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%I #39 Aug 09 2020 01:05:50
%S 3,8,15,24,35,46,63,80
%N Maximal length of the shortest walk on any n X n maze that starts in one corner and visits the other three corners.
%C The maze is a 4-connected n X n grid consisting of empty cells and walls. The walk can visit adjacent empty cells, but cannot go through walls. Every corner must be reachable; i.e., cannot contain a wall. The walk can revisit cells.
%C a(14) >= 196, which makes n=14 the smallest known n such that a(n) >= n*n.
%C Daniel Mathias conjectures that a(n) cannot exceed 10*n*n/9.
%H Dmitry Kamenetsky, <a href="https://puzzling.stackexchange.com/questions/98590/creating-the-hardest-6x6-maze">Creating the hardest 6x6 maze</a>, Puzzling StackExchange.
%H Dmitry Kamenetsky, <a href="https://puzzling.stackexchange.com/questions/98723/creating-the-hardest-10x10-maze">Creating the hardest 10x10 maze</a>, Puzzling StackExchange.
%H Dmitry Kamenetsky, Daniel Mathias, Benjamin Butin and Wladimir Leite, <a href="/A335753/a335753_3.txt">Best known solutions for n <= 20</a>
%H Topcoder, <a href="https://www.topcoder.com/challenges/30134026">Marathon Match 119: Hardest Maze</a>.
%e See links for examples.
%K nonn,hard,more
%O 2,1
%A _Dmitry Kamenetsky_, Jun 20 2020
%E Name clarified by _Dmitry Kamenetsky_, Aug 06 2020