This is a small game I wrote to demonstrate some of the combinatorics which appears when you study the representation theory of the symmetric group. First you need to choose a weakly decreasing sequence of positive numbers for example `4 3 2`

or `5 4 4 1`

. In representation theory, we call this a **partition**. You will be presented with a configuration which looks like:

1

2

3

4

5

6

7

8

9

Notice that the numbers increase by 1 as you go along the rows. The aim of the game is to transform the configuration so that the numbers increase by 1 along the columns:

1

4

7

9

2

5

8

3

6

When you click on a number, say `n`

, it will swap `n`

and `n+1`

as long as they are not in the same row or column. If they are in the same row or column nothing will happen. Also if `n`

is the largest number, then the game will not be happy because there is no `n+1`

to swap with.