**From New Scientist #2564, 12th August 2006**

Amber and Ben have a new game. They lay out a row of three coins, all showing heads. They take it in turns, beginning with Amber, to turn one of the coins over. They must not turn a coin so as to produce a pattern of heads and tails which is the same as a pattern that has occurred earlier in the game.

For example, if Amber’s first move is to THH then Ben cannot move back to HHH. The first person who cannot make a move is the loser.

**Question 1.** If both players play as well as possible, who is the winner?

They now change the game by playing with a row of four coins, but the other rules are unchanged.

**Question 2.** If again, both play as well as possible, who is the winner?

They now change the rules again. They go back to three coins, but the first person who cannot make a move is the winner.

**Question 3.** If again, both play as well as possible who is the winner?

[enigma1404]

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I found this one quite a satisfying problem to solve.

This Python program uses a recursive function to examine the game tree. It runs in 40ms.

Solution:1. Amber; 2. Amber; 3. Ben.