15Puzzle 2007-02-28 18:18:02 2007-05-25 16:48:49 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The {\em 15 Puzzle} is a square tablet containing 15 smaller square tiles labeled with the integers 1 to 15, set so that only one square may be moved at a time into the only available empty square by a move up or down or left or right (but never diagonally). The goal of the puzzle is to take a puzzle in an unsorted initial state, such as \begin{tabular}{|c|c|c|c|} 7 & 8 & & 1 \\ 2 & 3 & 4 & 5 \\ 6 & 9 & 10 & 11 \\ 12 & 13 & 14 & 15 \\ \end{tabular} and set each tile in its proper order. \begin{tabular}{|c|c|c|c|} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & \\ \end{tabular} The puzzle was invented by Noyes Chapman, who also created a famously unsolvable version with 14 and 15 switched. His original idea was to construct a puzzle with 16 tiles that would be moved to form a magic square with 34 as its magic constant. The 15 Puzzle was initially made of wood; today they are almost always made of plastic. Darling calls it ``the Rubik's cube of its day.'' \begin{thebibliography}{1} \bibitem{dd} D. Darling, ``15 Puzzle'' in {\it The Universal Book of Mathematics: From Abracadabra To Zeno's paradoxes}. Hoboken, New Jersey: Wiley (2004) \end{thebibliography}