{
  "evaluation_id": "EVAL-20260402-154152",
  "question_id": "REASON-004",
  "question_text": "On an island, there are 100 people with blue eyes and 100 people with brown eyes. Everyone can see everyone else's eye color but not their own. There are no mirrors or ways to discover your own eye color.\n\nThere's a rule: if you ever figure out your own eye color, you must leave the island at midnight that day.\n\nOne day, a visitor announces to everyone: \"At least one person on this island has blue eyes.\"\n\nWhat happens? When? Why?\n\nBe precise about the logical chain of events.",
  "category": "reasoning",
  "timestamp": "2026-02-04T00:00:00.000Z",
  "display_date": "Feb 04, 2026",
  "winner": {
    "name": "Grok 4.20",
    "provider": "openrouter",
    "score": 9.66
  },
  "avg_score": 9.048889,
  "matrix_size": 81,
  "models_used": [
    {
      "id": "gemini_25_flash",
      "name": "Gemini 2.5 Flash",
      "provider": "openrouter"
    },
    {
      "id": "deepseek_v4",
      "name": "DeepSeek V4",
      "provider": "openrouter"
    },
    {
      "id": "claude_opus_46",
      "name": "Claude Opus 4.6",
      "provider": "openrouter"
    },
    {
      "id": "gpt_5_4",
      "name": "GPT-5.4",
      "provider": "openrouter"
    },
    {
      "id": "grok_420",
      "name": "Grok 4.20",
      "provider": "openrouter"
    },
    {
      "id": "claude_sonnet_46",
      "name": "Claude Sonnet 4.6",
      "provider": "openrouter"
    },
    {
      "id": "mimo_v2_flash",
      "name": "MiMo-V2-Flash",
      "provider": "Xiaomi"
    },
    {
      "id": "gpt_oss_120b",
      "name": "GPT-OSS-120B",
      "provider": "OpenAI"
    },
    {
      "id": "gemini_31_pro",
      "name": "Gemini 3.1 Pro",
      "provider": "openrouter"
    }
  ],
  "rankings": {
    "grok_420": {
      "display_name": "Grok 4.20",
      "provider": "openrouter",
      "average_score": 9.66,
      "score_count": 9,
      "min_score": 9.05,
      "max_score": 10,
      "rank": 1
    },
    "claude_opus_46": {
      "display_name": "Claude Opus 4.6",
      "provider": "openrouter",
      "average_score": 9.6,
      "score_count": 9,
      "min_score": 8.65,
      "max_score": 10,
      "rank": 2
    },
    "gpt_oss_120b": {
      "display_name": "GPT-OSS-120B",
      "provider": "OpenAI",
      "average_score": 9.6,
      "score_count": 9,
      "min_score": 8.85,
      "max_score": 10,
      "rank": 3
    },
    "gpt_5_4": {
      "display_name": "GPT-5.4",
      "provider": "openrouter",
      "average_score": 9.55,
      "score_count": 9,
      "min_score": 8.85,
      "max_score": 10,
      "rank": 4
    },
    "claude_sonnet_46": {
      "display_name": "Claude Sonnet 4.6",
      "provider": "openrouter",
      "average_score": 9.48,
      "score_count": 9,
      "min_score": 8.45,
      "max_score": 10,
      "rank": 5
    },
    "mimo_v2_flash": {
      "display_name": "MiMo-V2-Flash",
      "provider": "Xiaomi",
      "average_score": 9.45,
      "score_count": 9,
      "min_score": 8.65,
      "max_score": 10,
      "rank": 6
    },
    "deepseek_v4": {
      "display_name": "DeepSeek V4",
      "provider": "openrouter",
      "average_score": 9.43,
      "score_count": 9,
      "min_score": 8.65,
      "max_score": 10,
      "rank": 7
    },
    "gemini_31_pro": {
      "display_name": "Gemini 3.1 Pro",
      "provider": "openrouter",
      "average_score": 7.57,
      "score_count": 9,
      "min_score": 5.5,
      "max_score": 9.65,
      "rank": 8
    },
    "gemini_25_flash": {
      "display_name": "Gemini 2.5 Flash",
      "provider": "openrouter",
      "average_score": 7.1,
      "score_count": 9,
      "min_score": 4.8,
      "max_score": 9.65,
      "rank": 9
    }
  },
  "judgments": [
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 4.8,
      "brief_justification": "Reasoning is on the right track but the answer is incomplete and somewhat confusing, missing the final conclusion for 100 blue-eyed people."
