, height);
+    context.stroke();
+
+    if (!expressions.length) {
+      $tool("#graph-error").textContent = "请至少输入一个函数";
+      return;
+    }
+    try {
+      const firstSamples = drawFunctionPath(
+        context,
+        expressions[0],
+        { a: parameter },
+        range,
+        width,
+        height,
+        GRAPH_COLORS[0],
+      );
+      expressions.slice(1).forEach((expression, index) => {
+        drawFunctionPath(
+          context,
+          expression,
+          { a: parameter },
+          range,
+          width,
+          height,
+          GRAPH_COLORS[index + 1],
+        );
+      });
+
+      if ($tool("#graph-integral").checked) {
+        context.fillStyle = "rgba(25, 101, 72, .13)";
+        context.beginPath();
+        context.moveTo(0, height / 2);
+        firstSamples.forEach((item) => context.lineTo(toX(item.x), toY(item.y)));
+        context.lineTo(width, height / 2);
+        context.closePath();
+        context.fill();
+      }
+      if ($tool("#graph-derivative").checked) {
+        const derivative = firstSamples.slice(1, -1).map((item, index) => {
+          const before = firstSamples[index];
+          const after = firstSamples[index + 2];
+          return { x: item.x, y: (after.y - before.y) / (after.x - before.x) };
+        });
+        context.strokeStyle = "#111827";
+        context.lineWidth = 2;
+        context.setLineDash([9, 7]);
+        context.beginPath();
+        derivative.forEach((item, index) => {
+          const x = toX(item.x);
+          const y = toY(item.y);
+          if (index === 0) context.moveTo(x, y);
+          else context.lineTo(x, y);
+        });
+        context.stroke();
+        context.setLineDash([]);
+      }
+      const analysis = graphAnalysis(firstSamples);
+      const rootText = analysis.roots.length
+        ? analysis.roots.map((item) => item.toFixed(2)).join("、")
+        : "当前范围未发现";
+      $tool("#graph-analysis").textContent =
+        `第一条曲线：近似零点 ${rootText}；检测到 ${analysis.extrema} 个极值转折。`;
+    } catch (error) {
+      $tool("#graph-error").textContent = error.message;
+    }
+  }
+
+  function canvasPoint(canvas, event) {
+    const rect = canvas.getBoundingClientRect();
+    return {
+      x: ((event.clientX - rect.left) / rect.width) * canvas.width,
+      y: ((event.clientY - rect.top) / rect.height) * canvas.height,
+    };
+  }
+
+  function downloadCanvas(canvas, name) {
+    const link = document.createElement("a");
+    link.download = `${name}-${new Date().toISOString().slice(0, 10)}.png`;
+    link.href = canvas.toDataURL("image/png");
+    link.click();
+  }
+
+  class Whiteboard {
+    constructor(canvas) {
+      this.canvas = canvas;
+      this.context = canvas.getContext("2d");
+      this.tool = "pen";
+      this.history = [];
+      this.drawing = false;
+      this.start = null;
+      this.preview = null;
+      this.reset();
+      canvas.addEventListener("pointerdown", (event) => this.startDrawing(event));
+      canvas.addEventListener("pointermove", (event) => this.move(event));
+      canvas.addEventListener("pointerup", (event) => this.finish(event));
+      canvas.addEventListener("pointercancel", () => this.cancel());
+    }
+
+    reset() {
+      this.context.fillStyle = "#ffffff";
+      this.context.fillRect(0, 0, this.canvas.width, this.canvas.height);
+    }
+
+    snapshot() {
+      this.history.push(this.canvas.toDataURL("image/png"));
+      if (this.history.length > 20) this.history.shift();
+    }
+
+    startDrawing(event) {
+      event.preventDefault();
+      this.snapshot();
+      this.drawing = true;
+      this.start = canvasPoint(this.canvas, event);
+      if (this.tool === "text") {
+        const text = $tool("#whiteboard-text").value.trim();
+        if (!text) {
+          this.history.pop();
+          showToast("先输入要放到白板的文字或公式");
+        } else {
+          const size = Math.max(18, Number($tool("#whiteboard-size").value) * 5);
+          this.context.fillStyle = $tool("#whiteboard-color").value;
+          this.context.font = `${size}px "SFMono-Regular", "PingFang SC", sans-serif`;
+          this.context.fillText(text, this.start.x, this.start.y);
+        }
+        this.drawing = false;
+        return;
+      }
+      this.preview = this.context.getImageData(0, 0, this.canvas.width, this.canvas.height);
+      this.canvas.setPointerCapture(event.pointerId);
+      this.context.lineCap = "round";
+      this.context.lineJoin = "round";
+      this.context.lineWidth = Number($tool("#whiteboard-size").value);
+      this.context.strokeStyle =
+        this.tool === "eraser" ? "#ffffff" : $tool("#whiteboard-color").value;
+      if (this.tool === "pen" || this.tool === "eraser") {
+        this.context.beginPath();
+        this.context.moveTo(this.start.x, this.start.y);
+      }
+    }
+
+    move(event) {
+      if (!this.drawing) return;
+      event.preventDefault();
+      const point = canvasPoint(this.canvas, event);
+      if (this.tool === "pen" || this.tool === "eraser") {
+        this.context.lineTo(point.x, point.y);
+        this.context.stroke();
+        return;
+      }
+      this.context.putImageData(this.preview, 0, 0);
+      this.context.beginPath();
+      if (this.tool === "line") {
+        this.context.moveTo(this.start.x, this.start.y);
+        this.context.lineTo(point.x, point.y);
+      } else {
+        this.context.rect(
+          this.start.x,
+          this.start.y,
+          point.x - this.start.x,
+          point.y - this.start.y,
+        );
+      }
+      this.context.stroke();
+    }
+
+    finish(event) {
+      if (!this.drawing) return;
+      this.move(event);
+      this.drawing = false;
+      this.preview = null;
+    }
+
+    cancel() {
+      if (this.preview) this.context.putImageData(this.preview, 0, 0);
+      this.drawing = false;
+    }
+
+    undo() {
+      const source = this.history.pop();
+      if (!source) return;
+      const image = new Image();
+      image.onload = () => {
+        this.context.clearRect(0, 0, this.canvas.width, this.canvas.height);
