This page is a compilation of all the interesting puzzles I came across, or that others have shared with me. I tried my best to give proper credit to the source of each puzzle, but if you believe I incorrectly credited a riddle, please email me!
Cheryl’s Birthday
Source: Joseph Yeo Boon Wooi at Singapore’s National Institute of Education for the Singapore and Asian Schools Math Olympiad (SASMO) in 2015.
Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:
- May 15, May 16, May 19,
- June 17, June 18,
- July 14, July 16,
- August 14, August 15, August 17.
Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know either.
Bernard: At first, I didn’t know when Cheryl’s birthday was, but now I know.
Albert: Then I also know when Cheryl’s birthday is.
So, when is Cheryl’s birthday?
Click here for the solution!
Cheryl's birthday is on July 16.
Cheryl initially tells Albert the month, and Bernard the day. Clearly, Albert could not immediately know Cheryl's birthday from the month alone, as each month contains more than one date. However, Bernard would have been able to correctly guess the exact date had he been given 18 or 19, since each of those numbers does not occur more than once. The fact that Albert claims Bernard does not know the date already indicates that Bernard could not have possibly got 18 or 19, which rules out May and June.
Bernard then proceeds to claim that he did not know when Cheryl's birthday was before Albert talked, but could correctly guess it after Albert's first sentence. Since Albert's first remark allowed us to rule out May and June, this indicates that Bernard obtained a unique number among July and August: 15, 16, or 17.
Finally, upon hearing that, Albert confirms knowing the date. Among the remaining dates (July 16, August 15 and 17), July is the only month containing exactly one possible date. If Albert had got August instead, he would not have been able to correctly choose between August 15 and 17. This, therefore, leaves us with July 16 as the last standing survivor.
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