## Dr Sam T. CarrInstitut fur Theorie der Kondensierten MaterieUniversitat Karlsruhe Room: 10-08 Tel: ++49 721 608-7006 Email: carr@tkm.uni-karlsruhe.de |

This is a game for one player. Each frog can either jump to the empty space next to it, or jump over one other frog to get to the empty space. The aim is for the frogs of two colours to swap positions, so that the blue frogs all end up on the left, and the red frogs all end up on the right. The question is then: what is the minimum number of moves needed to do this?

Can you see the pattern? What about if there were 100 frogs of each colour on 201 lilly pads. What would be the minimal number of moves then? More advanced - can you prove that this is the minimum number?

Notes: This is one of the first java programs I ever wrote, before I was familiar with concepts of scaling and resizing. I'm rewriting the program to fit more nicely in the window - but it turns out that the API I originally used is now deprecated, so its taking me longer than planned.