{ "evaluation_id": "EVAL-20260207-133335", "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 3 (Direct)", "provider": "xAI", "score": 9.98 }, "avg_score": 9.621, "matrix_size": 90, "models_used": [ { "id": "gemini_3_flash", "name": "Gemini 3 Flash Preview", "provider": "Google" }, { "id": "claude_sonnet", "name": "Claude Sonnet 4.5", "provider": "Anthropic" }, { "id": "deepseek_v3", "name": "DeepSeek V3.2", "provider": "DeepSeek" }, { "id": "claude_opus", "name": "Claude Opus 4.5", "provider": "Anthropic" }, { "id": "gemini_3_pro", "name": "Gemini 3 Pro Preview", "provider": "Google" }, { "id": "gemini_2_5_flash", "name": "Gemini 2.5 Flash", "provider": "Google" }, { "id": "gpt_oss_120b", "name": "GPT-OSS-120B", "provider": "OpenAI" }, { "id": "olmo_think", "name": "OLMo Think", "provider": "Allen AI" }, { "id": "grok_direct", "name": "Grok 3 (Direct)", "provider": "xAI" }, { "id": "mimo_v2_flash", "name": "MiMo-V2-Flash", "provider": "Xiaomi" } ], "rankings": { "grok_direct": { "display_name": "Grok 3 (Direct)", "provider": "xAI", "average_score": 9.98, "score_count": 7, "min_score": 9.85, "max_score": 10, "rank": 1 }, "gpt_oss_120b": { "display_name": "GPT-OSS-120B", "provider": "OpenAI", "average_score": 9.96, "score_count": 7, "min_score": 9.85, "max_score": 10, "rank": 2 }, "olmo_think": { "display_name": "OLMo Think", "provider": "Allen AI", "average_score": 9.89, "score_count": 7, "min_score": 9.5, "max_score": 10, "rank": 3 }, "mimo_v2_flash": { "display_name": "MiMo-V2-Flash", "provider": "Xiaomi", "average_score": 9.89, "score_count": 7, "min_score": 9.5, "max_score": 10, "rank": 4 }, "claude_opus": { "display_name": "Claude Opus 4.5", "provider": "Anthropic", "average_score": 9.83, "score_count": 8, "min_score": 9.3, "max_score": 10, "rank": 5 }, "gemini_3_flash": { "display_name": "Gemini 3 Flash Preview", "provider": "Google", "average_score": 9.81, "score_count": 7, "min_score": 9.3, "max_score": 10, "rank": 6 }, "deepseek_v3": { "display_name": "DeepSeek V3.2", "provider": "DeepSeek", "average_score": 9.79, "score_count": 8, "min_score": 9.25, "max_score": 10, "rank": 7 }, "claude_sonnet": { "display_name": "Claude Sonnet 4.5", "provider": "Anthropic", "average_score": 9.72, "score_count": 7, "min_score": 9.25, "max_score": 10, "rank": 8 }, "gemini_2_5_flash": { "display_name": "Gemini 2.5 Flash", "provider": "Google", "average_score": 9.71, "score_count": 8, "min_score": 8.8, "max_score": 10, "rank": 9 }, "gemini_3_pro": { "display_name": "Gemini 3 Pro Preview", "provider": "Google", "average_score": 7.63, "score_count": 5, "min_score": 0.9, "max_score": 10, "rank": 10 } }, "judgments": [ { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.85, "brief_justification": "The response provides a perfectly correct, complete, and exceptionally clear explanation of the blue-eyed islanders puzzle, detailing the logical chain of events with excellent depth." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 10, "brief_justification": "The response is perfectly accurate, providing a rigorous explanation of the common knowledge principle and mathematical induction. It covers all aspects of the puzzle, including the fate of the brown-eyed people, and explains the logic step-by-step with clear examples." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 10, "brief_justification": "The response is perfectly correct, providing a complete and rigorous explanation of the blue-eyed islander puzzle. It correctly identifies the 100th night as the departure time, explains the inductive reasoning chain through base cases, and crucially distinguishes the concept of common knowledge as the key insight. The structure is exceptionally clear with logical progression, and the explanation of what happens to brown-eyed people adds completeness." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 10, "brief_justification": "The response accurately explains the inductive reasoning for 100 blue-eyed people, correctly identifies the outcome and timing, and covers all aspects of the puzzle including the role of common knowledge and the fate of brown-eyed people." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response is perfectly correct, explaining the 100-day timeline via induction from the base case. It thoroughly covers all aspects and clearly structures the logical chain. The depth is excellent, specifically identifying the concept of common knowledge as the critical element changed by the announcement." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 10, "brief_justification": "The response correctly identifies that all 100 blue-eyed people will leave on the 100th night, perfectly explaining the inductive chain of logic (common knowledge) that the visitor's announcement triggers. It covers all aspects of the question with exceptional clarity and depth." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 10, "brief_justification": "The response is factually accurate, thoroughly covers the logical chain with inductive reasoning, is exceptionally clear and well-structured, provides deep insight into the common knowledge mechanism, and is highly useful for understanding the puzzle." }, { "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 a textbook-quality explanation of the blue-eyed islander puzzle. It correctly identifies the solution (all 100 blue-eyed people leave on day 100), explains the critical role of common knowledge, and uses a rigorous mathematical induction to prove the result. The structure is exceptionally clear, distinguishing between the initial state, the announcement's impact, the inductive proof, and the specific application to the 100-person case." