Home > Riddles > Cheryl's Enigma (Birthday)
Albert and Bernardo have just met Cheryl. Cheryl tells them: 'My birthday is one of these 10 days: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17.' Then he tells Albert only the month, and Bernardo only the day.
Albert says: 'I don't know when your birthday is, but I know Bernardo doesn't know either.' Bernardo responds: 'At first I didn't know, but now I know when your birthday is.' Albert says, 'So now I know too.' When is Cheryl's birthday?
Answer: July 16.
Step by step analysis:
Possible dates:
Deletion summary (the gist):
| Step | Who speaks | What is deduced | Remaining dates |
|---|---|---|---|
| 1 | Albert | Your month cannot contain a single day (18 or 19) | Jul 14, Jul 16, Aug 14, Aug 15, Aug 17 |
| 2 | Bernard | Now you can know the day → it can't be 14 | Jul 16, Aug 15, Aug 17 |
| 3 | Albert | If it were August, I would still hesitate (15/17) → it's July | July 16 |
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