November 02, 2008The 144 GameMy son is learning factors, multiples, and primes in school. That means we can play the 144 game. (You could actually use any number.) It also means we have a new puzzle for you. Here is how you play. Two players take turns naming positive integers. The only rules are that:
For example, you could play: Player 1: 1 Player 1 has an advantage. Why? Can you figure out the right first move? Posted by David at November 2, 2008 08:24 AMComments
I, as player 1, open with 12. Valid moves remaining are {18,24,48,72}. This is a nice small set, and we can reason about each case in turn. In practice, then, after player 1 plays 12, they keep the following two pairs in mind: {18,24} and {48, 72}. If their opponent plays an element of a pair, they play the other element. I'd like to try to find an elegant proof for why that strategy works, but at the moment I'm a bit too sleepy. Posted by: Iain at November 2, 2008 09:11 AMAfter 12, actually there are more valid moves  8, 9, 16, 36. Can you find a way to visualize the game? Player One has an advantage in games for not just 144, but any number larger than 1. There is a nonconstructive argument why this is true... Posted by: David at November 2, 2008 05:05 PMPost a comment

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