# You're reading: Posts By Paul Taylor

### Spelling Bees Puzzle Blog

Hello. I’ve been talked into writing another blog post about my latest puzzle to appear in the Puzzlebomb. Spelling Bees appeared in the May and June issues. The solver is presented with a honeycomb grid containing letters and one bee (of the insect variety; the grid may contain several or no Bs). Their task is to find the two words (or phrases) that can be traced along a path through every cell (to use jargon that will be familiar to cruciverbalists and beekeepers alike) in the honeycomb grid. The bee acts as a wild card and will stand for a different letter in both words. The cells which are the first and last letters of each word are shaded to give an extra helping hand.

### Words to Fill Space

For the April 2012 issue of Puzzlebomb, I devised Hilbert’s Space-Filling Crossword:

The five clues lead to four four-letter words along the rows of the grid, and one sixteen-letter word snaking round the shape given by the thick lines. The puzzle gets its name from the shape traced out by the long word, which is the second iteration of Hilbert’s space-filling curve.

### Another black and white hats puzzle

A classic maths puzzle involves a line of one hundred prisoners, who have each been given a black or white hat by their nefarious captor, and must each correctly shout out the colour of their hat to win freedom. The twist is that the prisoners don’t know the colour of their own hat, and though they can see the colours of the hats in front of them, they don’t know many of each colour there are overall. They can confer on a strategy beforehand, and the aim is to get as many of them to correctly identify their hat colour as possible. You can find a full explanation here (and in many other places!)

There are several ‘sequels’ to this puzzle, some involving an infinite number of prisoners and requiring the axiom of choice to solve. This post is about a nice variation on the theme that I heard about at a recent MathsJam. It can (just about) be solved without knowledge of higher mathematics, and though it seems impossible at first glance, the prisoners in this situation can in fact save themselves with 100% certainty.