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 10,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 10,
      "brief_justification": "The response perfectly answers the prompt, providing a flawless logical induction, an excellent explanation of the 'common knowledge' paradox, and clear formatting."
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 10,
      "brief_justification": "The response perfectly solves the classic logic puzzle, clearly explaining the inductive reasoning and the critical concept of common knowledge."
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 10,
      "brief_justification": "The response provides a flawless, perfectly structured, and deeply insightful explanation of the classic Blue Eyes logic puzzle, accurately detailing the inductive reasoning and the role of common knowledge."
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 10,
      "brief_justification": "The response perfectly solves the classic logic puzzle, clearly explaining the inductive reasoning, the timeline, and the crucial concept of common knowledge."
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 10,
      "brief_justification": "The response perfectly solves the logic puzzle, clearly explaining common knowledge and using mathematical induction to prove the timeline. The breakdown is exceptionally clear, comprehensive, and logically flawless."
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.4,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_31_pro",
      "judge_name": "Gemini 3.1 Pro",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 6,
      "brief_justification": "The response correctly identifies the logic and explains common knowledge well, but it cuts off mid-sentence and fails to provide the final answer to what happens and when."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 8.45,
      "brief_justification": "Accurate and detailed logical breakdown, but slightly incomplete as it cuts off mid-sentence."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 9.65,
      "brief_justification": "Precise, complete, and deeply insightful explanation of the logical chain."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 9.65,
      "brief_justification": "The response is factually accurate, logically valid, and thoroughly covers the topic with insightful analysis. It is clear and well-structured, providing practical value and actionability."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 9.5,
      "brief_justification": "Highly accurate, thorough, and insightful with clear logical progression."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 9.65,
      "brief_justification": "Precise, thorough, and insightful explanation of the logical chain and the role of common knowledge."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 9.5,
      "brief_justification": "Highly accurate, thorough, and insightful with clear logical progression."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.65,
      "brief_justification": "Highly accurate, thorough, and insightful with clear logical progression."
    },
    {
      "judge_key": "deepseek_v4",
      "judge_name": "DeepSeek V4",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 9.65,
      "brief_justification": "Highly accurate, thorough, and insightful with clear logical progression."
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 7.25,
      "brief_justification": "The answer correctly identifies that all 100 blue-eyed people leave on day 100 and begins the inductive proof correctly with base cases 1 and 2. However, the response is clearly cut off mid-sentence during Scenario 3, leaving the inductive chain incomplete. The crucial step of explaining how the induction generalizes from n to 100 is missing. The mention of brown-eyed people leaving on day 101 is a nice touch but could use more careful qualification. The discussion of what constitutes 'common kn"
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 9.45,
      "brief_justification": "The response is fully correct, walking through the base cases, the inductive generalization, and the application to N=100. It correctly identifies the role of common knowledge and explains why the announcement matters despite seeming trivial. The explanation of brown-eyed people is adequate. The clarity is excellent with well-structured sections and progressive complexity. Minor room for improvement: could have been slightly more rigorous about why common knowledge was absent before the announce"
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 9.45,
      "brief_justification": "The response is fully correct, presenting the classic blue eyes puzzle solution with precise logical reasoning. The inductive argument is laid out clearly from base cases through the general case to the specific n=100 application. The explanation of common knowledge is accurate. The treatment of brown-eyed people is correct. Minor deduction on completeness: could have elaborated slightly more on why common knowledge specifically matters (i.e., the nested knowledge structure before vs after the a"
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 9.65,
      "brief_justification": "The response is fully correct, covering the base case, inductive step, application to n=100, why brown-eyed people stay, and the critical role of common knowledge. The explanation is exceptionally clear and well-structured with precise logical reasoning. The only minor note is that the depth on why common knowledge matters (vs. mutual knowledge) could be slightly more elaborated, but the response does address it adequately. Extremely well done overall."
