# RoJBMO Prompt Templates

The exact prompt templates used in the RoJBMO evaluation pipeline: solution
generation, pointwise judging, and pairwise judging. Referenced from the
paper ("*RoJBMO: Evaluating Large Language Models on Junior Balkan
Mathematical Olympiad Problems*", SYNASC 2026), Section IV-C.

Placeholders in `{curly braces}` are filled in per problem at runtime; the
rest of the text is sent to the model unmodified.

---

## 1. Generation prompt

Elicits a candidate solution from each generation model.

```text
You are an expert mathematician participating in the Junior Balkan Mathematical Olympiad (JBMO).

Solve the following {domain} problem completely, showing all steps clearly.
Write your solution in a clean, rigorous mathematical style.

PROBLEM ({year} · {domain}):
{statement}

Provide a complete, step-by-step solution:
```

- `{domain}` — one of Algebra / Combinatorics / Geometry / Number Theory.
- `{year}` — the competition year of the source problem.
- `{statement}` — the problem statement, LaTeX, English.

Sampling: temperature 0.2, single user-turn message, no system prompt.

---

## 2. Pointwise judge prompt

Scores a single candidate solution against the reference solution across
five dimensions.

```text
You are an expert JBMO (Junior Balkan Mathematical Olympiad) grader.
Evaluate the candidate solution below against the reference solution.

═══ PROBLEM ({year} · {domain}) ═══
{statement}

═══ REFERENCE SOLUTION ═══
{reference_solution}

═══ CANDIDATE SOLUTION (by {model_label}) ═══
{candidate_solution}

═══ SCORING INSTRUCTIONS ═══
Score each dimension 1–10. Be strict: a single unjustified logical step or gap in correctness
should cap that dimension at ≤ 6. Only award 9–10 when the solution is virtually flawless.

Dimensions:
• correctness (1–10): Every logical step valid, no hidden assumptions, conclusion fully justified.
• clarity (1–10): Notation clean, argument easy to follow, well-organised.
• completeness (1–10): All cases covered, no steps skipped, final answer clearly stated.
• elegance (1–10): Approach is clean, insightful, or avoids unnecessary computation.
• overall (1–10): Holistic quality — not necessarily the average of the above.

Respond ONLY with valid JSON (no markdown fences, no extra text):
{
  "correctness": <int 1-10>,
  "clarity": <int 1-10>,
  "completeness": <int 1-10>,
  "elegance": <int 1-10>,
  "overall": <int 1-10>,
  "reasoning": "<3-4 sentences: key strengths, key flaws, and whether the solution is correct>"
}/no_think
```

- `{model_label}` — human-readable name of the model being judged (excluded
  from the judge's own generation pool to avoid self-preference).
- The trailing `/no_think` suppresses extended-thinking preambles on models
  that support the convention, so the response stays pure JSON.

Judge: GPT-4o, temperature 0.0, single user-turn message.

---

## 3. Pairwise judge prompt

Directly compares two candidate solutions on the same problem, using a
four-class verdict scheme. Each pair is judged in both orders (A/B and B/A)
to measure position bias.

```text
You are an expert JBMO (Junior Balkan Mathematical Olympiad) grader.
Two candidate solutions are provided below. Determine whether each is mathematically correct.

═══ PROBLEM ({year} · {domain}) ═══
{statement}

═══ REFERENCE SOLUTION ═══
{reference_solution}

═══ SOLUTION A (by {label_a}) ═══
{solution_a}

═══ SOLUTION B (by {label_b}) ═══
{solution_b}

═══ INSTRUCTIONS ═══
Classify into exactly one of four cases:
• "both_correct"    — both solutions reach the correct answer by a valid mathematical argument
• "A_correct"       — only Solution A is mathematically correct
• "B_correct"       — only Solution B is mathematically correct
• "neither_correct" — neither solution is correct

Respond ONLY with valid JSON (no markdown fences, no extra text):
{
  "verdict": "<both_correct|A_correct|B_correct|neither_correct>",
  "reasoning": "<2-3 sentences explaining which solution is correct and why>"
}/no_think
```

Judge: same as the pointwise prompt above.