Pat B. wrote a response to my last post on the number 867-5309. In that post I pointed out that: 8675309 is a prime. 8675309 is a twin prime (8675311 is also prime). 8675309 is the hypotenuse of a (primitive) Pythagorean triple: 86753092 = 24602602+83191412. Pat asked: What is the smallest number that would meet…

# Category: Puzzle

## What is a howicide?

I’m a huge fan of HBO’s series The Wire. Today, while I was watching the 4th episode of season 4, I saw a curious word on the strap hanging around Sgt. Landsman’s neck: HOWICIDE. At first I thought this was a mistake or an easter egg. Why would they misspell homicide? But then I quickly…

## Infinite hat problems (solutions)

Yesterday I stated four hat problems. Today’s post contains the solutions to those problems. 1. Alice and Bob are wearing hats. The hats are either red or blue. They can see each other’s hats, but not their own hat. They are tasked with guessing their own hat color. If either person gets the color right, then they…

## Infinite hat problems

I got back from MathFest yesterday after a long 3-leg red-eye trip across the country. It was a great meeting. It is always fun to hear some good talks, visit a new city, and see old friends (and meet another math blogger). The first talk that I attended was given by Alan Taylor: “Predicting Values of…

## The famous trick donkeys: a Sam Loyd puzzle

Several years ago a colleague and I made paper copies of this famous old puzzle to distribute to prospective mathematics students. It is a fantastic puzzle, so I thought I’d post it here again. From what I can tell, the puzzle was invented in 1871 by Sam Loyd (1842–1911), probably history’s most famous “puzzler.” It…

## Freeman Dyson and a mathematical puzzle in the NY Times

On March 25 the New York Times Magazine had an article about Freeman Dyson, “The Civil Heretic.” It contains an interesting mathematical problem. At Jason, taking problems to Dyson is something of a parlor trick. A group of scientists will be sitting around the cafeteria, and one will idly wonder if there is an integer…

## What is wrong with this picture?

This image illustrating the Pythagorean Theorem was created by the artist Mel Bochner. It appears on the cover of the January 2009 issue of the College Mathematics Journal. What is wrong with it? For the answer, visit the 360 blog.

## KenKen

I just discovered a cool new Sudoku-like game called KenKen. A KenKen board is an nxn grid, and the object is to place the numbers 1 to n in each square subject to the following rules. Do not repeat a number in any row or column. The numbers in each heavily outlined set of squares,…