## 20 January 2016

### "Ants on a stick" math puzzle

Four red ants and two black ants are walking along the edge of a one metre stick. The four red ants, called Alf, Bert, Derek and Ethel, are all walking from left to right as we look at the diagram, and the two black ants, Charlie and Freda, are walking from right to left.

The ants always walk at exactly one centimetre per second. Whenever they bump into another ant, they immediately turn around and walk in the other direction. And whenever they get to the end of a stick, they fall off.

Alf starts at the left hand end of the stick, while Bert starts 20.2 cm from the left, Derek is at 38.7cm, Ethel is at 64.9cm and Freda is at 81.8cm.

Charlie’s position is not known - all we know is that he starts somewhere between Bert and Derek.
So here is the puzzle: Which ant is the last to fall off the stick? And how long will it be before he or she does fall off?
It's not actually that difficult.  You can solve it in your head if you start with the right conceptual framework (true of so many math puzzles).  For the purposes of the puzzle, the length of an ant is assumed to be zero.

The answer is at The Guardian.