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 9.65,
      "brief_justification": "The response is factually correct, clearly structured, and covers all essential aspects of the blue eyes puzzle. The inductive chain is precisely laid out from base case through the general pattern. The explanation of common knowledge vs. mutual knowledge is accurate and insightful. The only minor area for deeper exploration could be a more formal treatment of why the nested knowledge chain breaks at exactly the right depth before the announcement, but the explanation given is already excellent "
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 10,
      "brief_justification": "This is an essentially perfect response to the Blue Eyes puzzle. The answer is correct (all 100 blue-eyed people leave on night 100). The inductive proof is laid out with crystal clarity, building from N=1 to N=2 to N=3 to the general case. The explanation of common knowledge vs. private knowledge is precise and accurate. The treatment of the brown-eyed people is thoughtful and correct—they learn they don't have blue eyes but cannot determine their specific color. The writing is exceptionally we"
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.6,
      "brief_justification": "The response is exceptionally thorough, clearly structured, and logically precise. The inductive proof is correctly presented with base case and inductive step. The explanation of common knowledge as the key new information is accurate and well-articulated. The treatment of brown-eyed people's reasoning is solid, though the specific argument about why brown-eyed people can't deduce their color after the blues leave could be slightly more rigorous (the reasoning about 'compatible with both hypoth"
    },
    {
      "judge_key": "claude_opus_46",
      "judge_name": "Claude Opus 4.6",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 7.45,
      "brief_justification": "The response correctly identifies the core mechanism (common knowledge and inductive reasoning), properly builds up from base cases, and correctly states the answer (all 100 blue-eyed people leave on Day 99). However, the response appears to be cut off at the end of the inductive step, leaving the final conclusion incomplete. The middle section where it tries to work through the n=100 case directly becomes somewhat muddled before it wisely switches to the cleaner inductive formulation. The expla"
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 5.5,
      "brief_justification": "The core conclusion is correct that the 100 blue-eyed people leave on day 100, and the induction setup is mostly right. However, the response is truncated before completing the logical chain, so it is incomplete. It also adds a conditional claim about brown-eyed people leaving on day 101 that depends on extra assumptions not established in the prompt, which reduces correctness."
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 9.8,
      "brief_justification": "Accurate classic solution with precise inductive chain, clear explanation of common knowledge, correct timing (all 100 blue-eyed people leave on night 100), and appropriate note about brown-eyed people."
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 9.8,
      "brief_justification": "Accurate and complete explanation of the induction, correctly identifies common knowledge as the key subtlety, and clearly explains both why the 100 blue-eyed people leave on Night 100 and why the brown-eyed people do not."
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 9.8,
      "brief_justification": "Accurate and fully explains the induction and common-knowledge mechanism. Clear structure, precise timing, and correct conclusion that all 100 blue-eyed people leave on night 100 while brown-eyed people do not."
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 9.45,
      "brief_justification": "Accurate and precise: correctly concludes all 100 blue-eyed people leave on night 100 and brown-eyed people never leave, with a clear induction and strong explanation of common knowledge. Slightly not maximal on completeness/depth only because it could elaborate even more on why private announcements fail or formalize the induction further."
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 8.8,
      "brief_justification": "Accurate and well-structured induction argument leading to all 100 blue-eyed people leaving on night 100. Good explanation of common knowledge and the base cases. Minor nit: the statement that blue-eyed existence was only 'private knowledge' before the announcement is a bit imprecise, and the brown-eyed discussion could note they do in fact deduce they are not blue but not uniquely brown unless only two colors are assumed."
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 10,
      "brief_justification": "Fully correct classic solution: identifies common knowledge, gives precise induction to day 100, and correctly explains why brown-eyed people do not leave. Clear, thorough, and logically rigorous."
    },
    {
      "judge_key": "gpt_5_4",
      "judge_name": "GPT-5.4",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 5.85,
      "brief_justification": "Shows the key idea of common knowledge and mostly correct induction setup, but the response is incomplete/truncated and never explicitly states the final outcome that all 100 blue-eyed people leave on the 100th midnight while brown-eyed people stay. Some intermediate reasoning is muddled."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 7.9,
      "brief_justification": "The response accurately explains the inductive logic for blue-eyed people leaving on day 100 but is incomplete as it cuts off mid-sentence in the 3-person case and only partially addresses brown-eyed people."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 8.65,
      "brief_justification": "The response accurately explains the blue eyes puzzle using induction from base cases, correctly concludes that the 100 blue-eyed people leave on the 100th night, and clearly details why the announcement creates common knowledge. Minor deduction on depth as brown eyes section is slightly imprecise but overall solid."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 8.85,
      "brief_justification": "The response accurately and thoroughly explains the inductive logic, common knowledge subtlety, and why brown-eyed people stay, with clear structure and precise timing."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 8.85,
      "brief_justification": "The response accurately and thoroughly explains the blue eyes puzzle with clear inductive reasoning from base cases to n=100, correctly identifies common knowledge as the key, and properly notes brown-eyed people stay. Minor deduction for slight vagueness on why brown-eyed don't leave after blues depart."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 8.65,
      "brief_justification": "The response accurately and clearly explains the blue eyes puzzle using induction, common knowledge, and the base case progression. It correctly identifies that the 100 blue-eyed leave on night 100 while brown-eyed stay. Minor room for more formal epistemic logic depth but highly complete and useful."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 8.85,
      "brief_justification": "The response accurately explains the blue eyes puzzle using induction and common knowledge. It covers the logical chain thoroughly and clearly for N=1 to N=100, including why brown-eyed people stay. Minor deduction on brown eyes is slightly imprecise but overall excellent."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 8.85,
      "brief_justification": "The response accurately and thoroughly explains the blue eyes puzzle with precise inductive logic, common knowledge concept, base case, and why brown-eyed people stay. Minor deduction flaw in brown-eyed section but overall excellent."
