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Least number of 2 X 2 rotations required to solve an n X n Simon Tatham's Twiddle puzzle.
1

%I #51 Dec 16 2023 21:43:12

%S 0,2,10,24

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

%C 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 0-based) is n*n - (r*n + c). The task is to perform rotations of 2 X 2 sub-grids (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.

%C Wladimir Leite found strong upper bounds for the next few terms: 48, 88 and 146 (see links). - _Dmitry Kamenetsky_, Apr 20 2020

%H greenturtle3141, <a href="https://puzzling.stackexchange.com/questions/47124/what-is-the-strategy-to-solve-simon-tathams-twiddle/">What is the strategy to solve Simon Tatham's Twiddle?</a>, Puzzling StackExchange, Dec 24 2016.

%H greenturtle3141, <a href="https://puzzling.stackexchange.com/questions/84396/a-guide-to-the-number-rotation-puzzle">A Guide to the Number Rotation Puzzle</a>, Puzzling StackExchange, May 27 2019.

%H Dmitry Kamenetsky, <a href="https://puzzling.stackexchange.com/questions/93775/rotating-numbers-in-a-3x3-grid">Rotating numbers in a 3x3 grid</a>, Puzzling StackExchange, Feb 15 2020.

%H Dmitry Kamenetsky and Wladimir Leite, <a href="/A330280/a330280_2.txt">Best known solutions for 3 <= n <= 7</a>

%H Simon Tatham, <a href="https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/twiddle.html#3x3n2:9,8,7,6,5,4,3,2,1">Twiddle 3x3 puzzle</a>

%H Topcoder, <a href="https://www.topcoder.com/challenges/30122730">Marathon Match 117 - RotatingNumbers</a>

%K nonn,hard,more

%O 1,2

%A _Dmitry Kamenetsky_, Feb 29 2020

%E Removed a(5) as it was found to be suboptimal - _Dmitry Kamenetsky_, Apr 16 2020