凭群属性，弗一把！Guess the hidden finite group by its properties.
A group-theoretic take on the "Guess Who" / Wordle formula — select a difficulty level, make guesses, and get color-coded feedback on 6-12 group invariants to identify the mystery group.
- 125 finite groups spanning orders 1-7920: every group of order ≤30, plus selected larger groups including symmetric/alternating, dihedral, dicyclic, Frobenius, quaternion, semidihedral, linear (SL/GL/PGL/PSL), unitary, Heisenberg, hyperoctahedral, and Mathieu groups
- 3 difficulty levels (6 modes) with increasing attribute sets (6 / 10 / 12 invariants) and time limits (90s / 3min / 5min), plus three L3 variants (L3.2 no-size-hint, L3.5 order hidden, L3.7 masked Sylow)
- Guess limits — L1: 6, L2: 7, L3+: 8
- Daily Challenge — one mystery group per day (seeded by date), 10 guesses, no time limit, Wordle-style matrix share
- Bilingual (中文 / English) — language switcher with instant re-render of history and share texts
- Weighted random sampling — rarer groups appear more often than cyclic groups
- Attribute legend on welcome page and in-game, with description dropdowns for each invariant
- HELP button in-game showing input syntax rules (
x/×for direct product,:/⋊for semidirect,{a,b|...}for presentation) - Share — markdown text and image export (with color legend) for normal and daily games
- Dark & light themes
- Responsive — horizontal scrolling card layout on mobile
- Auto-suggest search with aliases, reversed-order matching, presentation notation, and product symbols
| Level | Attributes | Guesses | Time |
|---|---|---|---|
| L1 简单 | Order · Abelian · Nilpotent · Simple · Conjugacy classes · Structure | 6 | 90s |
| L2 中等 | + Center order · Exponent · Rank · Involution count | 7 | 3min |
| L3 困难 | + Sylow type · Min nonlinear degree | 8 | 5min |
| L3.2 困难·无阶数提示 | 同 L3（12 项），但阶数反馈仅显示是否匹配，无大小提示（↑/↓） | 8 | 5min |
| L3.5 困难·隐藏阶数 | L3 去掉 Order 属性（11 项，完全看不到阶数） | 8 | 5min |
| L3.7 困难·隐蔽Sylow | 同 L3.5，且 Sylow 型不显示正确个数，未猜到的素因子显示为 ?:? | 8 | 5min |
The L3 level offers three harder variants (toggle with −/+ on the start screen): L3.2 keeps all 12 invariants but removes the size direction hint on order feedback, L3.5 hides the order attribute entirely, and L3.7 additionally masks the Sylow type counts.
Difficulty pools:
- L1 (20 groups): cyclic groups C1-C12, D4-D6, V4, Q8, S3, A4, C2³
- L2 (50 groups): L1 + cyclic groups C13-C20, non-abelian groups ≤20, 16-order p-groups
- L3 / L3.2 / L3.5 / L3.7 (125 groups): all groups ≤30 + larger simple, linear, Frobenius and p-groups (SL(2,5/7/9), GL(2,3/4/5), PGL(2,7), S6, M10, PSU(3,2), AGL, F56/F110/F240/F42/F57, 32-order D16/Q32/SD32/M32, Heisenberg UT(3,p), hyperoctahedral B4)
- One mystery group per day, picked deterministically from all 125 groups via a date-seeded hash (the same for every player on a given day)
- 10 guesses, no time limit
- Progress persists in
localStorageand carries across the day; a new puzzle resets the next day - Share a Wordle-style color matrix (
🟩🟨⬜) when playing, won, or lost
npm install
npm run dev # http://localhost:5173npm run build # production build → dist/
npm run preview # preview production build- Pick a difficulty level on the start screen (double-click to begin), or jump into the Daily Challenge.
- Type a group name (e.g.
A5,C3xC6,C3:C2,{a,b|a^3=b^2=1}) and press Enter. - Each guess returns a color-coded attribute grid:
- green — exact match
- yellow — close (numeric hint ↑↓)
- red — mismatch
- Find the group before time or attempts run out.
MIT