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

KEYWORD

nonn,more

AUTHOR

Rodolfo Kurchan, Jun 11 2022

STATUS

approved