The tower of Benares


In a temple in the Indian city Benares are appropriate for 64 precious disks from diamond to a tower stacked up. Each disk is a little smaller than the disk on that it rests. Priest order has now the task receives the tower considering holy rules to another place in the temple to induce. The disks are so preciously that they may lie only on one of three places in the temple, the place where the tower at the beginning stood, where it to be developed are and a place between them. The disks are heavy and fragile, therefore only one of the disks may be moved, never several at the same time. The last rule means that at no time a disk may lie on a smaller disk. If the tower in a place were diminished and developed again completely to other place, the temple will disintegrate and with it the whole world to dust.

For 3 disks     7 courses are needed.
For 4 disks   15 courses are needed.
For 5 disks   31 courses are needed.
For 6 disks   63 courses are needed.
For 7 disks 127 courses are needed.

The monks need 18,446,744,073,709,551,615 courses for the tower of Benares (64 disks) altogether. This number is implemented better clarified, if one accepts, that in each second 1 course and the monks constantly, without each interruption, works and it not one error to make, takes the change 584,554,049,253 years 312 days 10 hours 32 minutes and 39 seconds!