Re: Lunch Bunch arrangement problem

I ran across similar problems in my undergrad math, and its been quite a while, but i swear there was a way to generate these "schedules" with modular equations, although that approach is probably isomorphic to using Galois fields.

Is it possible to use a field defined by generators whose orders are the prime factors of the desired composite order? For instance for 6 people, could you do something with generating the list (somehow) with galois fields of orders 2 and 3.

Sorry if this is rambling, its been quite a while, but i swear something along those lines works.
When you say that you think its impossible for composite orders, do you mean impossible to generalize, or that there are no solutions? I assume that you mean the former.

Comment on Re: Lunch Bunch arrangement problem

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Re: Re: Lunch Bunch arrangement problem by tall_man (Parson) on May 16, 2003 at 19:39 UTC
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.	[reply]
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]