New Puzzle
Press this button to scramble the tiles. Each time you press this button, the tiles are scrambled a little more.

Solve Puzzle
If you’d like the computer to solve the puzzle, press this button. The computer will prepare the solution and create a graph you can use as a set of hints. If you’d like to watch the computer move the pieces into place, press reset, or use the hints to solve the puzzle yourself.

How the hints work
Each bar of the graph is what is called a "heuristic distance" and represents the distance you are from the solution. You can use each bar as a hint as to which piece you might move next. The red-bar represents the move you are currently on and the blue bar to the right of the red-bar represents the distance of the puzzle from the solution (if you take the correct path). If the next bar is larger, you’ll want to choose a move that takes you farther from the solution. If it is smaller then choose a move that takes you closer.

Now you’ll need to know what "nearer" and "farther" mean in terms of the puzzle. When each piece is in its home position, the heuristic distance for the puzzle is zero. If one tile is moved on space from its home position, the heuristic distance of the puzzle increases by 1 or 2.

 This pictures illustrates the tiles in their home positions. The goal of the puzzle is to move the tiles into this configuration. The six tile is one tile down from its home postion. The distance is represented as (x1-x2)(x1-x2) + (y1-y2)(y1-y2) where x1 is the current x-coordinate of the tile and x2 is x-coordinate of the home position. The same for the y-coordinates.

Its interesting to note that the computer finds an optimized path to the solution and that the distance from the initial problem to the final solution is quite bumpy. The moral of the story: Progress is not smooth – you sometimes have to make a move that takes you farther from your goal in order to achieve it.

The Reset Button
The computer doesn’t know what the solution to a puzzle is until you press the "Solve it" button. Following this, the computer "knows" the solution. You can watch the computer animate the solution by pressing this button.

The Next Button
After the computer solves the puzzle, you can ask the computer to execute the next logical move of the optimized solution.

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