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Even following this restriction on a grid:

I'm at (1,1) and I want to get to (4,4). Assuming a restrictive interpretation of most direct[1] and no one-way streets factored in[2], there are still two equally direct and valid paths:

(1,1) -> (1,4) -> (4,4)

and

(1,1) -> (4,1) -> (4,4)

Which is most direct? If the cab driver chooses to go with the later because his buddy pays him to go past the billboard at (3,1), what's to stop him? What's wrong with that?

[1] If most direct means "shortest path", then there are many more equivalent routes.

[2] One way streets also offer a nice choice of where to do turns around a block under favorable circumstances. Similarly road construction offers extra choices by detour.




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