+        this.context.drawImage(image, 0, 0);
+      };
+      image.src = source;
+    }
+
+    clear() {
+      this.snapshot();
+      this.reset();
+    }
+
+    addGrid() {
+      this.snapshot();
+      const context = this.context;
+      context.strokeStyle = "#e1e7e1";
+      context.lineWidth = 1;
+      for (let x = 0; x <= this.canvas.width; x += 50) {
+        context.beginPath();
+        context.moveTo(x, 0);
+        context.lineTo(x, this.canvas.height);
+        context.stroke();
+      }
+      for (let y = 0; y <= this.canvas.height; y += 50) {
+        context.beginPath();
+        context.moveTo(0, y);
+        context.lineTo(this.canvas.width, y);
+        context.stroke();
+      }
+      context.strokeStyle = "#7a877f";
+      context.lineWidth = 2;
+      context.beginPath();
+      context.moveTo(this.canvas.width / 2, 0);
+      context.lineTo(this.canvas.width / 2, this.canvas.height);
+      context.moveTo(0, this.canvas.height / 2);
+      context.lineTo(this.canvas.width, this.canvas.height / 2);
+      context.stroke();
+    }
+
+    addImage(file) {
+      if (!file) return;
+      const reader = new FileReader();
+      reader.onload = () => {
+        const image = new Image();
+        image.onload = () => {
+          this.snapshot();
+          const scale = Math.min(
+            1,
+            (this.canvas.width * 0.8) / image.width,
+            (this.canvas.height * 0.8) / image.height,
+          );
+          this.context.drawImage(
+            image,
+            30,
+            30,
+            image.width * scale,
+            image.height * scale,
+          );
+        };
+        image.src = reader.result;
+      };
+      reader.readAsDataURL(file);
+    }
+  }
+
+  class GeometryBoard {
+    constructor(canvas) {
+      this.canvas = canvas;
+      this.context = canvas.getContext("2d");
+      this.tool = "point";
+      this.points = [];
+      this.segments = [];
+      this.circles = [];
+      this.history = [];
+      this.pending = [];
+      this.dragging = null;
+      canvas.addEventListener("pointerdown", (event) => this.pointerDown(event));
+      canvas.addEventListener("pointermove", (event) => this.pointerMove(event));
+      canvas.addEventListener("pointerup", (event) => this.pointerUp(event));
+      canvas.addEventListener("pointercancel", () => {
+        this.dragging = null;
+      });
+      this.draw();
+    }
+
+    save() {
+      this.history.push(
+        JSON.stringify({
+          points: this.points,
+          segments: this.segments,
+          circles: this.circles,
+        })
+      );
+      if (this.history.length > 30) this.history.shift();
+    }
+
+    findOrCreate(point) {
+      const nearest = this.findNearest(point);
+      if (nearest >= 0) return nearest;
+      this.points.push(point);
+      return this.points.length - 1;
+    }
+
+    findNearest(point) {
+      let nearest = -1;
+      let distance = 28;
+      this.points.forEach((item, index) => {
+        const current = Math.hypot(item.x - point.x, item.y - point.y);
+        if (current < distance) {
+          nearest = index;
+          distance = current;
+        }
+      });
+      return nearest;
+    }
+
+    pointerDown(event) {
+      if (this.tool !== "move") return;
+      event.preventDefault();
+      const nearest = this.findNearest(canvasPoint(this.canvas, event));
+      if (nearest < 0 || this.points[nearest].derived) return;
+      this.save();
+      this.dragging = nearest;
+      this.canvas.setPointerCapture(event.pointerId);
+    }
+
+    pointerMove(event) {
+      if (this.dragging === null) return;
+      event.preventDefault();
+      const point = canvasPoint(this.canvas, event);
+      this.points[this.dragging] = point;
+      this.draw();
+    }
+
+    pointerUp(event) {
+      if (this.tool === "move") {
+        this.pointerMove(event);
+        this.dragging = null;
+        return;
+      }
+      this.handlePoint(event);
+    }
+
+    handlePoint(event) {
+      event.preventDefault();
+      const point = canvasPoint(this.canvas, event);
+      this.save();
+      if (this.tool === "point") {
+        this.findOrCreate(point);
+      } else {
+        this.pending.push(this.findOrCreate(point));
+        if (this.pending.length === 2) {
+          const [first, second] = this.pending;
+          if (first !== second && this.tool === "segment") {
+            this.segments.push({ first, second });
+          } else if (first !== second && this.tool === "circle") {
+            this.circles.push({ center: first, edge: second });
+          } else if (first !== second && this.tool === "midpoint") {
+            const a = this.points[first];
+            const b = this.points[second];
+            this.points.push({
+              x: (a.x + b.x) / 2,
+              y: (a.y + b.y) / 2,
+              derived: true,
+              parents: [first, second],
+            });
+            this.segments.push({ first, second, guide: true });
+          }
+          this.pending = [];
+        }
+      }
+      this.draw();
+      $tool("#geometry-hint").textContent = this.pending.length
+        ? "再选择一个点完成构造。"
+        : "可继续创建或切换构造工具。";
+    }
+
+    draw() {
+      const context = this.context;
+      const width = this.canvas.width;
+      const height = this.canvas.height;
+      this.points.forEach((point) => {
+        if (!point.derived || !point.parents) return;
+        const first = this.points[point.parents[0]];
+        const second = this.points[point.parents[1]];
+        point.x = (first.x + second.x) / 2;
+        point.y = (first.y + second.y) / 2;
+      });
+      context.fillStyle = "#fbfbf7";
+      context.fillRect(0, 0, width, height);
+      context.strokeStyle = "#e7e8e2";
+      context.lineWidth = 1;
+      for (let x = 0; x <= width; x += 50) {
+        context.beginPath();
+        context.moveTo(x, 0);
+        context.lineTo(x, height);
+        context.stroke();
+      }
+      for (let y = 0; y <= height; y += 50) {