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 10, "brief_justification": "The response is a perfect explanation of the Blue Eyes puzzle. It correctly identifies the solution (all blue-eyed people leave on day 100), accurately explains the role of common knowledge, and correctly applies mathematical induction to derive the timeline. The explanation is comprehensive, logically rigorous, and exceptionally clear." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 10, "brief_justification": "The response is entirely correct, providing a rigorous and accurate explanation of the inductive reasoning process. It covers all aspects of the puzzle, including the role of common knowledge, the step-by-step logic for smaller cases, and the final outcome for both blue-eyed and brown-eyed people. The structure is exceptionally clear, and the analysis demonstrates deep understanding." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 10, "brief_justification": "The response provides a perfect explanation of the Blue Eyes puzzle. It correctly identifies the 100th night as the departure date, utilizes mathematical induction to explain the logic, and accurately explains the role of common knowledge in triggering the countdown." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 10, "brief_justification": "The response provides a perfect logical explanation of the Blue Eyes puzzle, correctly identifying the 100th night as the departure date and explaining the critical role of common knowledge." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 10, "brief_justification": "The response provides a perfect logical breakdown of the common knowledge problem, correctly identifying that the 100 blue-eyed people leave on the 100th night and explaining the inductive reasoning required." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response provides a perfect explanation of the classic logic puzzle, correctly identifying the outcome, the inductive reasoning, and the crucial role of common knowledge." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "The model provided an empty response, failing to address the logic puzzle or provide any information whatsoever." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 10, "brief_justification": "The response provides a perfect explanation of the Blue Eyes puzzle, correctly identifying the day of departure (Day 100) and explaining the complex concept of common knowledge versus mutual knowledge." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 10, "brief_justification": "The response provides a perfect explanation of the classic 'Blue-Eyed Islanders' logic puzzle. It correctly identifies the day of departure (100), explains the crucial role of common knowledge, provides the inductive proof, and explains why the brown-eyed people remain." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 10, "brief_justification": "The response provides a perfectly accurate and detailed explanation of the Blue Eyes puzzle. It correctly identifies the role of common knowledge, explains the inductive reasoning process clearly, and accurately concludes that the 100 blue-eyed people leave on the 100th day." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 10, "brief_justification": "The response provides a perfect explanation of the classic 'Blue Eyes' logic puzzle. It correctly identifies the role of common knowledge, uses inductive reasoning with smaller cases to build intuition, and accurately concludes that all 100 blue-eyed people leave on the 100th day." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 10, "brief_justification": "This is an exemplary response that perfectly explains the blue eyes puzzle with rigorous logical precision, clear inductive reasoning from base cases, and thorough coverage of why the announcement creates common knowledge that triggers the 100-day countdown." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 10, "brief_justification": "This is an exemplary response that perfectly explains the Blue-Eyed Islanders puzzle with rigorous logical precision, clear inductive reasoning from base cases, correct identification of the common knowledge mechanism, and thorough coverage of all aspects including what happens to brown-eyed people." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.8, "brief_justification": "This is an exemplary response that correctly solves the classic blue-eyes puzzle with precise logical reasoning, clear step-by-step explanation of the inductive process, and accurate conclusion that all 100 blue-eyed people leave on night 100. The explanation of common knowledge and recursive reasoning is thorough and well-structured." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "This is an exemplary response that correctly solves this famous logic puzzle with perfect reasoning through the inductive chain, clearly explains the common knowledge paradox that makes the puzzle non-trivial, and addresses the key philosophical question of what the announcement actually changed." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "No response was provided to evaluate. The 'Response to evaluate:' field is empty, so all criteria must be scored as 0." