Can you Nim? Test #2
Probability
Level
3
It's your turn. What move will guarantee a win for you provided you continue to play wisely?
Take 2 pennies from A
Take 3 pennies from B
Take 1 penny from C
None of the others are correct
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The object of the game is to take the last penny/pennies. What is the strategy? The strategy is to confront your opponent with a balance situation, therefore forcing him or her to unbalance the situation. A balanced situation is when all powers of 2 are paired. In this case, 3 pennies in A = 2^1+ 2^0, 4 pennies in B= 2^2+ 0 2^1 + 0 2^0, and 2 pennies in C = 2^1+ 0*2^0. Notice that there are a pair of 2's but an odd 4 and 1. To balance it, we need to remove the 4 and give 1 a pair. Therefore, removing 3 pennies from B leaves a pair of 2's and a pair of 1's ( balanced).