From:

~~~ Subject:

There is a puzzle that has been around for several years called

something like "Nuts To You" or "Drives You Nuts" or some variation

thereof. It consists of 7 hexagonal pieces (each resembling a nut,

hence the name) each with the numbers 1 through 6 inscribed around its

perimeter in some order. The idea is to play a kind of hexagonal

dominoes with these pieces; a solution is found when all 7 pieces are

arranged in a hexagon (the puzzle comes complete with a hexagonal

frame for arranging them, it also resembles a nut) such that every

pair of adjacent pieces are labeled the same along their common edge.

For example one piece might look like this:

_____ / 6 \ /3 1\ / \ \ / \2 5/ \__4__/ 6 which I shall abbreviate by: 3 1 2 5 4

which might participate in the following solution:

5 6 4 6 1 2 3 3 1 3 2 4 2 5 3 1 6 4 5 1 5 4 2 6 5 5 2 4 6 1 3 1 4 3 2 6 1 3 4 5 2 6

Each piece can be rotated (of course), but it cannot be flipped over.

(This restriction is enforced by simply not printing the numbers on

the other side!)

The seven pieces I have represented in my sample solution are

definitely NOT the ones that make up the commercially sold puzzle. I

don't have that anymore, I just made these up. It did have the

property that no two pieces were alike, just like my hypothetical set.

The commercial set of pieces seemed to have the property that there

was JUST ONE possible solution, although I cannot be 100% certain that

this was the case.

Now the puzzle itself is a bit dry. But what I wonder about is the

following meta-problem:

Given that there are many (how many?) different sets of 7 pieces that

can be chosen, how "interesting" a property is it for there to be only

ONE solution? Do you have to try hard to achieve that property? Or

do most of them have it? Indeed, do ANY of the have it (remember I

only SUSPECT that the commercial set has it!).

How about if we relax the restriction about duplicate pieces?

-Alan