Mutually Orthogonal Latin Squares

Euler conjectured that there were no Graeco-Latin squares of order 2 mod 4. He was correct at 2 and 6 (this, of course, is the famous 36 officer problem). Beyond that the conjecture was false. Below is a Graeco-Latin square of order 10 as exhibited by Bose, Shrikhande and Parker in 1960 in "Further results on the construction of mutually orthogonal latin squares and the falsity of Euler's conjecture.

0A 7E 8B 6H 9C 3J 5I 4D 1G 2F
6I 1B 7F 8C 0H 9D 4J 5E 2A 3G
5J 0I 2C 7G 8D 1H 9E 6F 3B 4A
9F 6J 1I 3D 7A 8E 2H 0G 4C 5B
3H 9G 0J 2I 4E 7B 8F 1A 5D 6C
8G 4H 9A 1J 3I 5F 7C 2B 6E 0D
7D 8A 5H 9B 2J 4I 6G 3C 0F 1E
4B 5C 6D 0E 1F 2G 3A 7H 8I 9J
1C 2D 3E 4F 5G 6A 0B 9I 7J 8H
2E 3F 4G 5A 6B 0C 1D 8J 9H 7I




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