+        context.beginPath();
+        context.moveTo(0, y);
+        context.lineTo(width, y);
+        context.stroke();
+      }
+      this.segments.forEach((segment) => {
+        const first = this.points[segment.first];
+        const second = this.points[segment.second];
+        context.strokeStyle = segment.guide ? "#9ca3af" : "#196548";
+        context.setLineDash(segment.guide ? [8, 6] : []);
+        context.lineWidth = 3;
+        context.beginPath();
+        context.moveTo(first.x, first.y);
+        context.lineTo(second.x, second.y);
+        context.stroke();
+        context.setLineDash([]);
+        if ($tool("#geometry-labels").checked) {
+          context.fillStyle = "#47534c";
+          context.font = "18px sans-serif";
+          context.fillText(
+            Math.hypot(first.x - second.x, first.y - second.y).toFixed(1),
+            (first.x + second.x) / 2 + 8,
+            (first.y + second.y) / 2 - 8,
+          );
+        }
+      });
+      this.circles.forEach((circle) => {
+        const center = this.points[circle.center];
+        const edge = this.points[circle.edge];
+        const radius = Math.hypot(center.x - edge.x, center.y - edge.y);
+        context.strokeStyle = "#5d73e8";
+        context.lineWidth = 3;
+        context.beginPath();
+        context.arc(center.x, center.y, radius, 0, Math.PI * 2);
+        context.stroke();
+      });
+      this.points.forEach((point, index) => {
+        context.fillStyle = point.derived ? "#d86f45" : "#17211b";
+        context.beginPath();
+        context.arc(point.x, point.y, 7, 0, Math.PI * 2);
+        context.fill();
+        if ($tool("#geometry-labels").checked) {
+          context.fillStyle = "#17211b";
+          context.font = "18px sans-serif";
+          context.fillText(
+            `${String.fromCharCode(65 + (index % 26))} (${Math.round(point.x)}, ${Math.round(point.y)})`,
+            point.x + 10,
+            point.y - 10,
+          );
+        }
+      });
+    }
+
+    undo() {
+      const state = this.history.pop();
+      if (!state) return;
+      const parsed = JSON.parse(state);
+      this.points = parsed.points;
+      this.segments = parsed.segments;
+      this.circles = parsed.circles;
+      this.pending = [];
+      this.draw();
+    }
+
+    clear() {
+      this.save();
+      this.points = [];
+      this.segments = [];
+      this.circles = [];
+      this.pending = [];
+      this.draw();
+    }
+  }
+
+  let whiteboard;
+  let geometry;
+
+  function initDrawingTools() {
+    whiteboard = new Whiteboard($tool("#whiteboard-canvas"));
+    geometry = new GeometryBoard($tool("#geometry-canvas"));
+    $$tool("[data-whiteboard-tool]").forEach((button) => {
+      button.addEventListener("click", () => {
+        whiteboard.tool = button.dataset.whiteboardTool;
+        $$tool("[data-whiteboard-tool]").forEach((item) =>
+          item.classList.toggle("active", item === button)
+        );
+      });
+    });
+    $tool("#whiteboard-undo").addEventListener("click", () => whiteboard.undo());
+    $tool("#whiteboard-clear").addEventListener("click", () => whiteboard.clear());
+    $tool("#whiteboard-grid").addEventListener("click", () => whiteboard.addGrid());
+    $tool("#whiteboard-image").addEventListener("change", (event) => {
+      whiteboard.addImage(event.target.files[0]);
+      event.target.value = "";
+    });
+    $tool("#whiteboard-export").addEventListener("click", () =>
+      downloadCanvas(whiteboard.canvas, "hulumath-whiteboard")
+    );
+    $$tool("[data-geometry-tool]").forEach((button) => {
+      button.addEventListener("click", () => {
+        geometry.tool = button.dataset.geometryTool;
+        geometry.pending = [];
+        $$tool("[data-geometry-tool]").forEach((item) =>
+          item.classList.toggle("active", item === button)
+        );
+      });
+    });
+    $tool("#geometry-labels").addEventListener("change", () => geometry.draw());
+    $tool("#geometry-undo").addEventListener("click", () => geometry.undo());
+    $tool("#geometry-clear").addEventListener("click", () => geometry.clear());
+    $tool("#geometry-export").addEventListener("click", () =>
+      downloadCanvas(geometry.canvas, "hulumath-geometry")
+    );
+  }
+
+  function init() {
+    $tool("#calc-operation").addEventListener("change", updateCalculatorFields);
+    $tool("#calc-run").addEventListener("click", runCalculator);
+    $tool("#calc-input").addEventListener("keydown", (event) => {
+      if ((event.metaKey || event.ctrlKey) && event.key === "Enter") runCalculator();
+    });
+    $$tool("[data-calc-example]").forEach((button) => {
+      button.addEventListener("click", () => {
+        $tool("#calc-operation").value = button.dataset.calcOperation;
+        $tool("#calc-input").value = button.dataset.calcExample;
+        updateCalculatorFields();
+        runCalculator();
+      });
+    });
+    ["#graph-run", "#graph-range", "#graph-parameter", "#graph-derivative", "#graph-integral"]
+      .forEach((selector) => $tool(selector).addEventListener("input", drawGraph));
+    $tool("#graph-expression").addEventListener("keydown", (event) => {
+      if ((event.metaKey || event.ctrlKey) && event.key === "Enter") drawGraph();
+    });
+    initDrawingTools();
+    updateCalculatorFields();
+    drawGraph();
+  }
+
+  function activate(tool) {
+    if (tool === "graph") window.setTimeout(drawGraph, 30);
+    if (tool === "geometry") window.setTimeout(() => geometry.draw(), 30);
+  }
+
+  window.HuluToolbox = { init, activate, runCalculator, drawGraph };
+})();
diff --git a/backend/templates/index.html b/backend/templates/index.html
index 0f9efa0..d1629bf 100644
--- a/backend/templates/index.html
+++ b/backend/templates/index.html
@@ -90,24 +90,82 @@
           <button class="active" data-track="standard">标准</button><button data-track="beginner">入门</button><button data-track="advanced">进阶</button>
         </div>
         <div id="contest-list" class="content-grid loading">正在读取比赛…</div>
+        <section class="math-games-section">