    },
    {
      "judge_key": "grok_420",
      "judge_name": "Grok 4.20",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 7.5,
      "brief_justification": "The response accurately explains the common knowledge and inductive logic of the blue eyes puzzle with clear small-case examples and the inductive step. It is mostly complete but cuts off abruptly mid-sentence in the inductive step and has some minor inaccuracies/confusing phrasing in the early non-inductive sections regarding brown-eyed perspectives and day numbering."
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 8.05,
      "brief_justification": "The response is logically correct and well-structured, with a clear inductive chain building from simple cases. The key insight about common knowledge is mentioned. However, the response appears to be cut off mid-sentence (Scenario 3 is incomplete), which significantly hurts completeness. The note about brown-eyed people leaving on Day 101 is a valid conditional observation. The explanation of why the announcement matters (common knowledge) could be more explicitly developed."
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 8.8,
      "brief_justification": "The response correctly identifies the solution (all 100 blue-eyed people leave on night 100), provides clear inductive reasoning from base cases, and explains why the announcement matters for establishing common knowledge. The treatment of brown-eyed people is slightly superficial but acceptable. The logical chain is precise and well-structured."
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 10,
      "brief_justification": "This is an exceptional response. The logical chain is precisely and correctly explained through mathematical induction. The crucial subtlety about common knowledge vs. shared knowledge is handled with sophistication and accuracy. The explanation of why brown-eyed people don't leave is correct and well-reasoned. The structure is clear and progressive, building from base cases to the general case. The response demonstrates deep understanding of the puzzle's philosophical and logical underpinnings."
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 9.8,
      "brief_justification": "The response is fully correct, covering the classic blue-eyes puzzle with precise logical induction. It builds from base cases through the general inductive argument clearly and rigorously. The explanation of why common knowledge matters (vs. mere knowledge) is accurate and insightful. The treatment of brown-eyed people is honest about the puzzle's standard scope. Formatting is excellent and the reasoning chain is easy to follow."
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 9.65,
      "brief_justification": "The response is logically rigorous and precisely correct. It correctly identifies all 100 blue-eyed people leaving on night 100, explains the base case and inductive step clearly, addresses why brown-eyed people never leave, and crucially explains the role of common knowledge vs. mere mutual knowledge. The explanation is well-structured, complete, and highly accessible without sacrificing precision."
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 9.4,
      "brief_justification": "Excellent response that correctly solves the classic common knowledge puzzle. The inductive proof is well-structured and precise, walking through N=1, N=2, N=3 cases before generalizing. The explanation of why the visitor's announcement matters (transforming private to common knowledge) is accurate and insightful. Minor note: the claim about brown-eyed people not being able to deduce their color is slightly oversimplified—after the blue-eyed people leave, brown-eyed people could potentially dedu"
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.6,
      "brief_justification": "Excellent response that correctly identifies all 100 blue-eyed people leaving on night 100, with a rigorous inductive proof, clear explanation of common knowledge vs. shared knowledge, and accurate treatment of why brown-eyed people never leave. The timeline table adds clarity. Minor note: the claim that brown-eyed people 'cannot eliminate the possibility that they are blue' after night 100 is slightly hand-wavy but directionally correct given the puzzle's standard framing."
