

A330280


Least number of 2 X 2 rotations required to solve an n X n Simon Tatham's Twiddle puzzle.


1




OFFSET

1,2


COMMENTS

The puzzle is as follows. An n X n grid is filled with distinct integers from 1 to n*n, such that the number at row r and column c (both 0based) is n*n  (r*n + c). The task is to perform rotations of 2 X 2 subgrids (moves) to bring the numbers into their natural order, i.e., the number at row r and column c should become r*n + c + 1. Rotations are by 90 degrees in the clockwise or counterclockwise direction. See links for example puzzles and solutions.
Wladimir Leite found strong upper bounds for the next few terms: 48, 88 and 146 (see links).  Dmitry Kamenetsky, Apr 20 2020


LINKS

Table of n, a(n) for n=1..4.
greenturtle3141, What is the strategy to solve Simon Tatham's Twiddle?, Puzzling StackExchange, Dec 24 2016.
greenturtle3141, A Guide to the Number Rotation Puzzle, Puzzling StackExchange, May 27 2019.
Dmitry Kamenetsky, Rotating numbers in a 3x3 grid, Puzzling StackExchange, Feb 15 2020.
Dmitry Kamenetsky and Wladimir Leite, Best known solutions for 3 <= n <= 7
Simon Tatham, Twiddle 3x3 puzzle
Topcoder, Marathon Match 117  RotatingNumbers


CROSSREFS

Sequence in context: A293403 A316451 A120845 * A293412 A224837 A049450
Adjacent sequences: A330277 A330278 A330279 * A330281 A330282 A330283


KEYWORD

nonn,hard,more


AUTHOR

Dmitry Kamenetsky, Feb 29 2020


EXTENSIONS

Removed a(5) as it was found to be suboptimal  Dmitry Kamenetsky, Apr 16 2020


STATUS

approved