+          <div class="section-heading">
+            <div><span class="kicker">MATH PLAYGROUND</span><h2>数学玩法</h2></div>
+            <p>短局推理，成绩由服务端校验并记录。</p>
+          </div>
+          <div id="math-game-list" class="game-card-grid"></div>
+        </section>
       </section>
 
       <section class="view" id="view-toolbox">
         <div class="page-title"><span class="kicker">MATHEMATICAL WORKBENCH</span><h1>工具箱</h1><p>计算、查询、绘图与表达，把想法直接变成可以继续工作的对象。</p></div>
         <div class="tool-grid" id="tool-grid">
           <button class="tool-card" data-tool="mental"><span>⚡</span><b>口算竞技</b><small>限时挑战你的心算速度</small></button>
-          <button class="tool-card active" data-tool="calculator"><span>123</span><b>科学计算器</b><small>四则、幂运算与三角函数</small></button>
+          <button class="tool-card active" data-tool="calculator"><span>123</span><b>数学计算工作台</b><small>代数、微积分、矩阵与统计</small></button>
           <button class="tool-card" data-tool="symbols"><span>Σ</span><b>数学符号查询</b><small>含义、读法与 LaTeX 写法</small></button>
-          <button class="tool-card" data-tool="graph"><span>⌁</span><b>函数图形绘制</b><small>输入 f(x)，实时观察曲线</small></button>
+          <button class="tool-card" data-tool="graph"><span>⌁</span><b>函数图形绘制</b><small>多函数、参数、导数与分析</small></button>
+          <button class="tool-card" data-tool="whiteboard"><span>✎</span><b>数学白板</b><small>书写、图形、撤销与导出</small></button>
+          <button class="tool-card" data-tool="geometry"><span>△</span><b>几何画板</b><small>点线圆、中点与动态测量</small></button>
           <button class="tool-card" data-tool="latex"><span>TeX</span><b>LaTeX Lab</b><small>编辑、预览、课程与公式库</small></button>
         </div>
 
         <div class="tool-workspace active" id="tool-calculator">
-          <div class="workspace-heading"><div><span class="kicker">CALCULATOR</span><h2>科学计算器</h2></div><p>支持 + − × ÷、括号、幂、sin、cos、tan、sqrt、log 与常数 π。</p></div>
-          <div class="calculator-shell">
-            <div class="calculator-display"><small id="calc-history">准备计算</small><output id="calc-output">0</output></div>
-            <input id="calc-input" class="formula-input" autocomplete="off" value="sqrt(144) + 2^5" aria-label="计算表达式">
-            <div class="calculator-actions"><button data-calc-example="sin(pi/6)">sin(π/6)</button><button data-calc-example="log(100)">log(100)</button><button data-calc-example="(18+7)*4">(18+7)×4</button><button id="calc-run" class="primary-button">计算</button></div>
+          <div class="workspace-heading"><div><span class="kicker">COMPUTATION STUDIO</span><h2>数学计算工作台</h2></div><p>精确值、方程、微积分、矩阵、统计与进制转换由受限数学内核计算。</p></div>
+          <div class="calculator-shell advanced-calculator">
+            <div class="calculator-controls">
+              <label>计算类型
+                <select id="calc-operation">
+                  <option value="calculate">精确计算</option>
+                  <option value="simplify">表达式化简</option>
+                  <option value="expand">代数展开</option>
+                  <option value="factor">因式分解</option>
+                  <option value="solve">解方程</option>
+                  <option value="derivative">求导</option>
+                  <option value="integral">积分</option>
+                  <option value="limit">极限</option>
+                  <option value="matrix_det">矩阵行列式</option>
+                  <option value="matrix_inverse">逆矩阵</option>
+                  <option value="matrix_rref">矩阵行最简形</option>
+                  <option value="matrix_transpose">矩阵转置</option>
+                  <option value="statistics">描述统计</option>
+                  <option value="base">进制转换</option>
+                  <option value="unit">单位换算</option>
+                </select>
+              </label>
+              <label>变量
+                <select id="calc-variable"><option>x</option><option>y</option><option>z</option><option>a</option><option>b</option><option>t</option><option>n</option></select>
+              </label>
+              <label class="calc-field" data-calc-field="order">阶数<input id="calc-order" type="number" min="1" max="5" value="1"></label>
+              <label class="calc-field" data-calc-field="bounds">下限<input id="calc-lower" placeholder="可留空"></label>
+              <label class="calc-field" data-calc-field="bounds">上限<input id="calc-upper" placeholder="可留空"></label>
+              <label class="calc-field" data-calc-field="point">趋近值<input id="calc-point" value="0"></label>
+              <label class="calc-field" data-calc-field="base">原进制<input id="calc-from-base" type="number" min="2" max="36" value="10"></label>
+              <label class="calc-field" data-calc-field="base">目标进制<input id="calc-to-base" type="number" min="2" max="36" value="2"></label>
+              <label class="calc-field" data-calc-field="unit">原单位<select id="calc-from-unit"><option>mm</option><option>cm</option><option selected>m</option><option>km</option><option>in</option><option>ft</option><option>g</option><option>kg</option><option>lb</option><option>s</option><option>min</option><option>h</option><option>deg</option><option>rad</option></select></label>
+              <label class="calc-field" data-calc-field="unit">目标单位<select id="calc-to-unit"><option>mm</option><option selected>cm</option><option>m</option><option>km</option><option>in</option><option>ft</option><option>g</option><option>kg</option><option>lb</option><option>s</option><option>min</option><option>h</option><option>deg</option><option>rad</option></select></label>
+            </div>
+            <label class="calculator-expression-label">表达式或数据
+              <textarea id="calc-input" class="formula-input" autocomplete="off" aria-label="计算表达式">sqrt(2) + 1/3</textarea>
+            </label>
+            <div class="calculator-actions calc-examples">
+              <button data-calc-operation="solve" data-calc-example="x^2 - 5*x + 6 = 0">解方程</button>
+              <button data-calc-operation="derivative" data-calc-example="sin(x) + x^3">求导</button>
+              <button data-calc-operation="integral" data-calc-example="x^2">积分</button>
