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?

(In reply to Solution? by Ryan)

I agree with Ryan, the trick is that the man from city A makes a visit to his own city after visiting city B or city G.

I believe I have all possible detours listed for the man from city A to his destination at city X.  If I did not miss any, I count 42 different routes the tourist can take:

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

Posted by Dej Mar on 2007-11-18 11:12:11