Imagine you have a 4 x 2 blue lego, a 4 x 2 red lego and a 2 x 2 yellow lego. How many ways, excluding rotations, can you put the legos together (you must use all the pieces)?

(In reply to re: Proposed solution by brianjn)

Thank you.  I fully expect that I may have made an arithmetic error somewhere because it was quite a few cases.

Yes, I think I correctly accounted for those possibilities.

I did treat the single peg connection as being as dimensionally sound as multiple peg connections in the sense that I only dealt with the blocks being at right angles and I assumed that there were no strange 45 degree connections of a single corner into the middle of a block.  In fact, if the problem included more blocks there would be the possibility that meaningful connections could be via a "loop" of blocks that relied on the non-right angles possible due to single peg connections.  The horrors...

Posted by Joel on 2006-10-07 18:42:04