This is mind boggling.(adsbygoogle = window.adsbygoogle || []).push({});

There is an array of 16 squares, arranged in a 4 x 4 grid. A supply of 4 A's, B's, C's, and D's are given. How many distinguishable ways are there of placing each of the letters in a square, if, one letter must appear once in each row and each column?

I'm lost. There are 4! ways of placing the letters in the first row. But then when you get to the second row, you can place the A, which has 3 possible locations. But then the B, depends on where the A was placed. If the A was placed under the B in row 1, then you have 3 possible spots left, but if the A was placed under the C, then there are only 2 spots left. Shown below.

The letters represent their placement, the 0 represents a spot that a B can't be placed, and a - represents a spot the B CAN be placed.

R1: ABCD

R2: -A--

or

R1: ABCD

R2: -0A-

See the problem? How do I get around this????:surprised :surprised :surprised

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# Very difficult permutation

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