From Bob L. Peterson's post to geometry.puzzles: --------------------- From the star at the top how many paths are there without doubling back to the dollar sign. If you find the answer in the first few days just please post Merry Christmas. I should have used some other symbol but for most it is very hard to ignore at Christmas but lets try together. * / \ # # / \ / \ # # # / \ / \ / \ # # # # / \ / \ / \ / \ # # # # # / \ / \ / \ / \ / \ # # # $ # # || || Bob L. Petersen --------------------- I believe the answer will be: Routes(4, 2) where: Routes(n, m) = Routes(n-1, m) + Routes(n, m-1) and Routes(n <= 0, m) = 1 and Routes(n, m <= 0) = 1. Now i can't do actual math but i can write javascript, so here goes-