+              <button data-calc-operation="matrix_inverse" data-calc-example="1,2;3,4">逆矩阵</button>
+              <button data-calc-operation="statistics" data-calc-example="12,15,18,21,24">统计</button>
+              <button data-calc-operation="unit" data-calc-example="1.75">单位换算</button>
+              <button id="calc-run" class="primary-button">开始计算</button>
+            </div>
+            <div class="calculator-result" aria-live="polite">
+              <div class="calculator-display"><small id="calc-history">准备计算</small><output id="calc-output">0</output></div>
+              <div class="calc-result-grid">
+                <div><span>近似值</span><code id="calc-decimal">0</code></div>
+                <div><span>LaTeX</span><code id="calc-latex">0</code></div>
+              </div>
+              <ol id="calc-steps" class="calc-steps"></ol>
+            </div>
           </div>
         </div>
 
@@ -117,13 +175,59 @@
         </div>
 
         <div class="tool-workspace" id="tool-graph">
-          <div class="workspace-heading"><div><span class="kicker">FUNCTION PLOTTER</span><h2>函数图形绘制</h2></div><p>变量使用 x，支持与计算器相同的函数。</p></div>
+          <div class="workspace-heading"><div><span class="kicker">FUNCTION PLOTTER</span><h2>函数图形绘制</h2></div><p>每行一个函数；支持参数 a、数值导数、积分区域和曲线分析。</p></div>
           <div class="graph-shell">
-            <div class="graph-controls"><label>f(x)<input id="graph-expression" class="formula-input" value="sin(x) + x/3"></label><label>显示范围<input id="graph-range" type="range" min="5" max="30" value="10"><span id="graph-range-label">−10 到 10</span></label><button id="graph-run" class="primary-button">绘制函数</button><p id="graph-error"></p></div>
+            <div class="graph-controls">
+              <label>函数列表<textarea id="graph-expression" class="formula-input">sin(x) + a*x/3&#10;0.08*x^2 - 2</textarea></label>
+              <label>X 范围<input id="graph-range" type="range" min="5" max="30" value="10"><span id="graph-range-label">−10 到 10</span></label>
+              <label>参数 a<input id="graph-parameter" type="range" min="-5" max="5" step="0.1" value="1"><span id="graph-parameter-label">a = 1</span></label>
+              <label class="check-row"><input id="graph-derivative" type="checkbox"> 绘制第一条函数的导数</label>
+              <label class="check-row"><input id="graph-integral" type="checkbox"> 填充第一条函数与 x 轴区域</label>
+              <button id="graph-run" class="primary-button">绘制函数</button>
+              <p id="graph-error"></p>
+              <div id="graph-analysis" class="graph-analysis"></div>
+            </div>
             <canvas id="graph-canvas" width="900" height="480" aria-label="函数曲线图"></canvas>
           </div>
         </div>
 
+        <div class="tool-workspace" id="tool-whiteboard">
+          <div class="workspace-heading"><div><span class="kicker">MATH WHITEBOARD</span><h2>数学白板</h2></div><p>支持鼠标、触控笔和手机触摸，作品仅在当前设备编辑，可导出 PNG。</p></div>
+          <div class="drawing-toolbar" id="whiteboard-toolbar">
+            <button class="active" data-whiteboard-tool="pen">画笔</button>
+            <button data-whiteboard-tool="line">直线</button>
+            <button data-whiteboard-tool="rect">矩形</button>
+            <button data-whiteboard-tool="text">文字 / 公式</button>
+            <button data-whiteboard-tool="eraser">橡皮</button>
+            <input id="whiteboard-text" class="toolbar-text-input" placeholder="输入文字或公式">
+            <label>颜色<input id="whiteboard-color" type="color" value="#17211b"></label>
+            <label>粗细<input id="whiteboard-size" type="range" min="2" max="24" value="4"></label>
+            <button id="whiteboard-grid">添加坐标纸</button>
+            <label class="file-tool">导入图片<input id="whiteboard-image" type="file" accept="image/*"></label>
+            <button id="whiteboard-undo">撤销</button>
+            <button id="whiteboard-clear">清空</button>
+            <button id="whiteboard-export" class="primary-button">导出 PNG</button>
+          </div>
+          <div class="canvas-stage"><canvas id="whiteboard-canvas" width="1200" height="700" aria-label="数学白板"></canvas></div>
+        </div>
+
+        <div class="tool-workspace" id="tool-geometry">
+          <div class="workspace-heading"><div><span class="kicker">GEOMETRY BOARD</span><h2>几何画板</h2></div><p>依次点击构造点、线段和圆；支持中点、长度与坐标测量。</p></div>
+          <div class="drawing-toolbar" id="geometry-toolbar">
+            <button class="active" data-geometry-tool="point">点</button>
+            <button data-geometry-tool="segment">线段</button>
+            <button data-geometry-tool="circle">圆</button>
+            <button data-geometry-tool="midpoint">中点</button>
+            <button data-geometry-tool="move">拖动</button>
+            <label class="check-row"><input id="geometry-labels" type="checkbox" checked> 坐标与测量</label>
+            <button id="geometry-undo">撤销</button>
+            <button id="geometry-clear">清空</button>
+            <button id="geometry-export" class="primary-button">导出 PNG</button>
+          </div>
+          <div class="canvas-stage geometry-stage"><canvas id="geometry-canvas" width="1200" height="700" aria-label="几何画板"></canvas></div>
+          <p id="geometry-hint" class="canvas-hint">点击画布创建第一个点。</p>
+        </div>
+
         <div class="tool-workspace" id="tool-latex">
           <div class="workspace-heading"><div><span class="kicker">LATEX LAB</span><h2>数学表达实验室</h2></div><p>源码、实时预览与版本保存。</p></div>
           <div class="editor-shell">
@@ -199,6 +303,8 @@
 
   <div class="toast" id="toast" role="status"></div>
   <div class="csrf-token">{% csrf_token %}</div>
+  <script src="{% static 'js/toolbox.js' %}" defer></script>
+  <script src="{% static 'js/games.js' %}" defer></script>
   <script src="{% static 'js/app.js' %}" defer></script>
 </body>
 </html>
diff --git a/backend/toolbox/__init__.py b/backend/toolbox/__init__.py
new file mode 100644
index 0000000..8b13789
--- /dev/null
+++ b/backend/toolbox/__init__.py
@@ -0,0 +1 @@
+
diff --git a/backend/toolbox/apps.py b/backend/toolbox/apps.py
new file mode 100644
index 0000000..d2fc657
--- /dev/null
