The Conjecture Engine
State a rule the hidden process obeys, then let the engine try to kill it.
5
levels5–20 min
a run, player-paced4
samplesNo timer
player-paced, always
The Conjecture Engine
State a rule the hidden process obeys, then let the engine try to kill it.
A hidden sequence shows its first few terms. Each sample buys one more term, or tests one conjecture: the engine checks your rule against every term on the board and then against held-out terms you never saw. A rule that survives resolves the level. A rule that dies is kept on the wall with the counterexample that killed it, and your next conjecture revises it.
Levels
5 levelsThe tag on each level says how it gets harder. Levels gate on ideas, not on each other — jump wherever it gets interesting.
What decides the outcome
The game never restates the science — it imports it. These are the model layers that do the deciding.
The parser that reads both the hidden rule and the learner's (`parseExpression`), exact evaluation at each n (`substitute`, `evaluateExact`), and the printed and spoken notation (`printExpression`, `speakExpression`). The game has no arithmetic of its own.
Exact rationals, so a rule is equal to the process at n or it is not — no tolerance to argue with.
The highest common factor (`hcf`) that names the strongest surviving divisibility claim.
Why it teaches
The author's own delete-the-science argument: remove this game's substrate and there is nothing left to choose.
Every sample is a decision about evidence: probe one more term or commit a rule. The engine refutes a rule with a single held-out term, so a learner who matches only the terms they were shown loses to a quadratic, an exponential and, on the circle level, to doubling that stops at the sixth term. Without the substrate's exact evaluation there is no way to tell a rule that holds from one that matches five terms.
Accessibility
The contract's declarations, stated before you commit to a run.
Keyboard
Playable start to finish from the keyboard.
Screen reader
Every move is narrated — the narration is the state, not a description of a picture.
Motion
Reduced-motion: consequences render statically.
Audio
Silent — no sound, and nothing on screen moves on its own.