This applet demonstrates, by way of a puzzle, that Sn, 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.