there are three ways to use the workshop appletyou can attempt to solve the puzzle manuallyby dragging the disks from tower to tower you can repeatedly press the step button to watch the algorithm solve the puzzle at each step in the solutiona message is displayedtelling you what the algorithm is doing you can press the run button and watch the algorithm solve the puzzle with no intervention on your partthe disks zip back and forth between the posts to restart the puzzletype in the number of disks you want to usefrom to and press new twice (after the first timeyou're asked to verify that restarting is what you want to do the specified number of disks will be arranged on tower once you drag disk with the mouseyou can' use step or runyou must start over with new howeveryou can switch to manual in the middle of stepping or runningand you can switch to step when you're runningand run when you're stepping try solving the puzzle manually with small number of diskssay three or four work up to higher numbers the applet gives you the opportunity to learn intuitively how the problem is solved moving subtrees let' call the initial tree-shaped (or pyramid-shapedarrangement of disks on tower tree (this kind of tree has nothing to do with the trees that are data storage structuresdescribed elsewhere in this book as you experiment with the appletyou'll begin to notice that smaller tree-shaped stacks of disks are generated as part of the solution process let' call these smaller treescontaining fewer than the total number of diskssubtrees for exampleif you're trying to transfer four disksyou'll find that one of the intermediate steps involves subtree of three disks on tower bas shown in figure figure subtree on tower these subtrees form many times in the solution of the puzzle this happens because the creation of subtree is the only way to transfer larger disk from one tower to