%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