Friday, May 19, 2006

Territorial Teaser

I’ve created another puzzle. As before, I don’t yet know if it’s easy or hard. I also don’t know whether I’ve found the only solution or merely one solution. I’m counting on my readers/puzzle-solvers to help answer those questions. As with previous puzzles, I’m asking you not to post your answers in the comments, but to email them to me (at glen.whitman--AT--gmail.com) and tell me about how long it took you to get your answer. I’ll post the solution(s) at a later date. Here goes:

You have a group of eight people. There are two races, black and white; two genders, male and female; and two ages, young and old. All possible combinations are present in the group (so there is a black male young person, a black male old person, a white male young person, etc.). Your task: Divide the floor space of a square room into territories such that the following conditions hold:

1. There are exactly eight territories occupied by one person each.
2. For every demographic group, all territories containing that group’s members are contiguous.* Thus, all territories occupied by blacks are contiguous with each other, all territories occupied by whites are contiguous with each other, all territories occupied by men are contiguous with each other, etc.

* I use ‘contiguous’ in Merriam-Webster’s sense #4, the same sense in which we say all U.S. states but Alaska and Hawaii are contiguous. Two territories touching only at a single point, without achieving contiguity through other territories of the same demographic group, do not count as contiguous.

UPDATE 1: I've gotten two correct answers so far, both different from my intended solution, and with both authors saying it took them only a couple of minutes. The puzzle must be easier than I thought. So I'm adding another condition to harden the target, so to speak. Here it is:

3. At least two of the six demographic groups must be "landlocked," meaning none of the group's territories touches a wall of the room. (And, in case this wasn't clear from the original statement of the problem, the eight territories must completely fill the floor space.)

There. I hope that does it.

UPDATE 2: Still not hard enough? Okay, use this modified version of condition 3:

3a. Three of the six demographic groups must be landlocked.

I've already gotten one solution that satisfies this condition as well. I'm still searching for the set of conditions that makes my solution (or something like it) unique.

UPDATE 3: Answers posted here.

4 comments:

Ben said...

Does it have to be divided in equal parts? Can we use diagonal or curvy divisions?

Glen Whitman said...

There's no requirement of equal parts, and you can use diagonal or curvy borders.

I've already gotten a couple of correct answers, both of them different from mine (and each other). Now I'm wondering if there's an additional condition I can impose that will make my solution unique.

Glen Whitman said...

I've updated the post with an additional condition. If you're still working on the original version, feel free to ignore the new condition (for now!).

Gil said...

Maybe you need to add another condition:

4. The layout must look like my solution.