I believe the 6x6 case has no solutions. The proof is the 36 Officer Problem.

How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular 6x6 array such that no row or column duplicates a rank or a regiment? The answer is that no such arrangement is possible.

Suppose they were trying to form lunch bunches: the first arrangement is all the same rank, the second is all the same regiments. Then we know there is no third arrangement and the schedule fails.

In reply to Re: Re: Lunch Bunch arrangement problem by tall_man
in thread Lunch Bunch arrangement problem by tall_man

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