This puzzle was invented in 1883 by the French mathematician, Edward Lucas. Its origin is supposedly based on the following legend:
In the great temple at Benares beneath the dome which marks the center of the world, rests a brass plate in which are fixed three diamond needles, each a cubit high and as think as the body of a bee. On one of these needles, at the creation, God placed sixty-four discs of pure gold, the largest disc resting on the brass plate and the others getting smaller and smaller up to the top one. This is the Tower of Brahma. Day and night unceasingly, the priests transfer the discs from one diamond needle to another, according to the fixed and unbreakable laws of Brahma, which require that the priest on duty must not move more than one disc at a time and that he must place this disc on a needle so that there is no smaller disc below it. When the sixty-four discs shall have been thus transferred from the needle on which, at the creation, God first placed them, to one of the other needles, tower, temple, and Brahmans alike will crumble into dust, and with a thunderclap, the world will vanish.
According to the legend, when will the end of the world be?
The object of the game is to move all the disks from the center needle to either of the outside needles in as few moves as possible. There are only two rules:
1. You may only move one disk at a time
2. At no time may you put a larger disk on top of a smaller disk.
There are plenty of online versions of this game that you can use. My favorite is this no-bells-or-whistles version on GeoGebra:
https://www.geogebra.org/m/yvkha3hu
Try to find the minimum number of moves for whatever number of disks you have…
The minimum number of moves for 1 disk is _____.
The minimum number of moves for 2 disks is _____.
The minimum number of moves for 3 disks is _____.
The minimum number of moves for 4 disks is _____.
The REAL point of the game is to create an expression for the minimum number of moves necessary for n disks.
Good luck!
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