Quesiton: A Group Theoretic Analysis of 15-Puzzle

The 15-puzzle, invented by Noyes Palmer Chapman, and popularized by mathematical puzzle-maker Samuel Loyd in late 1980s, is a permutation puzzle best known for the hysteria surrounding it. Loyd even offered a prize of $1000 - a handsome amount at that time - to the first person with the correct solution. No one was able to solve the puzzle, which in words of Loyd "drove the whole world crazy". The reason for the hysteria - which, for Lyod, was justified - was due to the fact that no solution to the puzzle is possible. In this paper, we will present a brief description of the puzzle and will present a proof of the impossibility of the solution to the original puzzle using a group-theoretic approach.