# Category Archives: Thinking puzzles

## 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 … Continue reading

## A Number Riddle

My nephew Matthew sent me a number riddle (thanks, Matt!), which I pass on here: 1 is 3, 3 is 5, 5 is 4, and 4 is cosmic. Why is 4 cosmic? What happens to the other numbers? As is … Continue reading

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## 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; … Continue reading

## 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 … Continue reading

## 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 … Continue reading

## 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 … Continue reading

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## Puzzle: A Cube Of Resistors, Updated With Links To Solutions

I posted this puzzle a few days ago: Consider 12 identical resistors connected to form a cube. That is, each resistor lies on the edge of a cube, and there is an electrical connection joining three resistors at each of … Continue reading

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## Puzzle: A Cube Of Resistors

Here’s a puzzle I just read in Clifford Stoll‘s book High Tech Heretic (paraphrased by me): Consider 12 identical resistors connected to form a cube. That is, each resistor lies on the edge of a cube, and there is an … Continue reading

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## “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 … Continue reading

## Why Does A Propane Torch Get Cold When Used? Updated, With Refrigerators

I was fixing a leaky water pipe in my garage yesterday, and so I had occasion to use a propane torch to heat up the pipe and melt the solder into the joint. It’s not something I do often, but … Continue reading