Help me figure out this puzzle

May 3, 2010 7:04 PM

I have in mind a particular sort of puzzle. The problem is, I don't know if it a physical puzzle or mathematical or something else. I can only describe the general concept and it feels like it's on the tip of my brain.

The concept is something like this: you have, say, six "pieces" (again, I don't know if it's equations/numbers/wooden blocks/other) that you're trying to fit together. And it's like you can always fit together five, but no matter how you try to manipulate things the sixth never works. Or maybe putting the sixth in causes another to "pop out" - figuratively, at least. Anyway, something along those lines.

The analogy I'm drawing to this is the slapstick comedy scene where a guy guy keeps trying to pick something up, and every time he picks another thing up he knocks something else over.

I know this is pretty vague. Anyone know what this could be? It could be anything from some "rule" or "law" to a puzzle that involves piecing oddly shaped wooden blocks together. All I remember is the concept.

posted by resiny to Sports, Hobbies, & Recreation (8 answers total)

I don't know if the five-six pieces are part of your constraint, but are you possibly thinking of the four-colour map problem -- no matter how you draw a map of many regions, it takes no more than four colours to paint it such that no adjacent regions are coloured the same ... (coming together like a sliced pie, on a point, is not adjacency, I believe...). There's no popping here, but you cannot squeeze those pieces into any shape such that a fifth colour is necessary ...
posted by Bet Glenn at 7:54 PM on May 3, 2010

This is pretty common feature in all sorts of puzzles, so it could by anything.

A few things sprung to mind while reading your post:

Fitting oddly shaped pieces together to form a cube

Manipulating a "snake" of cubes into one large cube.

I had this toy when I was younger, where you had to fit together pieces to form a square.
posted by alligatorman at 7:58 PM on May 3, 2010 [1 favorite]

Tangrams?
posted by infinityjinx at 8:17 PM on May 3, 2010

It sort of reminds me of a Fifteen Puzzle.
posted by Crane Shot at 8:27 PM on May 3, 2010

If it's a physical puzzle, there's a good chance it's on Rob's Puzzle Page.
posted by DevilsAdvocate at 8:39 PM on May 3, 2010

It's funny that Bet should mention the four color theorem. I was actually just working on hypohamiltonian graphs this afternoon:
A graph (vertices and edges) is hamiltonian if you can start at a vertex, hit every other vertex exactly once, and return. A graph is hypohamiltonian if it's not hamiltonian but if any one vertex is removed then what remains is hamiltonian. Some snarks are hypohamiltonian graphs and are used in proving the four color theorem.

I was thinking of hypohamiltonian graphs when I read resiny's question, since it's a case of "all but one fit in, and that one isn't unique". It's awesome that another's answer was so close to mine!
posted by monkeymadness at 8:59 PM on May 3, 2010

For spheres (circles, hyperspheres) this is the kissing number (for uniformly sized spheres) or a sphere packing problem (for a variety of sphere sizes).

Also, this reminds me of a Douglas Adams book.
posted by anaelith at 9:25 PM on May 3, 2010

There's a magic trick that does this affect wherein the pieces that fill a wooden frame are dumped out, then put back in and somehow the pieces don't fit anymore. So one piece is set aside, then they are dumped out and put back in once again only to have there be 1 too many pieces again, so that piece is set aside as well. Then, of course it turns out that they can all fit in the frame, since that's where you started.
posted by Four Flavors at 2:52 PM on May 4, 2010