One Percent Club Episode 07 Feb 2026

Overview

This post compares how three major AI models (OpenAI, Anthropic, and Gemini) approached a dice-sum question from The 1% Club episode aired on February 7, 2026.

True Answer: 16

Problem: How many different totals are possible when rolling three standard six‑sided dice?

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Model Responses Summary

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Detailed Analysis by Model

1. OpenAI (gpt-5-nano)

Final Answer: Correct ✅

Reasoning:

• The three dice sums range from 3 (1+1+1) to 18 (6+6+6)
• By giving explicit constructions for sums from 3 to 18, every integer in this interval is achievable
• The number of distinct totals is $18 - 3 + 1 = 16$
• This matches the generating-function view where the sumset is continuous over that interval

Key Factors:

1. Possible sums for three standard dice: 3 to 18
2. All sums within this range are achievable
3. Number of distinct totals equals $18 - 3 + 1 = 16$
4. Reasoning can be viewed via constructions or generating functions

Timestamp: 08/02/2026, 15:30:53

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2. Anthropic (claude-sonnet-4-5)

Final Answer: Correct ✅

Reasoning:

• Minimum total: 3 (1+1+1)
• Maximum total: 18 (6+6+6)
• All integers from 3 to 18 are achievable (verified with example combinations)
• Therefore, the total number of distinct sums is $18 - 3 + 1 = 16$

Key Factors:

1. Minimum possible total is 3 (three ones)
2. Maximum possible total is 18 (three sixes)
3. All integers from 3 to 18 are achievable with various combinations
4. Total count: $18 - 3 + 1 = 16$ different totals

Timestamp: 08/02/2026, 15:30:36

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3. Gemini (gemini-3-flash-preview)

Final Answer: Correct ✅

Reasoning:

• The sum of three standard dice ranges from 3 to 18
• Because die values are consecutive integers, every sum in between is possible
• The number of unique totals is $18 - 3 + 1 = 16$

Key Factors:

1. Minimum sum: 1 + 1 + 1 = 3
2. Maximum sum: 6 + 6 + 6 = 18
3. Continuity: All integer values between 3 and 18 are achievable
4. Range calculation: $18 - 3 + 1 = 16$ unique totals

Timestamp: 08/02/2026, 15:30:33

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Conclusion

All three models answered correctly. The key observation is that the minimum sum is 3 and the maximum sum is 18, and every integer in between is achievable. Therefore, the number of distinct totals is $18 - 3 + 1 = 16$.