OFFSET
4,1
COMMENTS
We start with 2 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 2 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 (see bottom animation and label for different options).
Rodolfo Kurchan, Puzzle Fun, Snake Number Problem, March 2022.
EXAMPLE
4 INSTRUCTIONS
URDL: 32
-- 30 31 -- -- --
25 26 32 7 8 --
24 20 2 3 9 13
17 18 1 4 15 14
16 12 6 5 19 21
-- 11 10 29 23 22
-- -- -- 28 27 --
1) Both snakes start in square 1.
2) First snake go U = 2, second snake can't go Up.
3) First snake goes R = 3.
4) Second snake goes R = 4.
5) First snake cannot go D, so second snake D = 5.
6) First snake cannot go L, so second snake goes L = 6
7) First snake can go U = 7, and second cannot go U.
8) First snake can go R = 8, second snake cannot go R.
9) First snake can go D = 9, second snake can go D = 10.
10) First snake cannot go L, second snake can go L = 11.
11) First snake cannot go U, second snake can go U = 12.
12) First snake can go R = 13, second snake cannot go R.
13) First snake can go D = 14, second snake cannot go D.
14) First snake can go L = 15, second snake can go L = 16.
And so on.
| Instructions that give
n | Maximum length | the maximal length
--------------------------------------------
4 32 URDL
5 44 URDLU
6 138 UURDLL
7 226 UURDUUL
8 326 UURDLUUL
9 310 UUUURDUUL
10 409 URUDLLDURR
11 1138 UDDRDDRDUDL
12 5265 URUDRDURDDDL
13 10499 UUDRUDDLUULDD
Computer solutions found by Giorgio Vecchi.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Rodolfo Kurchan, May 01 2022
STATUS
approved