Overview
This puzzle went viral in 2015 as a Singapore exam question. It's a lesson in reasoning about knowledge itself — using what others do and don't know as evidence.
How to solve Cheryl's Birthday
- Albert (month) says he's sure Bernard (day) can't know yet. That's only possible if his month has no unique day — eliminating May and June, which contain 19 and 18.
- Bernard now knowing means the day is unique among the survivors; 14 appears twice, so it's ruled out.
- Albert then knowing means the month is now unique; August still has two dates, so it must be July — July 16.
The key insight
Each statement is data about what a person can deduce, not about the date directly. 'I know that you don't know' is a powerful constraint that prunes whole months at once.
Variations & echoes
- It belongs to the family of 'common knowledge' puzzles like the blue-eyed islanders.
- Epistemic logic formalises exactly this kind of reasoning-about-reasoning.
Frequently asked questions
How does eliminating a unique day help?
If Cheryl's day were 18 or 19, Bernard would already know the date. Albert being certain Bernard doesn't know means the month can't contain those days.