## 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 the case for most riddles, the answer is all over the internet, so give this … 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

## 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 I do remember learning from my father (who was experienced in plumbing, and was somewhat … Read more

## The Logic Puzzles Of Raymond Smullyan; Updated With Solution

Update: Scroll to the bottom of this post to see the solution to Smullyan’s logic puzzle discussed below. Raymond Smullyan has written many books. What is the Name of This Book?, published in 1978, is a collection of logic puzzles and paradoxes that culminate in a development of Gödel‘s incompleteness theorem. The first page of Chapter … Read more