In this problem you will construct 4 mutually orthogonal latin squares of order

Question

In this problem you will construct 4 mutually orthogonal latin squares of order 5. We will be doing all arithmetic mod 5. The rows and columns of each square will be indexed by 0, 1, 2, 3, 4 from top to bottom and left to right. The m-th Latin square will have the symbol b in position (i, j) if and only if j - m * i is b mod 5. So for example, the first Latin square (the one with m = 1) is: Find the Latin squares for m = 2, m = 3 and m = 4. Choose two of the Latin squares and verify that they are orthogonal to each other.

Explanation / Answer

a.Latin squares for m=2 is

for m=3

for m=4,

0 4 3 2 1 4 3 2 1 0 3 2 1 0 4 2 1 0 4 3 1 0 4 3 2

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