In Gridland, the cities are arranged in a 4 by 6 grid:

A-B-C-D-E-F
| | | | | |
G-H-I-J-K-L
| | | | | |
M-N-O-P-Q-R
| | | | | |
S-T-U-V-W-X

A man born in A (and never ventured outside his city) has to visit a man in X but wants to take a detour to get there. He wants to visit every city but not enter any city more than once during his tour. How should his trip go?

Since he is already in A when he starts his tour, he could go to B, then return to A (making his visit to A).  If this is possible, it's pretty easy to trace a path (e.g. BAGMSTNHICDJPOUVWQKEFLRX)

If not, it doesn't really seem possible, unless there's some other trick (which there probably is).

Can anyone prove how many different paths there are, using my method above?

Posted by Ryan on 2004-05-19 08:53:08