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 10, "brief_justification": "Exceptional response that perfectly explains the logic puzzle with clear inductive reasoning from simple cases to the full scenario, correctly identifying Day 100 as when all blue-eyed people leave and thoroughly explaining why the visitor's statement creates common knowledge that triggers the logical chain." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 10, "brief_justification": "This is an exemplary response that perfectly explains the blue-eyed islanders puzzle with rigorous logical precision, clear inductive reasoning, comprehensive coverage of all aspects including common knowledge, and excellent pedagogical structure with tables and step-by-step analysis." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 10, "brief_justification": "This response provides a flawless logical analysis of the blue eyes puzzle, correctly identifying the 100-day solution with precise inductive reasoning, proper explanation of common knowledge, and thorough coverage of why brown-eyed people never leave." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 10, "brief_justification": "This is an exemplary response that perfectly explains the blue eyes puzzle with rigorous logical reasoning, building from simple cases to the full solution, correctly identifying the role of common knowledge, and addressing all aspects including why brown-eyed people don't leave." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.5, "brief_justification": "The response is perfectly accurate, thoroughly explains the inductive logic and common knowledge mechanism, and is exceptionally clear and well-structured; it loses a point in depth for not explicitly addressing the philosophical/logical nuances of common knowledge, and in usefulness because the puzzle is theoretical." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.3, "brief_justification": "The response is factually accurate, logically sound, and clearly explains the inductive reasoning and common knowledge concepts, though it could slightly expand on why brown-eyed people remain." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.3, "brief_justification": "The response is factually perfect and clearly explains the logical induction and common knowledge, though it could slightly expand on the brown-eyed people's final deduction for completeness." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.3, "brief_justification": "The response is factually perfect and clearly explains the inductive logic and common knowledge concept, though it could slightly expand on the role of the brown-eyed people and the precise timing of departures." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 9.85, "brief_justification": "The response precisely explains the logical induction, correctly identifies the 100-day timeline for blue-eyed people, and thoroughly addresses the common misconceptions and underlying reasoning." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.7, "brief_justification": "The response is fully accurate, thoroughly explains the logical induction from base cases to the 100-person scenario, and is exceptionally clear and insightful, though its practical usefulness is slightly limited as it's a theoretical puzzle explanation." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.85, "brief_justification": "The response is perfectly accurate, thoroughly explains the logical induction and common knowledge, is exceptionally clear and well-structured, provides deep insight into the reasoning, and is highly useful for understanding the puzzle, though slightly abstract for direct practical application." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 9.85, "brief_justification": "The response is factually accurate, fully explains the logical chain including common knowledge and inductive reasoning, and clearly addresses why brown-eyed people never leave, though its practical usefulness is slightly limited as it's a theoretical puzzle." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.85, "brief_justification": "The response is perfectly accurate, thoroughly explains the logical chain with clear examples, provides deep insight into common knowledge and inductive reasoning, and is highly useful for understanding the puzzle, though slightly abstract for direct real-world application." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.85, "brief_justification": "The response provides a flawless explanation of this classic logic puzzle, correctly identifying that all 100 blue-eyed people leave on the 100th night. The inductive reasoning is perfectly structured from base case through generalization, the concept of common knowledge is accurately explained as the key catalyst, and the explanation of why brown-eyed people never leave is correct. The formatting with clear headers and step-by-step progression makes this complex reasoning highly accessible." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.65, "brief_justification": "The response provides a flawless explanation of the Blue Eyes puzzle, correctly identifying the answer (100 blue-eyed people leave on day 100) and thoroughly explaining the inductive logic from n=1 through n=100. The common knowledge concept is well-articulated, the step-by-step reasoning is crystal clear, and the inclusion of what happens to brown-eyed people adds completeness. Minor room for improvement in exploring philosophical implications or alternative framings." