Graeco-Latin Squares


The first Graeco-Latin squares were named so by Leonhard Euler (Bazel, 15 april 1707 – Sint-Petersburg, 18 september 1783) .

The square gives combinations of Greek and Latin letters, so that:

1. No two the same Greek or Latin letter are shown on the same row or column

2.  Each Greek/Latin combination appears once in the square

Examples for 3×3, 4×4 and 5×5


Strange enough there exist no 6×6 Graeco-Latin square!

Euler tried to proof that, but he did not succeed. He also thought that every even Graeco-Latin square with size 2 + 4.n (2, 6, 10, ..) does not exist. But later was proven that a 6×6 Graeco-Latin square does not exist and examples of 10×10, 14×14 and so on were found.

Voor de Nederlandse uitleg: