In this applet a mathematical graph with 5 to 8 nodes is given. Each node is labeled 0,1, 2, 3, ... around the outside, and there are numbered sliding tiles within all but one of the nodes.
A "move" is initiated by clicking a tile, which slides the tile from its current node to an empty node along an edge of the graph. The puzzle is solved once each numbered tile matches the label of the node it is on.
The point is to solve the puzzle and to do it in as few moves as possible. In the applet presented here, we provide 30 puzzles of increasing level of difficulty, from very easy to very complex. You receive 1 to 3 star rating depending on how many moves it took you to solve the puzzle in comparison with the minimal possible solution. A three-star rating means that you solved the puzzle in the minimum possible number of moves. A two-star rating means you did it pretty well, and a one-start rating is the consolation prize for solving it at all.