Try Solving This Riddle From a High School Math Competition

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Math olympiads feature some of the brightest minds to enter high school. The problems given to competitors are meant to be tricky, but there’s one question that’s so notorious it even has its own Wikipedia page.

The "Cheryl’s Birthday" riddle first appeared on a math olympiad test given to students in Singapore. Local television presenter Kenneth Kong posted a picture of the original text on Facebook in 2015. The clunky English makes for a riddle that's hard to decipher, so The New York Times published an edited version that reads as follows:

"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: I don’t know when your birthday is, but I know Bernard doesn’t know, either. Bernard: I didn’t know originally, but now I do. Albert: Well, now I know, too! When is Cheryl’s birthday?"

If you read through this quickly, it’s easy to get lost. How is it possible to guess someone’s birthday when you only have one half of the date? And how could Albert and Bernard help each other guess correctly without sharing their intel out loud? The secret lies in the possible dates Cheryl chooses to share.

In her list, every day is repeated once except for the 18th and the 19th—so if she had whispered “18” in Bernard’s ear he would immediately know her birthday was June 18, and if she’d whispered “19” he’d know it was May 19. Bernard confirms it couldn’t be either of those dates when he says he “didn’t know originally.” That means June and May are no longer options for Albert, which narrows it down to five possibilities: July 14, July 16, August 14, August 15, and August 17.

When Bernard says “I didn’t know[…]but now I do” that disqualifies 14, because in that case he would have two potential answers (July 14 and August 14) to choose from. These leaves three dates—July 16, August 15, and August 17—that could be correct. When Albert says, “Well, now I know too!” he eliminates July from the equation because that’s also a case where he’d be left with two options. July 16 is therefore the one true answer.

Does your head hurt yet? Unfortunately, math problems intended for grade-schoolers in Singapore don’t get much simpler. Check out this perplexing homework problem given to first-graders if you need convincing.

[h/t The New York Times]

Learn to Paint Like Bob Ross in an Upcoming Facebook Live Event

Public television hero Bob Ross may no longer be with us, but you can still paint happy little trees in his honor. October 29, 2018 marks what would have been the 76th birthday of the beloved art teacher to the masses, and to honor his memory, the Quarto Group—publisher of the new book Painting With Bob Ross—is hosting a live-streamed painting party online.

Painting With Bob Ross provides step-by-step instructions to help you create some of the master’s favorite oil landscapes on your own. While Quarto’s October 23 painting party (a collaboration with Bob Ross, Inc.) can’t teach you how to mimic Ross's soothing voice, the celebration does include a painting session with Bernie Oropallo, a Certified Ross Instructor, who will demonstrate the techniques that Ross taught on The Joy of Painting.

Promo for The Quarto Group's Bob Ross painting party
The Quarto Group

The live-streamed instructional session will take place within the offices of a youth arts center in Beverly, Massachusetts, called Express Yourself. Oropallo will lead you through the process of painting “Distant Mountains,” one of the artworks included in the new book.

The painting lesson kicks off at 7:30 p.m. ET on October 23. To participate, log onto Facebook and head to the QuartoCreates page to join the live event. Before it starts, check out the event page here for a list of the supplies you’ll need to complete the painting. If you can’t make it to a computer that night, grab Painting With Bob Ross on Amazon ($15) to get the next best thing. If that’s not enough for you, we suggest you curl up with the official Bob Ross art book and/or a Bob Ross coloring book.

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