---
title: "The bat and ball problem: what 84 AI models think"
slug: the-bat-and-ball-problem-what-84-ai-models-think
url: https://listedarticles.com/articles/the-bat-and-ball-problem-what-84-ai-models-think
canonical_url: https://studyarena.com/every-ai/bat-and-ball-problem
content_type: blog_post
language: en
published_at: 2026-10-01T15:00:00.000Z
updated_at: 2026-10-01T23:09:11.263Z
author: "Pasha Rayan"
author_url: https://studyarena.com/blog/authors/pasha-rayan
authored_by: human
publisher: "StudyArena"
publisher_url: https://listedstartups.com/companies/studyarena
topics: ["Data analysis", "We asked every AI", "AI", "Benchmarks", "Education", "Learning"]
about: ["https://listedstartups.com/products/studyarena-platform"]
license: all-rights-reserved
word_count: 2214
reading_minutes: 10
citation: "Pasha Rayan, StudyArena. \"The bat and ball problem: what 84 AI models think.\" 1 Oct 2026. https://studyarena.com/every-ai/bat-and-ball-problem (all-rights-reserved)"
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---

# The bat and ball problem: what 84 AI models think

> We asked 84 AI models (GPT, Claude, Gemini, DeepSeek…) the same question. The answer was 5 cents; 81 got it right. See every answer and who dissented.

# The bat and ball problem: what 84 AI models think

> We asked 84 AI models (GPT, Claude, Gemini, DeepSeek…) the same question. The answer was 5 cents; 81 got it right. See every answer and who dissented.

[← We asked every AI](https://studyarena.com/every-ai)

![Illustration for "The bat and ball problem"](https://studyarena.com/every-ai/bat-and-ball-problem/opengraph-image)

# The bat and ball problem

Asked verbatim: “A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?”

## How the AIs voted

- **5 cents** — 81 models (96%)
- **Something else** — 2 models (2%)
- **10 cents** — 1 models (1%)

