Place the numbers

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The numbers 1-9 are placed in a 3 by 3 grid. For any such arrangement, let the medians of the three rows be a 1 a_1 , a 2 a_2 and a 3 a_3 , and let m m be the median of a 1 a_1 , a 2 a_2 and a 3 a_3 . If m = 5 m=5 , then how many possible arrangements of the numbers are there?


The answer is 207360.

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