Dr. Giarusso's Problem:

In 1779, Euler posed the following problem:

A meeting 36 officers of six different ranks and from six different regiments must be arranged in a square in such a manner that each row and each column contains 6 officers from different regiments and different ranks.

It has been shown that this problem has no solution. But what if we have 9 officers with 3 different ranks and 3 different regiments? That does have a solution.

Let A, B, C be the regiments and 1, 2, 3 be the ranks. One solution would be

A1	B2	C3
B3	C1	A2
C2	A3	B1

Show that this can be done with 16 officers with 4 different ranks and 4 different regiments, and show that this can be done with 25 officers with 5 different ranks and 5 different regiments.

Due Friday, February 2^nd at Noon.