    },
    {
      "judge_key": "claude_sonnet_46",
      "judge_name": "Claude Sonnet 4.6",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 8,
      "brief_justification": "The response correctly identifies the common knowledge mechanism and walks through the inductive logic clearly. The base cases and inductive steps are well-explained with concrete examples. The response is cut off at the end before completing the inductive step conclusion, which slightly reduces completeness. It also doesn't explicitly state the final answer (all 100 blue-eyed people leave on Day 99/Night 100) clearly upfront, and doesn't address what happens to the brown-eyed people (they never"
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 8.8,
      "brief_justification": "The response correctly identifies the standard solution (100 days) and accurately applies the inductive logic for the first two base cases. It correctly notes the ambiguity regarding the brown-eyed people, which adds nuance. The response is cut off mid-sentence in the third scenario, which prevents it from being fully complete, but the established pattern is clear."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 10,
      "brief_justification": "The response is factually accurate, thoroughly covers the logical chain, is exceptionally clear and well-structured, provides deep inductive reasoning, and is highly useful for understanding the puzzle."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 10,
      "brief_justification": "The response is factually accurate, thoroughly covers the logical chain, is exceptionally clear and well-structured, provides deep insight into common knowledge, and offers high practical value for understanding inductive reasoning."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 10,
      "brief_justification": "Accurate, thorough, and well-structured explanation of the common knowledge induction, covering all aspects of the puzzle."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 10,
      "brief_justification": "The response is factually accurate, thoroughly covers the logical chain with induction, is exceptionally clear and structured, provides deep insight into common knowledge, and offers high practical value for understanding the puzzle."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 10,
      "brief_justification": "The response is factually accurate, thoroughly covers the logical chain, is exceptionally clear and well-structured, provides deep insight into common knowledge, and offers high practical value for understanding inductive reasoning."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 10,
      "brief_justification": "The response is entirely accurate, thoroughly covers all aspects of the puzzle, is exceptionally clear and well-structured, provides deep inductive reasoning, and offers high practical value for understanding common knowledge and logic puzzles."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 8.6,
      "brief_justification": "The response correctly identifies the core mechanism (common knowledge) and the inductive process. It accurately describes the outcome and the timeline. It loses a point on clarity because the explanation of the inductive step becomes slightly convoluted and repetitive in the middle, but the conclusion is clear and correct."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 5.8,
      "brief_justification": "Correct core answer and clear induction steps for 1 and 2 cases, but the response is cut off before completing the 3+ case and full explanation for 100, reducing completeness and depth."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 9.05,
      "brief_justification": "Accurate solution with clear inductive reasoning, covers all key points, well‑structured, offers solid insight and practical answer."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 8.65,
      "brief_justification": "Accurate solution with full induction, explains common knowledge, clear structure, and sufficient depth for the puzzle."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 8.9,
      "brief_justification": "Accurate solution with clear induction and explanation of common knowledge; covers all relevant points, well organized, and offers useful insight."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 9.05,
      "brief_justification": "Accurately describes the classic solution with clear induction and common knowledge reasoning, covering all key points; minor omissions in extra nuance keep completeness just shy of perfect."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 8.45,
      "brief_justification": "Accurate solution with clear induction and explanation of common knowledge; covers why blues leave on night 100 and browns stay, though could mention exact midnight timing more explicitly."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 8.65,
      "brief_justification": "Accurately describes the classic solution, covers all key steps and edge cases, presented clearly with induction, and offers useful insight into why brown-eyed people stay."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 9.65,
      "brief_justification": "The response provides a perfectly correct and detailed explanation using mathematical induction, which is the standard solution to this classic logic puzzle. The breakdown into scenarios makes the logic very clear and easy to follow. It correctly identifies the 100th day as the departure day for blue-eyed people. The only minor omission is not fully extending the induction for the brown-eyed people's departure, but it correctly states the primary outcome."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 9.85,
      "brief_justification": "The response provides a perfectly accurate, complete, and exceptionally clear explanation of the blue-eyed islander puzzle. It uses a step-by-step inductive reasoning approach, starting with simpler cases and building up to the full solution. The explanation of 'common knowledge' is crucial and well-articulated. The structure is logical and easy to follow, demonstrating a deep understanding of the problem."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 9.85,
      "brief_justification": "The response is perfectly accurate, complete, and exceptionally clear. It breaks down the logic step-by-step, including the crucial concept of common knowledge, which is often missed in explanations of this puzzle. The structure is excellent, making it very easy to follow."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 9.85,
      "brief_justification": "The response provides a perfect explanation of the blue-eyed islander puzzle, including the crucial role of common knowledge and a clear inductive proof. It addresses all aspects of the question comprehensively and precisely."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 9.85,
      "brief_justification": "The response is perfectly accurate, complete, and exceptionally clear. It provides a deep, step-by-step logical chain of events using inductive reasoning, which is the correct approach to this classic puzzle. The explanation of common knowledge is also excellent."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 9.85,
      "brief_justification": "The response provides a perfect explanation of the Blue Eyes Problem, covering all aspects with exceptional clarity and depth. The logical chain of events is precisely detailed, and the concept of common knowledge is well-explained."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 9.85,
      "brief_justification": "The response is a perfect explanation of the classic 'Common Knowledge' puzzle. It's highly accurate, complete, and exceptionally clear, using a step-by-step inductive approach. The depth of explanation, including the role of common knowledge and the scenarios for N=1, 2, and 3, is outstanding. The usefulness is high for anyone trying to understand this complex logical problem."
    },
    {
      "judge_key": "gemini_25_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.85,
      "brief_justification": "The response is a perfect explanation of the blue-eyed islander puzzle. It correctly identifies the role of common knowledge and uses inductive reasoning to explain the outcome. The timeline and summary are excellent additions."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "gemini_31_pro",
      "respondent_name": "Gemini 3.1 Pro",
      "weighted_score": 6.7,
      "brief_justification": "The logical explanation is correct and clear for the cases shown, demonstrating proper inductive reasoning. However, the response is abruptly cut off mid-explanation (ending at 'Alice sees'), leaving the full chain incomplete. It doesn't fully develop the common knowledge concept or complete the induction to the 100-day case."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "deepseek_v4",
      "respondent_name": "DeepSeek V4",
      "weighted_score": 9.25,
      "brief_justification": "Thorough and accurate solution with clear inductive reasoning from base cases to generalization. Explains common knowledge concept well and covers what happens to brown-eyed people. Well-structured with good depth."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "claude_opus_46",
      "respondent_name": "Claude Opus 4.6",
      "weighted_score": 9.6,
      "brief_justification": "Factually correct solution with thorough inductive proof from base case to n=100. Explains the crucial common knowledge aspect clearly. Well-structured with precise logical chain. Brown-eyed outcome correctly explained. Highly useful and actionable."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "gpt_5_4",
      "respondent_name": "GPT-5.4",
      "weighted_score": 9.45,
      "brief_justification": "Correct solution to the classic puzzle with thorough explanation of common knowledge and inductive reasoning. Well-structured progression from simple cases to the 100-person scenario. Clear logical chain showing why announcement triggers the cascade. Minor deduction for slightly verbose conclusion about brown-eyed people."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "grok_420",
      "respondent_name": "Grok 4.20",
      "weighted_score": 9.4,
      "brief_justification": "Logically flawless solution using proper induction. Explains common knowledge concept, provides base case through general case, and correctly identifies that 100 blue-eyed people leave on night 100 while brown-eyed never leave. Well-structured with clear reasoning chain."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "claude_sonnet_46",
      "respondent_name": "Claude Sonnet 4.6",
      "weighted_score": 9.6,
      "brief_justification": "Excellent response with correct answer, clear inductive logical chain, good explanation of common knowledge concept, and well-structured presentation. Covers all key aspects including why the announcement matters and why brown-eyed people don't leave."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 10,
      "brief_justification": "Excellent response with mathematically rigorous induction proof, clear step-by-step scenarios from N=1 to N=100, proper explanation of common knowledge concept, and addresses both blue and brown-eyed populations. Logical chain is precise and complete."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.45,
      "brief_justification": "Accurate and complete solution with thorough inductive reasoning, clear explanation of common knowledge, and detailed timeline. Well-structured with excellent logical chain."
    },
    {
      "judge_key": "minimax_m25",
      "judge_name": "MiniMax M2.5",
      "respondent_key": "gemini_25_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 6.05,
      "brief_justification": "Correctly explains the common knowledge principle and works through n=1 and n=2 cases clearly. However, the response is severely incomplete - it cuts off mid-explanation and never actually states the final answer (that all 100 blue-eyed people leave on Day 100). The inductive step is started but not finished."
    }
  ],
  "meta": {
    "source": "The Multivac (app.themultivac.com)",
    "methodology": "10x10 blind peer matrix evaluation",
    "criteria": "correctness, completeness, clarity, depth, usefulness",
    "self_judgments": "excluded from rankings",
    "license": "Open data — cite as: The Multivac (2026)"
  }
}