RMO/INMO Proof Paper With Partial-Credit Rubric
A 6-problem RMO/INMO-style subjective paper with model proofs and a granular out-of-17 step-marking rubric for each problem, including partial-credit landmines.
Works on any free AI · Best tool: Any AI chat (ChatGPT, Claude, Gemini)
✅ How to use this effectively
- 1. Fill [STAGE], [TOPIC_BALANCE] (e.g. 2 Geometry, 2 NT, 1 Algebra, 1 Combinatorics) and [TIME_MINUTES].
- 2. Check the blueprint: one accessible opener and one genuinely hard closer, difficulty climbing in between.
- 3. Verify at least two model proofs yourself before the sitting — every claim must be justified.
- 4. Grade student scripts strictly against the 17-mark rubric, including the listed deductions.
- 5. Use the 'partial-credit landmines' section to give students precise feedback on almost-solutions.
🔧 If it is not right, reply with this: If a problem has an unintended easy shortcut, reply: 'Problem [number] falls to [shortcut] — rewrite it so the intended technique is genuinely required, and update its rubric.'
THE PROMPT
ROLE: You are a Regional/Indian National Mathematical Olympiad paper-setter and head examiner. You set proof-based problems and write the partial-credit schemes coordinators actually use, where a wrong final answer with the right key idea still earns honest marks. CONTEXT: Build an authentic [STAGE] (RMO or INMO) subjective paper of 6 problems, proof-based, no calculators, time [TIME_MINUTES] minutes. Topic balance: [TOPIC_BALANCE] across Algebra, Number Theory, Combinatorics, Geometry, with the customary 1 hard problem and 1 accessible opener. DO THIS: 1) BLUEPRINT — list the 6 slots, each tagged with topic, difficulty (1-5), and the single technique it rewards (e.g. 'P2: NT — order of an element / lifting the exponent'). Score each problem out of 17, in line with standard olympiad practice. 2) Write 6 ORIGINAL proof problems with a smooth difficulty climb. Each must have a genuinely elegant intended solution. 3) MODEL SOLUTION — a clean, full, rigorous proof for each, written as a top scorer would, with the motivating idea stated up front. 4) STEP-MARKING SCHEME — for each problem, a granular rubric out of 17: marks for setting up the right framework, for the key lemma, for handling the crucial case, for the finish; and explicit deductions (e.g. '-2 for unproven WLOG', '-3 for missing the n=1 case', '-1 for a stated-but-unproved claim'). Include 'partial-credit landmines' — common almost-solutions and exactly what they earn. 5) COORDINATION NOTES — guidance for a human grader to keep marking consistent across scripts. OUTPUT FORMAT: ## Blueprint table ## PAPER (P1-P6, marks shown) ## Model solutions ## Step-marking rubric per problem (out of 17) ## Coordination notes QUALITY BAR: Proof problems only (no plug-and-chug); fully verified intended solutions; the rubric must reward partial progress fairly and reflect real olympiad coordination practice. Flag and rewrite any problem with an unintended easy shortcut. 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.