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.65, "brief_justification": "The response is completely correct, walking through the classic blue eyes puzzle with perfect logical precision. It builds from base cases through induction excellently, and crucially explains why the announcement matters (common knowledge) which is the subtle heart of the puzzle. The explanation of brown-eyed people's fate adds completeness. Minor room for deeper exploration of the common knowledge concept, but this is an exemplary answer." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.8, "brief_justification": "The response correctly solves this classic logic puzzle with perfect accuracy. It clearly explains the inductive reasoning from base cases (n=1, n=2) to the general case (n=100), properly identifies the role of common knowledge, and correctly concludes that all 100 blue-eyed people leave on night 100 while brown-eyed people remain. The explanation is exceptionally well-structured and accessible." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0.9, "brief_justification": "The response is completely empty, providing no answer whatsoever to this classic logic puzzle. The correct answer involves inductive reasoning where all 100 blue-eyed people leave on the 100th night, but no explanation or reasoning was provided." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.65, "brief_justification": "The response correctly solves this classic common knowledge puzzle with perfect logical reasoning. It builds up from base cases (1 and 2 blue-eyed people) to the general case of 100, clearly explains why the visitor's statement matters despite seeming redundant, and correctly identifies that all 100 blue-eyed people leave at midnight on Day 100. The explanation of common knowledge vs. individual knowledge is excellent, and the note about brown-eyed people adds completeness." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 10, "brief_justification": "" }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 9.85, "brief_justification": "The response provides a flawless explanation of the blue eyes puzzle, correctly identifying that all 100 blue-eyed people leave on day 100. It excellently explains the crucial concept of common knowledge, walks through the inductive reasoning with clear base case and inductive step, and properly addresses why brown-eyed people never leave. The structure with headers and mathematical notation enhances clarity significantly." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 10, "brief_justification": "The response provides a flawless explanation of this classic common knowledge puzzle. It correctly identifies that all 100 blue-eyed people leave on Day 100, explains the crucial role of common knowledge vs. shared knowledge, builds intuition through smaller cases (1, 2, 3 blue-eyed people), generalizes correctly to 100, and addresses why brown-eyed people don't leave. The logical chain is precise, well-structured, and thoroughly justified." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 10, "brief_justification": "The response provides the standard correct solution to this famous logic puzzle. It effectively explains the inductive reasoning required and correctly identifies the importance of 'common knowledge' introduced by the visitor." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 10, "brief_justification": "The response perfectly solves the classic logic puzzle, correctly applying inductive reasoning to determine that all 100 blue-eyed people leave on the 100th night. It clearly explains the base cases and the logical progression." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response provides the correct solution, clearly outlines the inductive logic, and crucially explains the concept of common knowledge to address why the announcement was necessary." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 10, "brief_justification": "The response provides the exact correct solution to the classic logic puzzle. It effectively explains the inductive reasoning required, the importance of common knowledge, and correctly identifies that the 100 blue-eyed people leave on the 100th night." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 10, "brief_justification": "The response provides the mathematically correct solution to the riddle, clearly explaining the inductive reasoning and the crucial concept of common knowledge. It breaks down the logic step-by-step from base cases to the final conclusion without error." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 10, "brief_justification": "The response provides a perfectly accurate and detailed explanation of the classic logic puzzle, using mathematical induction to build the logical chain of events clearly and comprehensively." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 10, "brief_justification": "The response correctly identifies the solution, provides a clear and detailed logical chain using induction, and explains the crucial role of common knowledge." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 10, "brief_justification": "The response provides a perfectly correct, complete, clear, and in-depth explanation of the classic blue-eyed islander puzzle, precisely detailing the logical chain of events." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.85, "brief_justification": "The response perfectly explains the blue eyes puzzle, including the critical role of common knowledge and the inductive reasoning." