Re: Re: Lunch Bunch arrangement problem

[tall_man]

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.

[shemp]

Sorry, I was misreading the original post. I was thinking more along the lines of pairwise scheduling, like for certain sports, where every team in the league plays each week, and plays each team exactly once.

This is a much different problem. It sounds like something Erdos would have worked on.
I know this wont help you, but could you point me at some info regarding the problem?

party on,
shemp

[tall_man]

I did a lot of digging around for ideas for this problem in the Wolfram Mathworld pages http://mathworld.wolfram.com. Some of the subjects I looked at were: Euler squares, Kirkman's Schoolgirl Problem, Block Design, and Finite Field.