Today's Puzzle
Thursday, April 1
In which we play with our food before eating it
You have a delicious cake whose top is covered with frosting. You're feeling hungry, so you cut yourself a nice 200-degree "slice" of cake (yes, that's five-ninths of the cake… so what?). But then, for reasons known only to yourself, you decide to turn that 200-degree wedge upside down and return it to its place, with the frosting now on the bottom.
We are going to pretend that the frosting sticks to the cake instead of coming off on the plate. Oh, and the cake magically fuses back together whenever you put back a slice. It's a special cake.
Not content with the amount of fun you've had so far, you then cut a new 200-degree slice, adjacent to the first (see figure below).
You turn this slice upside down and put it back, just like the first. You keep doing this (continuing counterclockwise around the cake). You are a strange person, but whatever makes you happy…
Eventually all the frosting is on top again! You have succeeded in your weird mission and now devour the entire cake in triumph! How many times did you cut a slice and turn it over? (Credit to Stan Wagon for this puzzle.)
Yesterday's Puzzle + Solution
I guess I'm just excited about produce this week. It's spring!
What do these tasty things have in common?
Hint
They all have two-word names (though some of them are also known by other names). What do those two-word names have in common?
Solution
They're all named after fruits other than themselves: pineapple guava, cherry tomato, banana pepper, apple pear.
I wanted to stick to a strict "[fruit name] [fruit name]" format, but maybe this would have been easier if I had stretched it to include grapefruit and pineapple.
Congratulations to yesterday's solvers Tori, Newton, Lemonade and Allie, Peter M., Jacob C., Ena, Maddy, Graham, Dr. Yetman, and the Greggs. Thanks to everybody who made a guess!
About This Site
Though he now teaches mathematics, Dr. (né Mr.) Shapiro's first job in a K–12 school was as a lunch monitor in Davis, CA. It was there that he originated the Puzzle of the Day, even rewarding correct answers with tickets in denominations like "15 points" (though without a clear idea of how he'd ultimately redeem these). Dr. Shapiro's favorite puzzle from this pre-professional era was "Tell me the location of the beehive on this campus."
Ten years later, Dr. Shapiro revived Puzzle of the Day at Proof School, writing each day's puzzle on a name tag. After 600 puzzles or so, he was just starting to feel normal about students reading his chest all the time when campus closed and the puzzle, like the rest of our lives, moved online. New puzzles are posted daily on school days.
Want to catch up on old PotDs? There's an archive currently containing puzzles from March to December 2020.