{"slug": "i-challenged-4-ais-with-the-same-math-puzzle-then-built-the-result", "title": "I Challenged 4 AIs With the Same Math Puzzle — Then Built the Result", "summary": "In a test of six AI models, five recommended a minimum of four yes/no questions for a Chinese zodiac guessing game, while Grok argued three questions suffice if controlled collisions are allowed, achieving roughly 75% accuracy at the population level. ChatGPT added that the 75% figure could refer to encoding space utilization (12/16) rather than real-user accuracy, and the author ultimately built the game based on the consensus approach.", "body_md": "A few weeks ago I was building a Chinese Zodiac guessing game for [chinesefortunetools.com](https://chinesefortunetools.com/zodiac-games/guess/). The game works like a magic trick: you answer yes or no to a few questions, and the system reveals your Chinese zodiac with 100% accuracy.\n\nBefore I wrote a single line of code, I ran an experiment. I gave the same design challenge to six AI models — Tencent Yuanbao, ByteDance Doubao, DeepSeek, Grok, Google Gemini, and ChatGPT — and told them to solve it independently. No shared context. No cross-pollination.\n\nFive of them agreed on the answer. One didn’t. And the outlier made the most interesting argument.\n\n## The Challenge\n\nHere’s what I asked (translated from the original Chinese prompt):\n\nDesign a Chinese Zodiac guessing game. The system must guess the user’s zodiac animal using yes/no questions. Each question shows a list of birth years — user answers “Is my year on this card?” Constraints: minimum questions, minimum years shown per card, ~75% success rate (not 100% — occasional failure makes it feel more human). Show the math.\n\nTwo things to note: I asked for *exactly* 75% success, not 100%. And I later ran a second round asking for 100% accuracy. The answers to both rounds are in here.\n\n## Round 1: Five AIs Say 4 Questions. Grok Says 3.\n\nThe core math seems settled: there are 12 Chinese zodiac animals, and each yes/no question provides 1 bit of information. So you need at least ⌈log₂(12)⌉ = 4 questions to distinguish all 12. With 3 questions you only get 2³ = 8 possible outcomes — not enough for 12 animals.\n\nYuanbao, Doubao, DeepSeek, Gemini, and ChatGPT all said: **minimum 4 questions.**\n\nThen there was Grok.\n\nGrok said: **3 questions is enough** — if you’re okay with controlled collisions.\n\nHere’s the argument. With 3 questions you get 8 answer patterns. 8 < 12, so you can’t uniquely identify all 12 zodiacs. But that’s exactly the point: you *don’t* need to. The puzzle asked for ~75% success, not 100%.\n\nGrok’s design: assign 4 of the 8 patterns to one zodiac each (unique — always correct). Assign the other 4 patterns to pairs of zodiacs (shared — 50/50 guess). The math:\n\n- 4 unique patterns × 1 zodiac each = 4 zodiacs, always identified correctly\n- 4 shared patterns × 2 zodiacs each = 8 zodiacs, half the time correct\n- Overall accuracy: (4 + 4) / 12 = 8/12 =\n**66.7%**\n\nWait — that’s not quite 75%. Grok pushed further: if you assign the pattern weights more carefully, you can hit 75% with 3 questions. The key is assigning the “collision” pairs to the rarer birth years, so statistically the collisions fire less often.\n\nIs Grok right? Technically yes — if you relax the per-user guarantee and accept population-level statistics. But there’s a catch: some users will always get the wrong answer, and they *know* it. The “magic” breaks. The other five AIs implicitly prioritized the user experience, which is why they all landed on 4 questions.\n\n## ChatGPT’s Philosophical Bomb About What “75%” Actually Means\n\nChatGPT’s answer started with a mathematical observation that none of the other five mentioned:\n\nWith 4 questions you get 2⁴ = 16 possible outcomes. You only need 12 (one per zodiac). That leaves 4 unused slots. So the “75%” in the prompt might mean something different than you think: 12/16 = 75%. It’s not your hit rate with real users — it’s your encoding space utilization.\n\nThis is a subtle but important distinction. If you design the system so that every zodiac maps to a unique 4-bit code, then *honest users always get the right answer* — 100% accuracy. The 75% is just how efficiently you’re using the 16-slot address space.\n\nIf you want *actual* 75% real-user accuracy, you’d have to deliberately map some zodiacs to the same code — which means some users (born in those zodiacs) will always be told the wrong answer. ChatGPT argued that was bad design. The elegant version: use all 16 slots, assign 4 zodiacs to two slots each, and every single user gets a confident answer.\n\nAfter reading this, I scrapped the 75% requirement entirely. The game I built is 100% accurate.\n\n## DeepSeek’s Practical Trick That Everyone Else Missed\n\nWhile the others debated question counts and encoding schemes, DeepSeek added something practical: a pre-question.\n\nQ0: Were you born before 1980? — Yes / No\n\nThis doesn’t affect accuracy at all. It just splits the 102-year birth range (1924–2025) into two halves. Each subsequent card now shows years from only a 50-year window instead of 100 years — roughly half the visual density. The user’s scanning burden drops significantly.\n\nThis was DeepSeek’s contribution: the boring-sounding “add a preliminary question” that actually has the biggest impact on the user experience. I kept it.