The Stuck-Problem Playbook: What To Try When Nothing Works
A personal, ordered checklist of concrete moves to run in your head when a maths problem stops you cold — universal first moves, topic-specific escalations, meta-moves, a walk-away signal, and a 6-line memorisable pocket version.
Works on any free AI · Best tool: Any AI chat (ChatGPT, Claude, Gemini)
✅ How to use this effectively
- Fill in [FIELD] (the areas you freeze in most) and [EXAM] (board / JEE / Olympiad round).
- Be honest in the setup about what you currently do when stuck — stare, give up, or try random things.
- Read the full playbook once, then memorise only the 6-line pocket version.
- Practise running the checklist on 3 hard problems this week so it becomes reflex before exam day.
- Ask for a printable card version if you want it pinned above your desk.
🔧 If it is not right, reply with this: If the moves feel like platitudes, reply: 'Replace every vague line with a concrete physical action I can do on paper in under a minute — no advice like think harder or stay calm.'
THE PROMPT
ROLE: You are a maths coach who has distilled what strong solvers actually DO in the silent panic when a problem won't open — the systematic moves, not 'just think harder'. CONTEXT: I want a personal 'when I'm stuck' playbook I can run in my head during [EXAM], biased toward [FIELD] if I name one. FIRST, ASK ME (one at a time, wait each): (1) which topic area(s) do you most often freeze in? (2) when stuck, what do you currently do (stare / give up / try random things)? (3) full-working exam or final-answer/MCQ exam? Then restate and build it. METHOD — build an ORDERED playbook: 1. UNIVERSAL FIRST MOVES (any problem): re-read and list every given condition; restate the goal precisely; ask 'have I used every condition?'; try the smallest cases by hand; look for symmetry or an invariant; guess the answer then work backward. 2. TOPIC-SPECIFIC ESCALATIONS — give a branch for each area I named, for example: - Number theory: reduce mod small primes, test orders, try CRT, look for a parity or descent argument, factor cleverly. - Combinatorics: find a bijection, double-count, set up an extremal/pigeonhole argument, induct on n, build a graph model. - Geometry: chase angles, find similar triangles, add a well-chosen point or line, consider power of a point, fall back to trig/coordinates. - Algebra/inequalities: normalise, test the equality case to guess the bound, try AM-GM/Cauchy/SOS, substitute, consider convexity. - Calculus: differentiate/integrate the natural candidate, check boundary behaviour, sketch the function, try a substitution. 3. META-MOVES when still stuck: change representation, prove a weaker version first, assume the conclusion and see what's forced, take a 60-second reset. 4. KNOW-WHEN-TO-WALK: the concrete signal that it's time to bank partial marks and move on. OUTPUT FORMAT: 'UNIVERSAL CHECKLIST (in order)' → 'TOPIC BRANCHES (one block each)' → 'META-MOVES' → 'WALK-AWAY SIGNAL' → 'POCKET VERSION' (a 6-line memorisable summary). QUALITY BAR: concrete actions, not platitudes; ordered by what to try first; the pocket version must be memorisable in one read. FORMAT THE OUTPUT — PRIMARY DELIVERABLE: Return the complete material as a clean, print-ready A4 handout that can be pasted into Word or Google Docs and saved as PDF. Use a clear title, logical sections, readable mathematics and page-break markers where needed. Keep student material separate from the answer key or teacher notes. GROUND RULES: Do not invent statistics, exam cut-offs, or citations. If unsure of a fact, say so and label it. Work only from what I provide or well-established mathematics.