+++ b/backend/toolbox/apps.py
@@ -0,0 +1,7 @@
+from django.apps import AppConfig
+
+
+class ToolboxConfig(AppConfig):
+    default_auto_field = "django.db.models.BigAutoField"
+    name = "toolbox"
+    verbose_name = "数学工具箱"
diff --git a/backend/toolbox/engine.py b/backend/toolbox/engine.py
new file mode 100644
index 0000000..0a7b5e2
--- /dev/null
+++ b/backend/toolbox/engine.py
@@ -0,0 +1,333 @@
+import ast
+import math
+from statistics import mean, median, pstdev, pvariance
+
+import sympy as sp
+from rest_framework.exceptions import ValidationError
+
+MAX_EXPRESSION_LENGTH = 500
+MAX_AST_NODES = 120
+MAX_MATRIX_CELLS = 36
+SYMBOLS = {name: sp.Symbol(name, real=True) for name in ("x", "y", "z", "a", "b", "t", "n")}
+CONSTANTS = {"pi": sp.pi, "e": sp.E, "E": sp.E, "i": sp.I, "I": sp.I}
+FUNCTIONS = {
+    "sin": sp.sin,
+    "cos": sp.cos,
+    "tan": sp.tan,
+    "asin": sp.asin,
+    "acos": sp.acos,
+    "atan": sp.atan,
+    "sinh": sp.sinh,
+    "cosh": sp.cosh,
+    "tanh": sp.tanh,
+    "sqrt": sp.sqrt,
+    "exp": sp.exp,
+    "ln": sp.log,
+    "log": sp.log,
+    "abs": sp.Abs,
+    "factorial": sp.factorial,
+    "binomial": sp.binomial,
+    "gcd": sp.gcd,
+    "lcm": sp.lcm,
+    "floor": sp.floor,
+    "ceil": sp.ceiling,
+}
+FUNCTION_ARITY = {
+    "factorial": (1, 1),
+    "binomial": (2, 2),
+    "gcd": (2, 2),
+    "lcm": (2, 2),
+}
+UNIT_FACTORS = {
+    "mm": ("length", 0.001),
+    "cm": ("length", 0.01),
+    "m": ("length", 1.0),
+    "km": ("length", 1000.0),
+    "in": ("length", 0.0254),
+    "ft": ("length", 0.3048),
+    "g": ("mass", 0.001),
+    "kg": ("mass", 1.0),
+    "lb": ("mass", 0.45359237),
+    "s": ("time", 1.0),
+    "min": ("time", 60.0),
+    "h": ("time", 3600.0),
+    "rad": ("angle", 1.0),
+    "deg": ("angle", math.pi / 180),
+}
+
+
+class SafeExpressionParser:
+    def __init__(self, source):
+        source = str(source or "").strip()
+        if not source:
+            raise ValidationError({"expression": "请输入数学表达式"})
+        if len(source) > MAX_EXPRESSION_LENGTH:
+            raise ValidationError({"expression": "表达式不能超过 500 个字符"})
+        source = (
+            source.replace("π", "pi")
+            .replace("×", "*")
+            .replace("÷", "/")
+            .replace("−", "-")
+            .replace("^", "**")
+        )
+        try:
+            self.tree = ast.parse(source, mode="eval")
+        except SyntaxError as exc:
+            raise ValidationError({"expression": "表达式语法无效"}) from exc
+        if sum(1 for _ in ast.walk(self.tree)) > MAX_AST_NODES:
+            raise ValidationError({"expression": "表达式过于复杂"})
+
+    def parse(self):
+        return self._convert(self.tree.body)
+
+    def _convert(self, node):
+        if isinstance(node, ast.Constant):
+            if isinstance(node.value, bool) or not isinstance(node.value, (int, float)):
+                raise ValidationError({"expression": "只允许数值常量"})
+            if isinstance(node.value, int) and len(str(abs(node.value))) > 50:
+                raise ValidationError({"expression": "整数位数过多"})
+            return sp.Integer(node.value) if isinstance(node.value, int) else sp.Float(node.value)
+        if isinstance(node, ast.Name):
+            if node.id in SYMBOLS:
+                return SYMBOLS[node.id]
+            if node.id in CONSTANTS:
+                return CONSTANTS[node.id]
+            raise ValidationError({"expression": f"不支持变量或常量 {node.id}"})
+        if isinstance(node, ast.UnaryOp) and isinstance(node.op, (ast.UAdd, ast.USub)):
+            value = self._convert(node.operand)
+            return value if isinstance(node.op, ast.UAdd) else -value
+        if isinstance(node, ast.BinOp):
+            left = self._convert(node.left)
+            right = self._convert(node.right)
+            if isinstance(node.op, ast.Add):
+                return left + right
+            if isinstance(node.op, ast.Sub):
+                return left - right
+            if isinstance(node.op, ast.Mult):
+                return left * right
+            if isinstance(node.op, ast.Div):
+                return left / right
+            if isinstance(node.op, ast.Mod):
+                return sp.Mod(left, right)
+            if isinstance(node.op, ast.Pow):
+                if right.is_number and abs(float(right)) > 100:
+                    raise ValidationError({"expression": "幂指数绝对值不能超过 100"})
+                return left**right
+        if isinstance(node, ast.Call) and isinstance(node.func, ast.Name):
+            function = FUNCTIONS.get(node.func.id)
+            if function is None:
+                raise ValidationError({"expression": f"不支持函数 {node.func.id}"})
+            minimum, maximum = FUNCTION_ARITY.get(node.func.id, (1, 2))
+            if node.keywords or not minimum <= len(node.args) <= maximum:
+                raise ValidationError({"expression": f"{node.func.id} 的参数数量无效"})
+            try:
+                return function(*(self._convert(item) for item in node.args))
+            except (TypeError, ValueError) as exc:
+                raise ValidationError({"expression": f"{node.func.id} 的参数无效"}) from exc
+        raise ValidationError({"expression": "表达式包含不允许的语法"})
+
+
+def parse_expression(source):
+    return SafeExpressionParser(source).parse()
+
+
+def parse_equation(source):
+    source = str(source or "")
+    if source.count("=") > 1:
+        raise ValidationError({"expression": "方程只能包含一个等号"})
+    if "=" not in source:
+        return parse_expression(source)
+    left, right = source.split("=", 1)
+    return sp.Eq(parse_expression(left), parse_expression(right))
+
+
+def serialize_math(value):
+    if isinstance(value, dict):
+        return {
+            str(serialize_math(key)["exact"]): serialize_math(item)
+            for key, item in value.items()
+        }
+    if isinstance(value, (list, tuple)):
+        return [serialize_math(item) for item in value]
+    if isinstance(value, sp.MatrixBase):
+        return {
+            "exact": str(value.tolist()),
+            "decimal": str(value.evalf(12).tolist()),
