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Find the number of ways of arranging the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 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.

 Apr 1, 2020
 #1
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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.

 Apr 1, 2020
 #2
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I'm not sure that's correct, as you could also have for example 10, 2, and 3 in a column or 7, 2, and 12.

JustAPotato  Apr 2, 2020

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