[Brian,
Sunday December 3, 2006 at 1:04pm]
Basic polynomino theory?
Little Princess Tao wanted to play Ubongo. So we played. (She finished most puzzles in time, and often beat me).
This got me to thinking about polyominoes. I can look at a basic grid arrangement and a set of -ominoes and tell if it's impossible by counting squares, and some arrangements because of parity issues. But I suspect that with some thought I could knock out more possibilities. Are there other tricks? Is there a good reference for the theory behind this that doesn't involve massive math?
The fact that Wikipedia had nothing leads me to believe I'm spelling this wrong, or missing a technical term.
http://mathworld.wolfram.com/Polyomino.html
Do you have a way of getting hold of old Scientific American articles? I know that Martin Gardner devoted several of his wonderful Mathematical Recreations articles to polyominos. I own most of the books. If you don't mind waiting, I can see if there's anything there. At the very least, I may be able to find a technical reference.
perhaps this helps (including references):
http://www.maa.org/mathland/mathtrek_9_27_99.html