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Find the number of ways of arranging the numbers 1, 2, 3, . . .12 in a 3x4 array (with three rows and four columns), so that the sum of the numbers in each column is divisible by 3. Each number must appear exactly once in the array.

 Jan 18, 2020
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You can enter the numbers as follows:

 

1 4 7 10

2 5 8 11

3 6 9 12

 

Then there are 3! = 6 ways of arranging the numbers in each column, so the number of ways is 6^4 = 1296.

 Feb 4, 2020

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