You have a box bounded by the planes x=0, x=K, y=0, y=L, z=0, z=M. My intuition is that confining the path to the surface of that box doesn't cost you anything. If that intuition is correct, the answer is sqrt(min((K+L)^2 + M^2, (K+M)^2 + L^2, (L+M)^2 + K^2)). On Mon, Nov 13, 2017 at 7:57 PM, Dan Asimov <dasimov@earthlink.net> wrote:

Let W denote the union of all coordinate planes given by

x = K

or

y = K

or

z = K

for K an integer. I.e.,

W = Z x R x R u R x Z x R u R x R x Z

with Z = integers, R = reals.

Question: ---------

Let P, Q belong to Z^3.

What is the length of the shortest path connecting P to Q that lies entirely in W ???

* * *

WLOG assume P = (K,L,M) and Q = (0,0,0). The answer is a function of form f(K,L,M).

What is f(K,L,M) ???

I'm not sure if this is easy or hard.

—Dan

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