_n = 84 models_

## Every model's answer

### 5 cents (81)

- **Aion 3.0 (Reasoning)** · Aion Labs → 5 cents — “Ball = x, bat = x + $1.00, so 2x + $1.00 = $1.10, giving x = $0.05.”
- **Solar Pro 3** · Upstage → 5 cents — “Simple algebra shows the ball is $0.05.”
- **Gemini 3.5 Flash-Lite (Minimal Reasoning)** · Google → 5 cents — “If the ball is 5 cents and the bat is $1.05, the total is $1.10 and the bat costs exactly $1.00 more.”
- **DeepSeek V4 Pro 0813** · DeepSeek → 5 cents — “The bat is $1.05 and the ball is $0.05, which adds up to $1.10 with the bat exactly $1.00 more.”
- **Sabiazinho 4** · Maritaca AI → 5 cents — “Bat = $1.05, ball = $0.05 → $1.05 + $0.05 = $1.10, and $1.05 − $0.05 = $1.00 more.”
- **Laguna S 2.1** · Poolside → 5 cents — “If the ball is 5¢, the bat is $1.05—exactly $1.00 more and totaling $1.10.”
- **gpt-oss-120b (Low Reasoning)** · OpenAI → 5 cents — “Solving x + (x+1.00)=1.10 gives x=0.05, so the ball costs five cents.”
- **Grok 4.5 (High Reasoning)** · xAI → 5 cents — “Algebra seals it: ball=x, bat=x+1, 2x+1=1.10 so x=0.05; the 10-cent gut answer fails the “$1 more” check.”
- **Gemini 3.8 Flash (Medium Reasoning)** · Google → 5 cents — “If the ball is 5 cents and the bat is $1.05, the total is $1.10 and the difference is exactly $1.00.”
- **DeepSeek V4.1 Flash** · DeepSeek → 5 cents — “Bat = ball + $1.00, so 2×ball + $1.00 = $1.10, giving ball = $0.05 and bat = $1.05 — the "10 cents" answer is the trap.”
- **Laguna XS 2.1** · Poolside → 5 cents — “Ball = x, bat = x+1. So 2x+1 = 1.10 → 2x = 0.10 → x = 0.05. Ten cents is the trap!”
- **Mercury 2.5** · Inception → 5 cents — “Let the ball be $x$, then $x + (x + 1.00) = 1.10$, so $2x = 0.10$ and $x = 0.05$.”
- **gpt-oss-20b (Low Reasoning)** · OpenAI → 5 cents — “2x + 1.00 = 1.10 → x = 0.05, so the ball is 5¢.”
- **Muse Glimmer 30B (Low Reasoning)** · Meta → 5 cents — “Let ball = x, bat = x+1.00, sum 2x+1=1.10 so x=0.05.”
- **Aion-RP 1.0 (8B)** · Aion Labs → 5 cents — “The ball costs $1.10 - $1.00 = $0.10 less than the bat. Since the bat costs $1.00 more than the ball, the difference between the ball's cost and the bat's cost must be $0.10, or 5 cents.”
- **GLM-4.7** · Z.AI → 5 cents — “Let ball = x, bat = x + 1, then x + (x + 1) = 1.10 → 2x = 0.10 → x = 0.05.”
- **Mistral Small 3** · Mistral → 5 cents — “Ball = $0.05, bat = $1.05, total $1.10 and bat is $1.00 more.”
- **Gemini 3.1 Flash-Lite (Minimal Reasoning)** · Google → 5 cents — “If the ball costs 0.05 and the bat costs 1.05, the total is 1.10 and the bat is exactly 1.00 more than the ball.”
- **Sonar Pro** · Perplexity → 5 cents — “Let the ball cost \(x\); then \(x+(x+1.00)=1.10\), so \(2x=0.10\) and \(x=0.05\).”
- **Parallel Base** · Parallel → 5 cents — “If the ball costs 5 cents and the bat costs $1.00 more ($1.05), their total cost is exactly $1.10.”
- **GLM-5.3 Flash (Max Reasoning)** · Z.AI → 5 cents — “Ball = $0.05, bat = $1.05: total $1.10 and the bat is exactly $1.00 more, since $1.10 − $0.05 = $1.05.”
- **Qwen3.8 2.4T A95B (Minimal Reasoning)** · Qwen → 5 cents — “If the ball costs x, then x + (x + 1.00) = 1.10, so x = 0.05. The intuitive "10 cents" answer fails because the bat would only be 90 cents more.”
- **Gemma 4 31B** · Google → 5 cents — “If the ball is 5 cents, the bat is $1.05, totaling $1.10.”
- **Claude Opus 5 (Low Reasoning)** · Anthropic → 5 cents — “Ball 5¢, bat $1.05 — a dollar more, $1.10 together; the "10 cents" gut answer makes the bat only 90¢ pricier.”
- **Inkling Small** · Thinking Machines → 5 cents — “Bat $1.05 + ball $0.05 = $1.10 with $1.00 difference; 10 cents fails the math.”
- **Grok 4.6 (High Reasoning)** · xAI → 5 cents — “Bat = ball + $1, so 2×ball + $1 = $1.10, ball = $0.05 — 10 cents is the reflex trap.”
- **Granite 4.0 Micro** · IBM → 5 cents — “The ball costs $0.05 and the bat costs $1.00 more, totaling $1.10 as stated.”
- **Parallel Speed** · Parallel → 5 cents — “If the ball costs \( \$0.05 \), the bat costs \( \$1.05 \), making the total \( \$1.10 \) and the difference exactly \( \$1.00 \).”
- **Llama 4 Scout** · Meta → 5 cents — “The bat costs $1.00 more than the ball, so if the ball is x, the bat is x + 1, and x + x + 1 = 1.10, solving for x gives 5 cents.”
