It wouldn't be a half bad idea to try and write a brute force solution and, if (as you might expect) it doesn't run in reasonable time or you run into some other implementation issue, you can then legitimize your somewhat off topic node by posting some code. ;)

There is plenty of precedent for nodes related to using Perl for solving tricky problems of this sort. An interesting example is Challenge: 2D random layout of variable-sized rectangular units..