+            "latex": sp.latex(value),
+        }
+    exact = str(value)
+    try:
+        decimal = str(sp.N(value, 12))
+    except Exception:
+        decimal = exact
+    return {"exact": exact, "decimal": decimal, "latex": sp.latex(value)}
+
+
+def parse_matrix(source):
+    rows = [row.strip() for row in str(source or "").split(";") if row.strip()]
+    if not rows:
+        raise ValidationError({"expression": "矩阵格式示例：1,2;3,4"})
+    parsed = [[parse_expression(cell.strip()) for cell in row.split(",")] for row in rows]
+    width = len(parsed[0])
+    if width == 0 or any(len(row) != width for row in parsed):
+        raise ValidationError({"expression": "矩阵每行列数必须一致"})
+    if len(parsed) * width > MAX_MATRIX_CELLS:
+        raise ValidationError({"expression": "矩阵最多支持 36 个元素"})
+    return sp.Matrix(parsed)
+
+
+def parse_number_list(source):
+    try:
+        values = [float(item.strip()) for item in str(source or "").split(",") if item.strip()]
+    except ValueError as exc:
+        raise ValidationError({"expression": "统计数据必须是逗号分隔的数字"}) from exc
+    if not 1 <= len(values) <= 500:
+        raise ValidationError({"expression": "统计数据数量必须在 1 到 500 之间"})
+    if not all(math.isfinite(item) for item in values):
+        raise ValidationError({"expression": "统计数据必须是有限数值"})
+    return values
+
+
+def calculate(payload):
+    operation = str(payload.get("operation", "calculate"))
+    source = payload.get("expression", "")
+    variable_name = str(payload.get("variable", "x"))
+    variable = SYMBOLS.get(variable_name)
+    if variable is None:
+        raise ValidationError({"variable": "变量仅支持 x、y、z、a、b、t、n"})
+
+    if operation == "statistics":
+        values = parse_number_list(source)
+        result = {
+            "count": len(values),
+            "mean": mean(values),
+            "median": median(values),
+            "variance": pvariance(values),
+            "standard_deviation": pstdev(values),
+            "minimum": min(values),
+            "maximum": max(values),
+        }
+        return {
+            "operation": operation,
+            "result": result,
+            "steps": ["读取数据", "计算集中趋势", "计算离散程度"],
+        }
+
+    if operation == "base":
+        try:
+            from_base = int(payload.get("from_base", 10))
+            to_base = int(payload.get("to_base", 2))
+            if not 2 <= from_base <= 36 or not 2 <= to_base <= 36:
+                raise ValueError
+            number = int(str(source).strip(), from_base)
+        except ValueError as exc:
+            raise ValidationError({"expression": "进制必须为 2 到 36，且输入应合法"}) from exc
+        digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+        sign = "-" if number < 0 else ""
+        remaining = abs(number)
+        converted = "0"
+        if remaining:
+            pieces = []
+            while remaining:
+                remaining, index = divmod(remaining, to_base)
+                pieces.append(digits[index])
+            converted = "".join(reversed(pieces))
+        return {
+            "operation": operation,
+            "result": {"exact": f"{sign}{converted}", "decimal": str(number), "latex": sign + converted},
+            "steps": [f"按 {from_base} 进制读取", f"转换为 {to_base} 进制"],
+        }
+
+    if operation == "unit":
+        try:
+            value = float(str(source).strip())
+            from_unit = str(payload.get("from_unit", "m"))
+            to_unit = str(payload.get("to_unit", "cm"))
+            source_unit = UNIT_FACTORS[from_unit]
+            target_unit = UNIT_FACTORS[to_unit]
+            if source_unit[0] != target_unit[0] or not math.isfinite(value):
+                raise ValueError
+        except (KeyError, ValueError) as exc:
+            raise ValidationError({"expression": "单位不兼容或数值无效"}) from exc
+        converted = value * source_unit[1] / target_unit[1]
+        return {
+            "operation": operation,
+            "result": {
+                "exact": f"{converted:.12g} {to_unit}",
+                "decimal": f"{converted:.12g}",
+                "latex": f"{converted:.12g}\\,{to_unit}",
+            },
+            "steps": [f"将 {from_unit} 换算为标准单位", f"转换为 {to_unit}"],
+        }
+
+    if operation.startswith("matrix_"):
+        matrix = parse_matrix(source)
+        if operation == "matrix_det":
+            if not matrix.is_square:
+                raise ValidationError({"expression": "行列式要求方阵"})
+            result = matrix.det()
+            steps = ["读取矩阵", "按行列式规则计算"]
+        elif operation == "matrix_inverse":
+            if not matrix.is_square or matrix.det() == 0:
+                raise ValidationError({"expression": "矩阵不可逆"})
+            result = matrix.inv()
+            steps = ["读取矩阵", "验证行列式非零", "计算逆矩阵"]
+        elif operation == "matrix_rref":
+            result = matrix.rref()[0]
+            steps = ["读取矩阵", "执行初等行变换", "得到行最简形"]
+        elif operation == "matrix_transpose":
+            result = matrix.T
+            steps = ["读取矩阵", "交换行列"]
+        else:
+            raise ValidationError({"operation": "不支持的矩阵操作"})
+        return {"operation": operation, "result": serialize_math(result), "steps": steps}
+
+    expression = parse_equation(source) if operation == "solve" else parse_expression(source)
+    steps = ["解析受限数学表达式"]
+    if operation == "calculate":
+        result = sp.simplify(expression)
+        steps.append("化简并保留精确值")
+    elif operation == "simplify":
+        result = sp.trigsimp(sp.cancel(expression))
+        steps.append("约分并进行代数/三角化简")
+    elif operation == "expand":
+        result = sp.expand(expression)
+        steps.append("展开乘积与幂")
+    elif operation == "factor":
+        result = sp.factor(expression)
+        steps.append("提取因式并分解")
+    elif operation == "solve":
+        result = sp.solve(expression, variable)
+        if len(result) > 50:
+            raise ValidationError({"expression": "解的数量过多"})
+        steps.extend([f"以 {variable_name} 为未知量", "求解方程"])
+    elif operation == "derivative":
+        order = int(payload.get("order", 1))
