Classic Nim [solution]

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Notice that in Classic Nim it is the one who takes the LAST counter that loses.

Suppose it is your opponent’s turn and any of the following two configurations (shown in Figure 1, a and b) is left. After your opponent’s turn, you can force a win.

So the strategy is to leave your opponent with one of these patterns.

If it is your opponent’s turn and she has the pattern as shown in Figure 2, then on your next turn you will either to be able to win right away, or you will be able to leave her with one of the patterns shown in Figure 1.

So, on the first move, take 3 counters from the row containing 4 counters.

 
Posted: December 11, 2007
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