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If A(0, 0, 0) and B(2, 2, 2) are points in coordinate space, how many paths are there from A to B that move from one lattice point to another in the positive x-, y- or z-direction?

 Mar 7, 2021
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By casework, the number of paths is 16 + 4 + 4 + 4 = 28.

 Mar 7, 2021

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