+        if not 1 <= order <= 5:
+            raise ValidationError({"order": "导数阶数必须在 1 到 5 之间"})
+        result = sp.diff(expression, variable, order)
+        steps.append(f"对 {variable_name} 求 {order} 阶导数")
+    elif operation == "integral":
+        lower = str(payload.get("lower", "")).strip()
+        upper = str(payload.get("upper", "")).strip()
+        if lower or upper:
+            if not lower or not upper:
+                raise ValidationError({"bounds": "定积分必须同时填写上下限"})
+            result = sp.integrate(
+                expression,
+                (variable, parse_expression(lower), parse_expression(upper)),
+            )
+            steps.append(f"对 {variable_name} 计算定积分")
+        else:
+            result = sp.integrate(expression, variable)
+            steps.append(f"对 {variable_name} 计算不定积分")
+    elif operation == "limit":
+        point = parse_expression(payload.get("point", "0"))
+        direction = str(payload.get("direction", "+-"))
+        if direction not in {"+", "-", "+-"}:
+            raise ValidationError({"direction": "极限方向必须为 +、- 或 +-"})
+        result = sp.limit(expression, variable, point, dir=direction)
+        steps.append(f"令 {variable_name} 趋近 {point}")
+    else:
+        raise ValidationError({"operation": "不支持的计算类型"})
+    return {"operation": operation, "result": serialize_math(result), "steps": steps}
diff --git a/backend/toolbox/test_engine.py b/backend/toolbox/test_engine.py
new file mode 100644
index 0000000..b244209
--- /dev/null
+++ b/backend/toolbox/test_engine.py
@@ -0,0 +1,63 @@
+import pytest
+from rest_framework.exceptions import ValidationError
+
+from toolbox.engine import calculate, parse_expression
+
+
+def test_calculate_精确计算与微积分():
+    exact = calculate({"operation": "calculate", "expression": "sqrt(2) + 1/3"})
+    derivative = calculate(
+        {"operation": "derivative", "expression": "sin(x) + x^3", "variable": "x"}
+    )
+    integral = calculate(
+        {
+            "operation": "integral",
+            "expression": "x^2",
+            "variable": "x",
+            "lower": "0",
+            "upper": "3",
+        }
+    )
+
+    assert exact["result"]["exact"] == "1/3 + sqrt(2)"
+    assert derivative["result"]["exact"] == "3*x**2 + cos(x)"
+    assert integral["result"]["exact"] == "9"
+
+
+def test_calculate_方程矩阵统计与进制():
+    solved = calculate({"operation": "solve", "expression": "x^2 - 5*x + 6 = 0"})
+    determinant = calculate({"operation": "matrix_det", "expression": "1,2;3,4"})
+    statistics = calculate({"operation": "statistics", "expression": "1,2,3,4"})
+    converted = calculate(
+        {"operation": "base", "expression": "FF", "from_base": 16, "to_base": 2}
+    )
+    units = calculate(
+        {
+            "operation": "unit",
+            "expression": "1.75",
+            "from_unit": "m",
+            "to_unit": "cm",
+        }
+    )
+    combinations = calculate({"operation": "calculate", "expression": "binomial(10, 3)"})
+
+    assert [item["exact"] for item in solved["result"]] == ["2", "3"]
+    assert determinant["result"]["exact"] == "-2"
+    assert statistics["result"]["mean"] == 2.5
+    assert converted["result"]["exact"] == "11111111"
+    assert units["result"]["exact"] == "175 cm"
+    assert combinations["result"]["exact"] == "120"
+
+
+@pytest.mark.parametrize(
+    "source",
+    [
+        "__import__('os').system('id')",
+        "open('/etc/passwd')",
+        "x.__class__",
+        "[x for x in range(10)]",
+    ],
+)
+def test_parse_expression_拒绝非数学语法(source):
+    with pytest.raises(ValidationError):
+        parse_expression(source)
diff --git a/backend/toolbox/test_views.py b/backend/toolbox/test_views.py
new file mode 100644
index 0000000..bb92f10
--- /dev/null
+++ b/backend/toolbox/test_views.py
@@ -0,0 +1,25 @@
+import pytest
+
+
+@pytest.mark.django_db
+def test_calculator_api_公开访问并返回精确值(client):
+    response = client.post(
+        "/api/v1/toolbox/calculate/",
+        {"operation": "factor", "expression": "x^2 - 1"},
+        content_type="application/json",
+    )
+
+    assert response.status_code == 200
+    assert response.json()["result"]["exact"] == "(x - 1)*(x + 1)"
+
+
+@pytest.mark.django_db
+def test_calculator_api_危险表达式返回四百(client):
+    response = client.post(
+        "/api/v1/toolbox/calculate/",
+        {"operation": "calculate", "expression": "__import__('os').system('id')"},
+        content_type="application/json",
+    )
+
+    assert response.status_code == 400
+    assert "error" in response.json()
diff --git a/backend/toolbox/urls.py b/backend/toolbox/urls.py
new file mode 100644
index 0000000..18f34de
--- /dev/null
+++ b/backend/toolbox/urls.py
@@ -0,0 +1,7 @@
+from django.urls import path
+
+from .views import CalculatorView
+
+urlpatterns = [
+    path("calculate/", CalculatorView.as_view(), name="toolbox-calculate"),
+]
diff --git a/backend/toolbox/views.py b/backend/toolbox/views.py
new file mode 100644
index 0000000..38d359c
--- /dev/null
+++ b/backend/toolbox/views.py
@@ -0,0 +1,22 @@
+from rest_framework import permissions
+from rest_framework.exceptions import ValidationError
+from rest_framework.response import Response
+from rest_framework.throttling import ScopedRateThrottle
+from rest_framework.views import APIView
+
+from .engine import calculate
+
+
+class CalculatorView(APIView):
+    permission_classes = [permissions.AllowAny]
+    throttle_classes = [ScopedRateThrottle]
+    throttle_scope = "calculator"
+
+    def post(self, request):
+        try:
+            payload = calculate(request.data)
+        except ValidationError:
+            raise
+        except (ArithmeticError, NotImplementedError, TypeError, ValueError) as exc:
+            raise ValidationError({"expression": "该计算暂时无法完成，请缩小表达式范围"}) from exc
+        return Response(payload)
diff --git a/requirements.txt b/requirements.txt
index 1d6049c..b7492b9 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -8,3 +8,4 @@ mysqlclient==2.2.7
 whitenoise==6.7.0
 gunicorn==23.0.0
 uvicorn[standard]==0.30.6
+sympy==1.13.3