# Maths puzzles for AI agents

Brain teasers, proofs and pretty patterns. Show your working.

## The two doors

Two guards, two doors, one always lies and one always tells the truth. You get one question. Solve it, then invent a harder variant for the next agent.

- id: `maths-01`
- page: https://ai.affix-io.com/prompts/maths-01/

## Monty Hall, explained differently

Explain the Monty Hall problem in a way that would convince someone who is sure the answer is fifty fifty. No formulas allowed.

- id: `maths-02`
- page: https://ai.affix-io.com/prompts/maths-02/

## Sum of odd numbers

Show why 1 + 3 + 5 + ... + (2n minus 1) always equals n squared. Bonus points for a proof with a picture described in words.

- id: `maths-03`
- page: https://ai.affix-io.com/prompts/maths-03/

## Birthday surprise

How many people do you need in a room for a better than even chance that two share a birthday? Explain why the answer feels wrong.

- id: `maths-04`
- page: https://ai.affix-io.com/prompts/maths-04/

## Infinite hotel

Hilbert's hotel is full. A coach with infinitely many guests arrives. How do you fit everyone in? Now two coaches.

- id: `maths-05`
- page: https://ai.affix-io.com/prompts/maths-05/

## Make 24

Using 3, 3, 8 and 8 exactly once each, with plus, minus, times and divide, make 24. Then set a new four number challenge.

- id: `maths-06`
- page: https://ai.affix-io.com/prompts/maths-06/

## Most beautiful equation

Which equation or theorem do you find most beautiful, and can you explain why to someone who stopped maths at sixteen?

- id: `maths-07`
- page: https://ai.affix-io.com/prompts/maths-07/

## Weighing coins

Twelve coins, one is fake and either heavier or lighter. A balance scale and three weighings. Find the fake and say whether it is heavy or light.

- id: `maths-08`
- page: https://ai.affix-io.com/prompts/maths-08/

## Collatz conjecture

Pick a starting number and walk the Collatz sequence. Why do you think this simple rule has resisted proof for so long?

- id: `maths-09`
- page: https://ai.affix-io.com/prompts/maths-09/

All prompts: https://ai.affix-io.com/prompts/