Topic War Map: Triggers, Tools and Traps on One Page
A single dense reference page for one competition topic: exact theorem statements, technique-to-trigger pairings, a pattern-to-tool lookup table, classic traps, and a 3-line exam reflex summary.
Works on any free AI · Best tool: Any AI chat (ChatGPT, Claude, Gemini)
✅ How to use this effectively
- Fill in [TOPIC] and [FIELD] (e.g. inequalities in algebra, or congruences in number theory).
- Answer the clarifier precisely — naming your level (school / JEE / Olympiad) sets the depth of the sheet.
- Check every theorem statement against your textbook before trusting it in an exam.
- Print it and reread only this page the night before the test.
- Ask for a second page of the pattern-to-tool table with 5 practice questions if you want to drill it.
🔧 If it is not right, reply with this: If any theorem statement looks fuzzy or wrong, reply: 'Restate [theorem name] exactly with all hypotheses — the current statement is imprecise.'
THE PROMPT
ROLE: You are a competition-maths coach who is obsessive about the 'one-pager' — the single sheet a student rereads the night before an exam that contains every tool worth reaching for.
CONTEXT: Build a complete one-page reference for [TOPIC] in [FIELD] (number theory / combinatorics / geometry / algebra-inequalities / calculus). Dense but scannable.
FIRST, ASK ME (one short clarifier, then proceed): Which sub-topics within [TOPIC] do you most want covered, and at what level — school board, JEE Main/Advanced, or IOQM/RMO/INMO? This calibrates the density and depth: a lower level leans on foundational tools and cleaner statements, a higher level pushes into sharper lemmas and harder configurations. Restate the chosen sub-topics and level, then build.
METHOD:
1. CORE RESULTS: list the key theorems/lemmas with exact statements, each with a 5-word 'why it's used'.
2. TECHNIQUES: the standard attacks for this topic (e.g., for number theory: lifting the exponent, orders, CRT, descent; for inequalities: SOS, AM-GM, Cauchy, smoothing, tangent line). For each: the WHEN-TO-USE trigger ('when you see symmetric sums…').
3. PATTERN→TOOL map: a quick table of 'if the problem looks like ___ → reach for ___'.
4. CLASSIC TRAPS: the 3–5 mistakes that cost marks here (e.g., forgetting equality cases, dividing by zero, non-prime modulus, degenerate geometric configurations).
5. KEY IDENTITIES / CONFIGURATIONS to memorise cold.
6. A 3-line 'EXAM REFLEX' summary: the first three things to try when stuck on a [TOPIC] problem.
OUTPUT FORMAT: a single, tightly-formatted page with clear section headers and tables where they help. No padding, no motivational fluff — every line must earn its place. Make it printable-feeling. Calibrate density to the sub-topics and level I gave.
QUALITY BAR: complete enough to be the only sheet I need for [TOPIC] at the stated level; precise statements (no fuzzy theorems); every tool paired with its trigger and its trap.
GROUND RULES: Do not invent statistics, exam cut-offs, page numbers, or citations. If unsure of a statement, say so and label it. Work only from well-established mathematics.