Cheryl's birthday

Question

Cheryl gives Albert and Bernard a list of 10 possible birthdays:

May 15, May 16, May 19; June 17, June 18; July 14, July 16; August 14, August 15, August 17.

She tells Albert only the month and Bernard only the day. Then:

Albert: "I don't know Cheryl's birthday, but I know Bernard doesn't know either."
Bernard: "At first I didn't know, but now I do."
Albert: "Then I also know Cheryl's birthday."

When is Cheryl's birthday?

Accepted Answer

The answer is July 16. Track what each statement rules out. The days available: 14, 15, 16, 17, 18, 19. Note the unique days: 18 (only June 18) and 19 (only May 19). If Cheryl's day were 18 or 19, Bernard would know immediately. Statement 1, Albert: "I know Bernard doesn't know." Albert knows only the month, yet is certain Bernard can't know. That's only possible if Albert's month contains no unique day (no 18 or 19). - May contains the 19 → could let Bernard know. Eliminated. - June contains the 18 → could let Bernard know. Eliminated. So the month is July or August. Remaining candidates: Ju…

Cheryl's birthday

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