A ball costs 5 cents more than a bat. Price of a ball and a bat is $1.10. Sally has 20 dollars. She stole a few balls and bats. How many balls and how many bats she has?

All LLMs I tried miss the point that she stole things and not bought them

gemini 2.5 give following response.

Conclusion:

We can determine the price of a single ball ($0.575) and a single bat ($0.525). However, we cannot determine how many balls and bats Sally has because the information "a few" is too vague, and the fact she stole them means her $20 wasn't used for the transaction described.

Google Gemini (2.0 Flash, free online version) handled this rather okay; it gave me an arguably unneccessary calculation of the individual prices of ball and bat, but then ended with "However with the information given, we can't determine exactly how many balls and bats Sally stole. The fact that she has $20 tells us she could have stolen some, but we don't know how many she did steal." While "the fact that she has $20" has no bearing on this - and the model seems to wrongly imply that it does - the fact that we have insufficient information to determine an answer is correct, and the model got the answer essentially right.

GPT-4o claims "This implies she did not pay the full $20. The total cost of the balls and bats she has is less than $20, but she still has items worth up to $20.", then bruteforces an 'answer' of "Balls = 25 Bats = 13".

It also managed to get the prices of the ball/bat wrong, presumably because it's using the more typical riddle:

> Ball = x dollars

> Bat = x + $0.05 (since it’s 5 cents more than the ball)

https://chatgpt.com/share/680ac88c-22d4-8011-b642-0397a01ec3...

Grok 3.0 wasn’t fooled on this one, either:

Final Answer: The problem does not provide enough information to determine the exact number of balls and bats Sally has. She stole some unknown number of balls and bats, and the prices are $0.575 per ball and $0.525 per bat.

There's a repo out there called "misguided attention" that tracks this kind of problems.

1-4 balls and bats // HoMM 3

It's interesting to me that the answers showing "correct" answers from current models still don't strike me as correct. The question is unanswerable, but not only because we don't know how many balls and bats she stole. We don't know that she had any intention of maxing out what she could buy with that much money. We have no idea how long she has been alive and accumulating bats and balls at various prices that don't match the current prices with money she no longer has. We have no idea how many balls and bats her parents gave her 30 years ago that she still has stuffed in a box in her attic somewhere.

Even the simplest possible version of this question, assuming she started with nothing, spent as much money as she was able to, and stole nothing, doesn't have an answer, because she could have bought anything from all bats and no balls to all balls and no bats and anything in between. We could enumerate all possible answers but we can't know which she actually did.

lol, nice way to circumvent the attention algorithm