This is one of the problems I was playing around with in my Mastering Perl chapter on tied variables (not that tie is the solution, just that the chapter was on tied variables). You can see the early version of all that stuff on my Mastering Perl website.

The upcoming issue of The Perl Review then attacks the same problem with bit vectors since in another article Eric Maki used the technique for Sudoku puzzles. If you're really in a bind I'll send you the draft of the article. :)