This applet demonstrates, by way of a puzzle, that S_n, the group of permutations of n objects, is generated by (1 2) and (1 2 ... n). Instructions:

1. Choose the number of letters you wish to sort. For starters, try 5 or 6.
2. Press the randomize button.
3. Sort the red letters back into their original positions using the a ~ b button and the rotation button.