> "you're stuck with checking all N! solutions" not quite -- once you have a solution that runs in time X, you no longer need to check any solution that has a

> "you're stuck with checking all N! solutions" not quite -- once you have a solution that runs in time X, you no longer need to check any solution that has a sub-component that is known to take longer than time X. So, for example, if you find that going between locations A, C, J, F, P, E, and Q in that order takes longer than your current best whole-map solution, then you no longer have to check any solution of which ACJFPEQ is a subset. You can eliminate whole categories of solutions with a single check, instead of having to test each of them one-by-one.