This Riddle Is Given at High School Math Competitions and It's Tricky as Hell

Kids who enter and compete in math tournaments are way smarter than I ever even thought about being in high school. I can’t solve regular math problems when I substitute-teach 6th grade, so this exceptionally tricky problem given to math olympiads in Singapore is just way, way above my pay grade.

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But if you’re into that sort of thing, here’s the New York Times’ edited version of the problem (to help smooth out the translation into English):

“Albert and Bernard just met Cheryl. ‘When’s your birthday?’ Albert asked Cheryl. Cheryl thought a second and said, ‘I’m not going to tell you, but I’ll give you some clues.’ She wrote down a list of 10 dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17. ‘My birthday is one of these,’ she said. Then Cheryl whispered in Albert’s ear the month – and only the month – of her birthday. To Bernard, she whispered the day, and only the day. ‘Can you figure it out now?’ she asked Albert. Albert said, ‘I don’t know when your birthday is, but I know Bernard doesn’t know either.’ And Bernard said, ‘I didn’t know originally, but now I do.’ Albert replied, ‘Well, now I know, too!’ So when is Cheryl’s birthday?”

As with any good word problem, the amount of reading is supposed to trip you up and get you a little lost. But how could Albert and Bernard help each other guess correctly without sharing their individual knowledge?

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The secret lies in the possible dates Cheryl chose to share…

If you’re ready for answers, turn the page!

Cheryl’s list repeats every day except the 18th and the 19th, which eliminates two of the dates from consideration – June 18 and May 19. If she had whispered 18 or 19 into Bernard’s ear, he would have known the whole answer right away, so it can’t be those – a fact he telegraphed to Albert when he says he “didn’t know originally.”

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If Cheryl had told Albert either June and May, he would not be able to say for sure that Bernard couldn’t know the answer. Therefore, June and May are now no longer options for Bernard, leaving him 5 possibilities: July 14, July 16, August 14, August 15, and August 17.

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When Bernard says “I didn’t know originally, but now I do”, Albert can take away any repeated dates (July 14 and August 14), because Bernard would not be able to know if there are two potential answers.

This leaves three possibly dates: July 16, August 15, and August 17.

Since Albert only knows the month, and he claims “Well, now I know too!,” we can again eliminate duplicates here (in this case, August), which leaves the answer: July 16.