A Number Riddle, Updated With Solution, And Some Comments On Iterative Playgrounds

Two weeks ago I posted a puzzle sent to me by my nephew Matthew: 1 is 3, 3 is 5, 5 is 4, and 4 is cosmic. Why is 4 cosmic? What happens to the other numbers? As I mentioned in the earlier post, I slept on this before solving it. I initially thought about … Read more

A Question From The USSR Olympiad Problem Book; Updated With Solution

A few days ago I posted on a problem (Problem 4(a) on Page 7) from the very nice The USSR Olympiad Problem Book, by D.O. Shklarsky, N.N. Chentzov, and I.M. Yaglom: We are given 80 coins of the same denomination; we know that one of them is counterfeit and that it is lighter than the … Read more

A Question From The USSR Olympiad Problem Book

I just picked up a copy of The USSR Olympiad Problem Book, by D.O. Shklarsky, N.N. Chentzov, and I.M. Yaglom, and it looks delightful. The book’s foreword states that it is intended for high-school students, although outstanding middle-school students might also give it a go. Complete solutions are given, which are particularly detailed for the … Read more

Round Trip On A Treadmill; Updated With Solution

Well, it’s been a while, but here at last is the promised solution to the treadmill puzzle posted here. I saw a version of the puzzle here (in the midst of a great discussion of extreme examples and counterexamples) at the excellent blog of Dave Richeson, who cites The Futility Closet. Here is the puzzle: … Read more

Mathematics Puzzle: Round-trip On A Treadmill

Alice and Basil are bored while waiting in an airport. They decide to play a game with one of the nearby “moving sidewalks” (treadmills). They decide that Alice will walk on the treadmill at constant speed $v$ (with respect to the treadmill) for a distance $y$, and then turn around and walk back to the … Read more

“The Coconut Problem” Updated With Solution

This is a famous old problem. I shall just state the problem here for you, and will follow up in a day or two with a solution and some of its amusing history. Update: Scroll down for a straightforward solution and a “trick” solution. There are also, by now, various generalizations and different versions. Here’s … Read more

Two Nice Probability Problems

Over at Freakonometrics, here is a pair of nice probability problems. The first problem also appears here as Problem #5. A number of solutions for your consideration are here. A very elegant solution by Ted Hwa is here. (This post first appeared at my other (now deleted) blog, and was transferred to this blog on … Read more