Monday, December 23, 2013

Nine Card Solution.

First I'm going to mention another game. Noughts and crosses  or tic-tac-toe. Everyone has played it and everyone older than 8 or so figured out how to play optimally. I'm going to claim that the nine card game is tic-tac-toe in a very precise sense.

Consider the magic square.

                      4  9  2
                                       3  5  7
                      8  1  6

It's known for every row, column and diagonal summing to 15. A little work will convince you that these are also the only ways to sum to 15, with exactly 3 distinct integers between 1 and 9.

As we all know how to play tic-tac-toe, we're done.

(edit: the middle row of the magic square appeared off-center,think it should be fixed now)

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