I don't know if it's easy or hard, but it's a very appealing question. It reminds me of the Kotani ant problem. I wasn't able to find an online PDF describing the Kotani ant problem, but I did find this related article about "hermit points": https://works.swarthmore.edu/cgi/viewcontent.cgi?article=1131&context=fac-ma... Jim Propp 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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