Group theory at work. A group theoretic analysis of a simple version of Rubic's cube or other permutation puzzle.

profilewuzhong712

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.

    • 5 years ago
    • 30
    Answer(1)

    Purchase the answer to view it

    blurred-text
    • attachment
      16puzzle.docx