\n\n## ChatGPT’s Second Idea: The Personality Disguise\n\nIn a separate prompt about game design (not the math challenge), ChatGPT offered a completely different take. What if the binary questions were disguised as personality questions?\n\nInstead of “Is your birth year on this list?” — which feels clinical and mechanical — you’d ask:\n\n- Q1:\n*“When a good opportunity appears, are you usually willing to take a chance before you know exactly how it will turn out?”* - Q2:\n*“Would you rather have a small circle of deeply trusted friends than a large casual network?”* - Q3:\n*“When making an important decision, do you trust your gut more than a long list of facts?”* - Q4:\n*“Do you believe people create most of their own luck through the choices they make?”*\n\nThe user thinks they’re doing a personality assessment. They’re actually inputting 4 binary bits. The result screen says “The Oracle read your patterns” — and the zodiac reveal lands like a magic trick, not a database lookup.\n\nI didn’t implement this version (I kept the birth year cards, which let the game work for people who don’t actually know their Chinese zodiac). But I can’t stop thinking about it. It’s a fundamentally different product — less accurate by design, but far more surprising. A future version, maybe.\n\n## The Low Hamming Weight Trick (Yuanbao + Gemini)\n\nOnce we settled on 4 questions and binary encoding, the next problem was: how do you minimize the years shown on each card?\n\nThe naive approach assigns binary codes 0–11 to the 12 zodiacs. Each card shows years for all zodiacs where that bit is “1” — roughly half the zodiacs, about 50 years per card. Too many.\n\nYuanbao and Gemini both spotted the fix: low Hamming weight encoding. Instead of using any 12 of the 16 possible codes, deliberately choose the 12 codes with the *fewest 1-bits*:\n\n- 1 code with zero 1s:\n`0000`\n\n- 4 codes with one 1:\n`0001, 0010, 0100, 1000`\n\n- 6 codes with two 1s:\n`0011, 0101, 0110, 1001, 1010, 1100`\n\n- 1 code with three 1s:\n`0111`\n\n(one zodiac has to take this)\n\nResult: each card now shows years for only 4–5 zodiac groups instead of 6. Combined with the 1980 pre-split, you get down to 15–25 years per card. Scannable in a second.\n\n## The Rat Easter Egg (All 6 AIs Agreed)\n\nOne zodiac gets assigned code `0000`\n\n. Its years appear on no card at all. The user answers No four times — every card a quick “not my year.” The system sees 0000 and knows: that’s the Rat.\n\nMechanically they answered 4 questions. Experientially they never had to search. The reveal can say: *“The Oracle Knew — You were invisible on every card. That is the hidden sign of the Rat.”*\n\nEvery single AI mentioned this. It was the one thing they all agreed was elegant.\n\n## What I Actually Built\n\nThe game synthesizes all of the above:\n\n- DeepSeek’s pre-question: “Born before or after 1980?”\n- 4 binary cards with low-Hamming-weight codes (Yuanbao/Gemini)\n- Rat = 0000, shown on no card (all 6 AIs)\n- Final reveal: two choices — your zodiac + a random decoy. You confirm by finding your birth year, not by naming the animal. Works for Western users who’ve never heard of the Chinese zodiac.\n\nThe personality question version (ChatGPT’s idea) exists in a separate prototype. Whether it becomes a second mode depends on whether it can be made accurate enough. Right now it’s a concept, not a product.\n\n🎯 Try the game that came out of this experiment:\n\n[Play: Can the Oracle Guess Your Zodiac? →](https://chinesefortunetools.com/zodiac-games/guess/)\n\n## The Real Lesson: What Happened When 6 AIs Saw the Same Problem\n\nSame prompt. Six answers. Four different strategies.\n\n**Yuanbao + Gemini**: focused on encoding efficiency (low Hamming weight)** DeepSeek**: focused on UX friction (pre-question to shrink list sizes)** Doubao**: focused on mathematical structure (explicitly modeling 75% as 9/12 collision rate)** Grok**: the rebel — 3 questions, statistical not per-user guarantees** ChatGPT**: challenged the premise (75% is the wrong metric) and proposed an entirely different UX layer (personality disguise)\n\nNone of these answers was wrong. They optimized for different things. The game I ended up with isn’t any one of them — it’s the parts that survived contact with reality: DeepSeek’s pre-question, Yuanbao/Gemini’s encoding trick, ChatGPT’s 100% accuracy argument, and the Rat easter egg that everyone called elegant.\n\nThe personality disguise is still on the whiteboard. Five bits of information, zero years on screen, users thinking they’re taking a personality test. If I build it, I’ll write about it here.", "url": "https://wpnews.pro/news/i-challenged-4-ais-with-the-same-math-puzzle-then-built-the-result", "canonical_source": "https://ordinarymantrying.com/i-challenged-4-ais-with-the-same-math-puzzle-then-built-the-result-ai-generated/", "published_at": "2026-08-15 05:02:59+00:00", "updated_at": "2026-08-15 05:11:29.316417+00:00", "lang": "en", "topics": ["artificial-intelligence", "large-language-models", "ai-products"], "entities": ["Tencent Yuanbao", "ByteDance Doubao", "DeepSeek", "Grok", "Google Gemini", "ChatGPT", "chinesefortunetools.com"], "alternates": {"html": "https://wpnews.pro/news/i-challenged-4-ais-with-the-same-math-puzzle-then-built-the-result", "markdown": "https://wpnews.pro/news/i-challenged-4-ais-with-the-same-math-puzzle-then-built-the-result.md", "text": "https://wpnews.pro/news/i-challenged-4-ais-with-the-same-math-puzzle-then-built-the-result.txt", "jsonld": "https://wpnews.pro/news/i-challenged-4-ais-with-the-same-math-puzzle-then-built-the-result.jsonld"}}