Tower of Hanoi
The game consists of three rods on which several perforated discs of different sizes are placed. At the beginning all discs are arranged according to size on one stick. The largest disc is at the bottom and the smallest at the top. Now move the tower to another rod! Always move only one disc and never put a bigger one on a smaller one! How many moves do you take? Can it be done with even fewer moves?
Further informationson the exhibit "Tower of Hanoi"
The towers of Hanoi are a mathematical puzzle and patience game whose solution strategy can be developed recursively. Recursive means: Once you have solved the first case, all further cases can be related back to the first.
To transfer two discs from one place to another, you need three moves. These are: First you move the smaller disc to one of the other rods. Then the larger disc is placed on the free space and finally the smaller disc on the larger one again. If you now have three disks, you first have to move the tower from two disks to one of the free places. You need three moves. Then you put the biggest disc on the last free place. Finally you have to build the part tower again on the biggest disc, for which you need another three moves. This results in a total of 3+1+3 = 7 steps. If you try this with four discs, you get 7+1+7 = 15 steps. For five disks (like here in Phänomania) you need at least 15+1+15 = 31 steps.