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Logic Puzzles 7.0/10

Solution

Cheryl's Birthday

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Cheryl gives Albert only the month and Bernard only the day of her birthday, which is one of: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17. Albert: "I don't know the birthday, but I know Bernard doesn't either." Bernard: "At first I didn't know, but now I do." Albert: "Now I know too." When is Cheryl's birthday?

Worked solution

The answer is July 16. Albert's certainty that Bernard doesn't know rules out May and June (they contain the unique days 19 and 18). Bernard now knows, so his day must be unique among the remaining July/August dates (eliminating the 14s), leaving July 16, August 15, August 17. Albert then knows too, so the month must contain only one remaining option: July. The birthday is July 16.

Where to go next

Source: Adapted from the Singapore and Asian Schools Math Olympiad (SASMO) 2015, where it appeared as a competition question.