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A335753
Maximal length of the shortest walk on any n X n maze that starts in one corner and visits the other three corners.
1
3, 8, 15, 24, 35, 46, 63, 80
OFFSET
2,1
COMMENTS
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.
a(14) >= 196, which makes n=14 the smallest known n such that a(n) >= n*n.
Daniel Mathias conjectures that a(n) cannot exceed 10*n*n/9.
LINKS
Dmitry Kamenetsky, Creating the hardest 6x6 maze, Puzzling StackExchange.
Dmitry Kamenetsky, Creating the hardest 10x10 maze, Puzzling StackExchange.
Dmitry Kamenetsky, Daniel Mathias, Benjamin Butin and Wladimir Leite, Best known solutions for n <= 20
EXAMPLE
See links for examples.
CROSSREFS
Sequence in context: A359056 A191414 A086959 * A083656 A013648 A258837
KEYWORD
nonn,hard,more
AUTHOR
Dmitry Kamenetsky, Jun 20 2020
EXTENSIONS
Name clarified by Dmitry Kamenetsky, Aug 06 2020
STATUS
approved