Tower of Hanoi 7 Disc Solution in the Fewest Moves

Tower of Hanoi 7 Disc Solution in the Fewest Moves
The smallest number of moves needed to solve a Tower of Hanoi puzzle is (2 to the power of n) minus 1, where n is the number of discs. In this case, using 7 discs, the fewest moves needed is:
(2 to the power of 7) - 1
= (2x2x2x2x2x2x2) - 1
= 128 - 1
= 127
The objective of Tower of Hanoi is to move all the discs from the left peg to the right peg, according to these 3 rules:
(1) A move is defined as lifting the upper disc from one of the stacks and placing it on top of another stack or empty peg
(2) No disc may be placed on top of a disc that is smaller than itself
(3) Only one disc may be moved at a time
Another important thing to note is that, however many discs the game is played with, there are never more or less than three pegs to transfer the discs between.
I know the game as Tower of Hanoi, but I was interested when fact checking this puzzle solution to find it is also known by the names: Tower of Brahma, The problem of Benares Temple, and Lucas’ Tower - and perhaps you know it better by one of these names.
The background photo is taken from a video called “Arc Shot of Diamond Flower Tower” by Housee Housee, courtesy of Pexels (treated with filter). The Diamond Flower Tower (Tòa nhà hỗn hợp) is in the city of Hanoi (Hà Nội) in Vietnam (Việt Nam), so it literally is a real Tower of Hanoi, though I very much doubt it was constructed elsewhere and moved to its current site in the same way as the puzzle!
Music: Symphony No. 5 by Beethoven
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