Cross-topic reference
Technique Encyclopedia
The cross-topic tools that show up across every domain — parity, symmetry, casework, and the rest. Each entry explains what the technique is, the signals that suggest reaching for it, when it works and when it doesn't, and two worked examples. Unlike the domain lessons, these aren't about one topic — they're the reasoning habits that apply everywhere.
17 of 17 entries built — the Technique Encyclopedia is complete.
Parity
Even/odd reasoning to prove impossibility or eliminate answer choices instantly.
Symmetry
Exploiting structural symmetry to skip work — pairing sums, symmetric polynomials.
Invariants
A quantity that never changes under a process, used to rule out final states.
Monovariants
A quantity that only increases (or only decreases), used to prove a process must terminate.
Complementary Counting
Counting what you don't want and subtracting from the total.
Casework
Splitting a problem into exhaustive, non-overlapping cases and solving each one.
Inclusion-Exclusion
Correcting for double-counted overlap when combining several sets.
Pigeonhole Principle
If items outnumber containers, some container must hold more than one.
Extremal Principle
Focusing on the largest or smallest element in a configuration to unlock a proof.
Working Backwards
Starting from the known end state and reversing each operation in turn.
Bounding
Showing a quantity must lie between two values to narrow down the answer.
Estimation
Approximating a quantity quickly enough to identify the correct answer choice.
Testing Small Cases
Trying small inputs first to discover or verify a pattern.
Strategic Substitution
Choosing specific values to plug in that reveal a relationship fast.
Exploiting Answer Choices
Using the multiple-choice format itself as information.
Auxiliary Lines
Adding a helpful line to a geometry figure to reveal hidden structure.
Coordinate Placement
Choosing coordinates strategically to simplify a geometry problem.