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The Tour (Posted on 2004-06-04) Difficulty: 2 of 5
You want to conduct a tour of this museum:

A-B-C
| | |
D-E-F
| | |
G-H-I
| | |
J-K-L

You want to walk through all the hallways once. What would be the least amount of walking you would need to do (each hallway is a kilometer long) to cover all the hallways at least once? (You can start and stop anywhere.)

See The Solution Submitted by Gamer    
Rating: 3.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
A modification to the puzzle + Solution | Comment 6 of 10 |

So if I'm reading Jer's Solution and Larry's additinoal explanation correctly, this slight modification to the puzzle diagram will show how to make some large number of 19 step traversals...

 A-B-C
| | |
D-E-F
(| | |)
G-H-I
| | |
J-K-L

By connecting the adjacent odd nodes to each other with an additional path you now change the network from a 6 odd-node network to a 2 odd-node network, and as stated by others a 2 odd-node always has a solution.

Is there a formula for figuring out the total number of solutions based on the number of odd and even nodes and the number of paths between them?


  Posted by Erik on 2004-06-04 11:08:38
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