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A354915
Maximum length of 3 finite snakes in the Snake Number Problem with n-periodic instructions in an infinite square grid (see Comments).
1
53, 82, 214, 321, 336, 472, 541, 4477
OFFSET
4,1
COMMENTS
We start with 3 infinite snakes, and 4 possible directions: up, right, down, left.
If on its turn one of the snakes cannot execute an order because that square is occupied, it goes to the next order, and so on.
The snakes can be blocked and finish there or can continue infinitely.
Which are the longest finite snakes using n instructions for 3 snakes that start in the same square (with n >= 4 because with 3 or fewer instructions are infinite)?
LINKS
Ariel Futoransky, Snake Program, Snake Program to try the snakes, April 2022 (to see more Snakes after the instruction you put :0 :0 for 3 snakes).
Rodolfo Kurchan, Puzzle Fun, Snake Number Problem, March 2022.
EXAMPLE
| Instructions that give
n | Maximum length | the maximal length
--------------------------------------------
4 53 URDL
5 82 URDLU
6 214 UURDUL
7 321 URUULDU
8 336 URURUULD
9 472 URDDDDDDL
10 541 UUURUDLLDD
11 4477 UUDDRDUUUDL
CROSSREFS
Sequence in context: A268753 A125876 A136065 * A234102 A234104 A212420
KEYWORD
nonn,more
AUTHOR
Rodolfo Kurchan, Jun 11 2022
STATUS
approved