Re: Re: Lunch Bunch arrangement problem

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.

Comment on Re: Re: Lunch Bunch arrangement problem

Replies are listed 'Best First'.
Re: Re: Re: Lunch Bunch arrangement problem by shemp (Deacon) on May 16, 2003 at 20:13 UTC
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	[reply]
Re^4: Lunch Bunch arrangement problem by tall_man (Parson) on May 16, 2003 at 20:29 UTC
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.	[reply]