Can you Nim?
Probability
Level
3
It is your turn. What has to be your choice to guarantee a win?
Assume your opposition is quite knowledgeable in this game.
None of the others is correct
Take 1 penny from C
Take 2 pennies from A
Take 3 pennies from B
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Convert each into its corresponding binary form A = 3 = 2+1, B = 4 = 4+0+0, and C = 5 = 4+0+1. Notice that the 4's and the 1's have pairs but not the 2's. The winning strategy in NIM is to balance the pairs thus forcing the opponent to unbalance it. So to balance this situation would be to remove 2 from A .
Taking 2 from A is not the same as taking 3 from B because taking 3 from B would leave all unbalanced pairs - i.e., what would be left are one 4, one 2 and three 1's.