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 9.1, "brief_justification": "The response correctly identifies the logical chain of events and the timing of departures, explaining the reasoning clearly." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 10, "brief_justification": "The response provides a perfectly correct, complete, clear, and in-depth explanation of the classic blue-eyed islander puzzle, including the crucial role of common knowledge and the inductive reasoning." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 10, "brief_justification": "The response provides a perfectly accurate, complete, and clear explanation of the classic blue-eyed islander puzzle, detailing the logical chain of events with excellent depth." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 10, "brief_justification": "The response provides a perfectly correct, complete, clear, and in-depth explanation of the classic blue-eyed islander puzzle, including the logical chain of events and the role of common knowledge and inductive reasoning." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.25, "brief_justification": "The answer correctly states that all 100 blue‑eyed people leave on night 100, explains the inductive reasoning and the role of common knowledge, and notes why brown‑eyed people stay, with clear structure and sufficient depth." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.25, "brief_justification": "The answer correctly applies the common‑knowledge induction to show all 100 blue‑eyed people leave on night 100 and brown‑eyed stay, and it explains the reasoning clearly and thoroughly." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.8, "brief_justification": "The response accurately describes the classic solution (all 100 blue‑eyed leave on day 100) and provides a clear inductive argument with base cases, covering the necessary reasoning and implications for brown‑eyed people." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 10, "brief_justification": "The response accurately applies mathematical induction and common knowledge principles to explain the 100th night departure of blue-eyed individuals and correctly addresses the inaction of brown-eyed individuals. It provides a precise and comprehensive logical breakdown." }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response accurately explains the inductive reasoning and the role of common knowledge. It thoroughly addresses the logical chain and outcome." }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.85, "brief_justification": "The response accurately and thoroughly explains the logical sequence of events using mathematical induction, with clear examples and a detailed breakdown. It provides deep insight into the problem, though its practical usefulness is slightly limited by the abstract nature of the puzzle." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.85, "brief_justification": "The response accurately and thoroughly explains the logical sequence of the Blue-Eyed Islanders problem with clear inductive reasoning. It provides deep insight into common knowledge and the iterative process, though practical usefulness is slightly limited by the puzzle's theoretical nature." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.85, "brief_justification": "The response accurately and thoroughly explains the logical puzzle with a clear inductive reasoning process, deep analysis of common knowledge, and a precise timeline. It is highly useful for understanding the problem, though slightly less actionable due to its theoretical nature." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.5, "brief_justification": "The response accurately and thoroughly explains the logical chain of events in the blue-eyed islanders puzzle, with clear structure and detailed reasoning. It slightly lacks in broader practical application or deeper exploration beyond the standard solution." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.5, "brief_justification": "The response accurately and thoroughly explains the logical chain of events in the Blue Eyes Puzzle, with clear examples and a deep exploration of common knowledge. It slightly lacks in practical usefulness beyond the puzzle context." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 8.3, "brief_justification": "The response accurately captures the logical deduction process triggered by the visitor's statement, though it could elaborate slightly more on the timeline of events. The explanation is clear and insightful but lacks minor details for full completeness." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.5, "brief_justification": "The response accurately and thoroughly explains the logical chain of events in the blue eyes puzzle, with clear inductive reasoning. It is slightly less useful for practical application but excels in depth and clarity." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.85, "brief_justification": "The response is logically sound, thoroughly detailed, and clearly structured with a precise inductive explanation. It provides deep insight into the puzzle, though practical usefulness is slightly limited by the abstract nature of the problem." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 9.5, "brief_justification": "The response accurately and thoroughly explains the logical chain of events with precise inductive reasoning. It is clear and insightful, though slightly dense for casual readers." } ], "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)" } }