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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]

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Hamilton Broadway
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Food
A Hamilton-Themed Cookbook is Coming
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Hamilton Broadway

Fans of Broadway hit Hamilton will soon be able to dine like the Founding Fathers: As Eater reports, a new Alexander Hamilton-inspired cookbook is slated for release in fall 2017.

Cover art for Laura Kumin's forthcoming cookbook
Amazon

Called The Hamilton Cookbook: Cooking, Eating, and Entertaining in Hamilton’s World, the recipe collection by author Laura Kumin “takes you into Hamilton’s home and to his table, with historical information, recipes, and tips on how you can prepare food and serve the food that our founding fathers enjoyed in their day,” according to the Amazon description. It also recounts Hamilton’s favorite dishes, how he enjoyed them, and which ingredients were used.

Recipes included are cauliflower florets two ways, fried sausages and apples, gingerbread cake, and apple pie. (Cue the "young, scrappy, and hungry" references.) The cookbook’s official release is on November 21—but until then, you can stave off your appetite for all things Hamilton-related by downloading the musical’s new app.

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fun
Never Buy Drawing Paper Again With This Endlessly Reusable Art Notebook
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Art supplies can get pricey when you’re letting your kid’s creativity run wild. But with an endlessly reusable notebook, you never have to worry about running out of paper during that after-school coloring session.

The creators of the erasable Rocketbook Wave have come out with a new version of their signature product meant especially for color drawings. The connected Rocketbook Color notebook allows you to send images drawn on its pages to Google Drive or other cloud services with your phone, then erase the pages by sticking the whole notebook in the microwave. You get a digital copy of your work (one that, with more vibrant colors, might look even better than the original) and get to go on drawing almost immediately after you fill the book.

An animated view of a notebook’s pages changing between different drawings.

There’s no special equipment involved beyond the notebook itself. The Rocketbook Color works with Crayola and other brands’ washable crayons and colored pencils, plus dry-erase markers. The pages are designed to be smudge-proof, so turning the page won’t ruin the art on the other side even if you are using dry-erase markers.

Rocketbook’s marketing is aimed at kids, but adults like to save paper, too. Break away from the adult coloring books and go free-form. If it doesn’t quite work out, you can just erase it forever.

The notebooks are $20 each on Kickstarter.

All images courtesy Rocketbook

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