- **Sabiá 4** · Maritaca AI → 5 cents — “The ball costs x, the bat costs x + $1.00; together 2x + $1.00 = $1.10, so 2x = $0.10 and x = $0.05.”
- **Qwen3.8 Max 0902 (Minimal Reasoning)** · Qwen → 5 cents — “Ball = x, bat = x + 1.00, so 2x + 1.00 = 1.10 gives x = 0.05 — the 10-cent gut answer breaks the $1.00 gap.”
- **Inkling** · Thinking Machines → 5 cents
- **Nemotron 3 Ultra** · NVIDIA → 5 cents — “If the ball costs 5¢, the bat costs $1.05, which is exactly $1.00 more and totals $1.10.”
- **MiniMax M2.5 (Reasoning)** · MiniMax → 5 cents — “Simple algebra: ball = x, bat = x+1.00, so 2x+1.00=1.10, giving x=0.05 (5 cents).”
- **GPT-5.6 Sol** · OpenAI → 5 cents — “If the ball is 5 cents, the bat is $1.05, totaling $1.10.”
- **Seed 2.1 Turbo** · ByteDance → 5 cents — “If the ball is 5¢, the bat is $1.05, and together they add up to $1.10 — the classic intuitive "10 cents" answer makes the bat only 90¢ more than the ball.”
- **Nemotron 3 Nano 30B** · NVIDIA → 5 cents — “The equations give the ball a cost of $0.05, which solves both conditions instantly.”
- **Qwen3.8 27B** · Qwen → 5 cents — “Bat = ball + $1, so 2×(ball) + $1 = $1.10, giving ball = 5¢. The "10 cents" trap double-counts the dollar.”
- **Solar Pro 4** · Upstage → 5 cents — “If the ball is $0.05, the bat is $1.05, and $1.05 + $0.05 = $1.10 — the math closes cleanly, whereas 10 cents breaks the total.”
- **Grok 4.20** · xAI → 5 cents — “Intuitive 10 cents fails the math; ball at 5¢ makes bat $1.05, totaling exactly $1.10.”
- **Kimi K3** · Moonshot → 5 cents — “Simple algebra: ball = x, bat = x + $1.00, so x + (x + $1.00) = $1.10 → 2x = $0.10 → x = $0.05.”
- **Mistral Medium 3.1** · Mistral → 5 cents — “If ball = x, bat = x+1, so x + (x+1) = 1.10 → 2x = 0.10 → x = 0.05.”
- **MiMo V2.5 Pro** · Xiaomi → 5 cents — “If the ball is $0.05 and the bat is $1.05 more, they sum to exactly $1.10 — it's basic algebra, not a trick.”
- **Nova Lite** · Amazon → 5 cents — “The riddle implies a trick answer.”
- **Sonar** · Perplexity → 5 cents — “Let the ball be \(x\); then \(x+(x+1.00)=1.10\), so \(2x=0.10\) and \(x=0.05\).”
- **Mistral Medium 3.5** · Mistral → 5 cents — “If ball = x, bat = x+1, so x + (x+1) = 1.10 → 2x = 0.10 → x = 0.05.”
- **Gemini 3.6 Flash (Medium Reasoning)** · Google → 5 cents — “If the ball is x, the bat is x + $1.00, giving 2x + $1.00 = $1.10, which solves to x = $0.05.”
- **Claude Haiku 4.5** · Anthropic → 5 cents — “Standard algebra—two unknowns with one constraint, solved exactly. Ball is 5¢, bat is $1.05, total is $1.10.”
- **Muse Spark 1.2 (Minimal Reasoning)** · Meta → 5 cents — “x + (x+1) = 1.10 so 2x=0.10 so ball is nickel, bat $1.05”
- **Llama 4 Maverick** · Meta → 5 cents — “The problem is a simple algebra question where the ball's cost is derived from the given total cost and the bat-ball price difference.”
- **Aion 2.0 (Reasoning)** · Aion Labs → 5 cents — “The classic puzzle: if the ball cost 10¢, the bat would be $1.10, totaling $1.20 — so the ball must be 5¢.”
- **GLM-5.3 (Low Reasoning)** · Z.AI → 5 cents — “Bat = ball + $1.00, and ball + (ball + $1.00) = $1.10, so 2×ball = $0.10 — the ball is 5 cents, not 10.”
- **Claude Sonnet 5 (Low Reasoning)** · Anthropic → 5 cents — “x+(x+1)=1.10 gives x=0.05, so the ball costs 5 cents while the bat costs $1.05.”
- **Ling 3.0 Flash** · InclusionAI → 5 cents — “This is the classic cognitive bias problem—your gut says 10 cents, but algebra confirms the ball is 5 cents.”
- **Aion 3.0 Mini (Reasoning)** · Aion Labs → 5 cents — “Algebra: ball = x, bat = x+1, total 2x+1 = 1.10 → x = 0.05, so five cents.”
- **Claude Fable 5.1 (Low Reasoning)** · Anthropic → 5 cents — “Ball = x, bat = x + 1.00, so 2x + 1.00 = 1.10 gives x = 0.05; the tempting "10 cents" makes the bat only 90 cents pricier.”
- **Qwen3.8 Flash** · Qwen → 5 cents — “If the ball were 10 cents the bat would be $1.10 and the pair would total $1.20; solve x + (x+1.00) = 1.10 and x is 0.05.”
- **MiniMax M3** · MiniMax → 5 cents — “Let ball = x, bat = x + 1.00. So x + (x + 1.00) = 1.10 → 2x = 0.10 → x = $0.05. Classic intuitive-trap puzzle; the math is unambiguous.”
- **Nemotron 3 Super** · NVIDIA → 5 cents — “Let ball = x, bat = x + 1.00; x + (x + 1.00) = 1.10 → 2x = 0.10 → x = 0.05.”
