%0 Journal Article
%T How to Solve the Torus Puzzle
%A Kazuyuki Amano
%A Yuta Kojima
%A Toshiya Kurabayashi
%A Keita Kurihara
%A Masahiro Nakamura
%A Ayaka Omi
%A Toshiyuki Tanaka
%A Koichi Yamazaki
%J Algorithms
%D 2012
%I MDPI AG
%R 10.3390/a5010018
%X In this paper, we consider the following sliding puzzle called torus puzzle. In an m by n board, there are mn pieces numbered from 1 to mn. Initially, the pieces are placed in ascending order. Then they are scrambled by rotating the rows and columns without the player¡¯s knowledge. The objective of the torus puzzle is to rearrange the pieces in ascending order by rotating the rows and columns. We provide a solution to this puzzle. In addition, we provide lower and upper bounds on the number of steps for solving the puzzle. Moreover, we consider a variant of the torus puzzle in which each piece is colored either black or white, and we present a hardness result for solving it.
%K torus puzzle
%K 15 puzzle
%U http://www.mdpi.com/1999-4893/5/1/18