Browsing category puzzles

A nice puzzle by way of @benjaminleis: This AIME problem is fun: pic.twitter.com/DhbviTqnqr — Benjamin Leis (@benjamin_leis) February 2, 2020 In case you can’t read that, we need to find the sum of the digits in $N = 9 + 99 + 999 + 999\dots999$, where the last number consists

When Jake’s father (Bradley Whitford) comes to town, Jake is excited to see him, but Charles is wary of his intentions; Holt challenges Amy, Terry, Gina and Rosa with a brain teaser in exchange for Beyonce tickets. Brooklyn 99, S02 E18, Captain Peralta “Surely it isn’t that hard?” I have

Once upon a time, I was a sudoku fiend. They provided an outlet, a distraction, a hiding place – I could bury my head in one for, say, half an hour and whatever had been troubling me before was somehow less of an issue. It’s not an effective strategy for

It’s always fun to tackle a puzzle from one of Cav’s posts - in this case, a Catriona Shearer puzzle; it looks like my solutions are completely unrelated to his, although in reality I tend to sneak the odd peek and take some inspiration1 I also liked that Cav shared

A puzzle that came to me via @sheena2907: Choose two numbers, $x$ and $y$, uniformly from $[0,1]^2$. What’s the probability that $\frac{x}{y}$ rounds to an even number? What’s the probability that it rounds down to an even number? As always, spoilers below the line. Rounding One of my best approaches

A nice thinker from Futility Closet: A rail one mile long is lying on the ground. If you push its ends closer together by a single foot, so that the distance between them is 5279 feet rather than 5280, how high an arc will the rail make? Feel free to

Over on Reddit, a couple of “last digit” puzzles crossed my path, and I thought I’d share the tricks I used, as much for my reference as anything else. 1) Show that the last digit of $6^k$ is 6, for any positive integer $k$. There’s a standard way to prove

A puzzle that came to me via @realityminus3, who credits it to @manuelcj89: $\sin(A) + \sin(B) + \sin(C) = 0$ $\cos(A) + \cos(B) + \cos(C) = 0$ Find $\cos(A-B)$. There’s something pretty about that puzzle. Interestingly, my approach differed substantially from all of my Trusted And Respected Friends’. Spoilers below