Due 10/17/18 Memo:    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. ...

1. Due 10/17/18
Memo:
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.