French mathematician Edouard Lucas was born in Amiens in 1842 and died 49 years later in Paris. he wrote four volumes of work recreational mathhas become a classic of recreational mathematics. In 1883 with “N. Claus de Siam” (an anagram of “Lucas d’Amiens”) he sold a solitaire game he called “Tower of Hanoi”.
He claimed that the game was a simplified version of the so-called “Tower of Brahma.” In this legend, monks had to move a tower made of 64 golden discs in a large temple. But before they can complete this mission, the temple will shatter and the end of the world will come.
The Tower of Hanoi consists of a small board to which three identical cylindrical bars are attached. The stick on the left has five disks of different sizes with a hole in the center. These are ordered by size, with the largest disk at the bottom. The goal of the game is to move all discs from the left rod to the right rod in as few moves as possible. In each move, only one disc can be taken from one rod and placed on another, a large disc cannot be placed on a small disc. How many and what kind of trips does it take to transport the disc?

Replace the disk with a number depending on its size. Now, start with a tower with only one disk and systematically build the solution. The solution is simple. Each movement moves one disk from left to right.

For a tower with two disks, first move disk 1 from left to center, then move disk 2 from left to right, and finally move disk 1 from center to right. So we need 3 = 22 – 1 move.

For towers with 3 discs, first remove disc 3 in your head. This reduces the problem to a task that uses only two disks, moving from left to center in three moves. The fourth move moves disk 3 three places from left to right. Now, mentally keep disc 3 off again and move the two discs from center to right in three moves again. Adding up is 3 + 1 + 3 = 7 = 2.3 – 1 move.

The four-disk tower problem can be alleviated in a very similar way to the three-disk tower problem. Therefore, we need 7 + 1 + 7 = 15 = 2.4 – 1 move. Finally, for a tower with 5 disks, we would need 15 + 1 + 15 = 31 = 2.5 – 1 move. Generally you need twon – For towers, move once. n disk. The original game by Edouard Lucas had eight discs.
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This puzzle was originally Wissenschaft spectrum Reprinted with permission.