Computer Science Field Guide: Tractability

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You are double-counting routes: If her first and last position is home, it would't matter if she went, Home-A-B-C-D-Home or Home-D-C-B-A-Home. It would be the same route just in reverse, and just delivering mail it wouldn't matter - the distance would be the same. So it's not 24 routes, it's only 12.

GhostlyJorg