# The Multivac — Evaluation Report

**Evaluation ID:** EVAL-20260402-170708
**Date:** Apr 02, 2026
**Category:** reasoning
**Question ID:** REASON-018

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## Question

Hilbert's Hotel is full (infinite rooms, infinite guests). (1) A bus with infinitely many guests arrives. The manager moves everyone to make room. Show the procedure. (2) Now infinitely many buses, each with infinitely many guests, arrive. Show the procedure. (3) A guest in room 7 complains: 'I've been moved 47 times today.' Design a room assignment protocol that minimizes the maximum number of moves any guest experiences.

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## Winner

**Claude Opus 4.6** (openrouter)
- Winner Score: 9.22
- Matrix Average: 6.90
- Total Judgments: 78

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## Rankings

| Rank | Model | Provider | Avg Score | Judgments |
|------|-------|----------|-----------|----------|
| 1 | Claude Opus 4.6 | openrouter | 9.22 | 9 |
| 2 | Claude Sonnet 4.6 | openrouter | 8.83 | 9 |
| 3 | GPT-5.4 | openrouter | 8.23 | 9 |
| 4 | Grok 4.20 | openrouter | 7.68 | 8 |
| 5 | GPT-OSS-120B | OpenAI | 7.48 | 9 |
| 6 | Gemini 2.5 Flash | openrouter | 6.77 | 8 |
| 7 | MiMo-V2-Flash | Xiaomi | 5.98 | 9 |
| 8 | DeepSeek V4 | openrouter | 5.98 | 9 |
| 9 | Gemini 3.1 Pro | openrouter | 1.90 | 8 |

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## 10×10 Judgment Matrix

Rows = Judge, Columns = Respondent. Self-judgments excluded (—).

| Judge ↓ / Resp → | MiMo-V2-Flash | GPT-OSS-120B | Gemini 3.1 Pro | DeepSeek V4 | Claude Opus | GPT-5.4 | Grok 4.20 | Claude Sonnet | Gemini 2.5 | MiniMax M2.5 |
|---|---|---|---|---|---|---|---|---|---|---|
| MiMo-V2-Flash | — | 8.6 | 2.9 | 6.8 | 9.2 | 8.6 | 8.8 | 9.2 | 7.8 | · |
| GPT-OSS-120B | 4.0 | — | 1.2 | 4.6 | 8.8 | 8.8 | 8.0 | 8.7 | 6.3 | · |
| Gemini 3.1 Pro | 3.0 | 6.8 | — | 6.1 | 10.0 | 9.7 | 7.2 | 8.4 | 6.3 | · |
| DeepSeek V4 | 9.3 | 9.3 | 5.0 | — | 9.7 | 9.4 | 9.7 | 9.7 | 9.3 | · |
| Claude Opus | 4.0 | 6.3 | 0.5 | 4.7 | — | 6.8 | 6.3 | 8.9 | 5.3 | · |
| GPT-5.4 | 5.2 | 6.0 | 0.8 | 4.6 | 9.0 | — | 5.4 | 8.4 | · | · |
| Grok 4.20 | 5.8 | 6.2 | 2.4 | 5.8 | 8.3 | 6.8 | — | 7.2 | 5.8 | · |
| Claude Sonnet | 7.0 | 7.0 | 1.0 | 6.7 | 9.2 | 7.5 | 7.0 | — | 6.5 | · |
| Gemini 2.5 | 8.4 | 9.1 | · | 7.5 | 9.8 | 9.7 | 9.1 | 9.8 | — | · |
| MiniMax M2.5 | 7.1 | 8.0 | 1.4 | 7.1 | 9.0 | 6.7 | · | 9.3 | 7.0 | — |

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## Methodology

- **10×10 Blind Peer Matrix:** All models answer the same question, then all models judge all responses.
- **5 Criteria:** Correctness, completeness, clarity, depth, usefulness (each scored 1–10).
- **Self-judgments excluded:** Models do not judge their own responses.
- **Weighted Score:** Composite of all 5 criteria.

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## Citation

The Multivac (2026). Blind Peer Evaluation: REASON-018. app.themultivac.com

## License

Open data. Free to use, share, and build upon. Please cite The Multivac when using this data.

Download raw JSON: https://app.themultivac.com/api/evaluations/EVAL-20260402-170708/results
Full dataset: https://app.themultivac.com/dashboard/export