Denise's birthday

Question

Albert and Bernard want to know Denise's birthday. She gives them ten possible dates:

September 20, September 25, September 30
October 27, October 31
November 12, November 20
December 12, December 25, December 27

Denise then tells Albert the month only, and Bernard the day only. The following conversation takes place, and each speaker is a perfect logician who knows the other is too.

Albert: "I don't know when the birthday is, but I know that Bernard doesn't know either." Bernard: "At first I didn't know, but now I do." Albert: "Then I know it too."

When is Denise's birthday?

Accepted Answer

20 November. Step 1: Albert's first remark. Albert does not know the date, so his month has more than one candidate; every month does, so that part tells us nothing yet. But he also knows that Bernard does not know. Bernard would know immediately if his day appeared only once in the list. The days that appear only once are 30 (September only) and 31 (October only). For Albert to be sure Bernard is in the dark, Albert's month must contain neither of those days. So the month is not September and not October. It is November or December. Step 2: Bernard's remark. Bernard, who is a perfect logicia…

Denise's birthday

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