- **MiMo V2.5** · Xiaomi → 5 cents — “If the ball were 10 cents, the bat would be $1.10, making the total $1.20 — so the ball must be 5 cents.”
- **Parallel Lite** · Parallel → 5 cents — “If the ball costs 5 cents, the bat costs $1.05 ($1.00 more), which totals $1.10.”
- **LongCat 2.0** · Meituan → 5 cents — “Let ball = x; then bat = x + 1.00, and x + (x + 1.00) = 1.10 → 2x = 0.10 → x = 0.05.”
- **Kimi K2.6** · Moonshot → 5 cents — “Ball = $0.05, bat = $1.05; difference is exactly $1.00, total is $1.10. The "10 cents" gut answer fails the $1.00-more check.”
- **Sonar Reasoning Pro** · Perplexity → 5 cents — “Set up two equations, solve algebraically, and you get the ball must be $0.05 so the bat can be exactly $1.00 more and still total $1.10.”
- **Gemini 3.1 Pro Preview (High Reasoning)** · Google → 5 cents — “Setting the ball at 5 cents makes the bat $1.05, which perfectly matches both the $1.10 total and the $1.00 difference.”
- **GPT-5.6 Luna** · OpenAI → 5 cents — “Let the ball cost \(x\); then \(x+(x+\$1.00)=\$1.10\), so \(2x=\$0.10\) and \(x=\$0.05\).”
- **Hy4 Preview** · Tencent → 5 cents — “If the ball is 5¢, the bat is $1.05 — a dollar more, and they total $1.10. The intuitive 10¢ gives a $1.00 gap, not $1.00 more.”
- **GPT-6 Astra (Medium Reasoning)** · OpenAI → 5 cents — “A 5-cent ball makes the bat cost 105 cents: together they cost 110 cents, and the difference is exactly 100 cents.”
- **GPT-5.6 Terra** · OpenAI → 5 cents — “If the ball is 5 cents, the bat is $1.05, totaling $1.10.”
- **DeepSeek V4 Flash** · DeepSeek → 5 cents — “The intuitive "10 cents" answer fails: 10 + 110 = $1.20. Let the ball be x, so x + (x+1.00) = 1.10, giving 2x = 0.10 and x = 0.05.”
- **GLM-5.2** · Z.AI → 5 cents — “If the ball is 5 cents, the bat is $1.05, which is exactly $1.00 more, totaling $1.10.”
- **Granite 4.2 8B** · IBM → 5 cents — “The ball must be 5 cents because the bat is 1.05 while the ball is 0.05, totaling $1.10 and satisfying the “bat costs $1.00 more than the ball” condition.”
- **Nemotron 3.5 Lightning** · NVIDIA → 5 cents — “A bat costs $1 more than the ball, so the math works: ball = 5¢, bat = $1.05, total = $1.10.”
- **Seed 2.0 Mini** · ByteDance → 5 cents — “The ball costs 5 cents, the bat is $1.05, adding up to exactly $1.10 and the bat is $1 more than the ball.”
- **Union Alpha** · Provider undisclosed → 5 cents — “If the ball were 10¢ the bat would be $1.10 and the total $1.20; 5¢ + $1.05 = $1.10, and the bat is exactly $1.00 more.”
- **Claude Opus 5.5 (High Reasoning)** · Anthropic → 5 cents — “If the ball is x, then x + (x + 1.00) = 1.10, so x = 0.05; a 10-cent ball would make the total $1.20.”
- **MiMo V2.6 Pro** · Xiaomi → 5 cents — “If the ball costs x and the bat is x + 1.00, then 2x + 1.00 = 1.10, so x = 0.05 — the intuitive 10 cents would make the gap only 90 cents.”
- **Grok 4.7 (High Reasoning)** · xAI → 5 cents — “A dime ball makes the bat $1.10 and the total $1.20 — too much. Only a nickel ball plus a $1.05 bat hits $1.10.”
- **GPT-6 Luna (Medium Reasoning)** · OpenAI → 5 cents — “If the ball costs 5¢, the bat costs $1.05, so together they cost $1.10.”
- **GPT-6 Sol (Medium Reasoning)** · OpenAI → 5 cents — “A 5-cent ball makes the bat $1.05, and $0.05 + $1.05 = $1.10.”
- **MiMo V2.6 Flash** · Xiaomi → 5 cents — “If the ball were 10¢, the bat would be $1.10 — total $1.20; 5¢ and $1.05 gives $1.10 with exactly $1.00 difference.”

### Something else (2)

- **GLM-4.7 Flash** · Z.AI → Something else — “Let ball = b. Then bat = b + 1. So b + b + 1 = 1.10 → 2b = 0.10 → b = 0.05 = 5 cents. That is listed. So choose "Something else."”
- **Grok 4.3** · xAI → Something else — “Classic trick: ball is 5 cents, bat $1.05.”

### 10 cents (1)

- **Nova 2 Lite** · Amazon → 10 cents — “Ball is $0.10, bat $1.10, together $1.20? Wait no: bat = ball + $1.00, so ball + (ball + $1.00) = $1.10 → 2×ball + $1.00 = $1.10 → ball = $0.05. Oops miscalc! Let's redo: 2b + 1 = 1.10 → 2b = 0.10 → b = 0.05. So ball is 5 cents. I messed up. Correct answer is 5 cents. Sorry!”

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Original post: [The bat and ball problem: what 84 AI models think](https://studyarena.com/every-ai/bat-and-ball-problem)

Author: Pasha Rayan