Start with n disks on one peg, as suggested in the draw- ing. Move all disks from the starting peg onto another peg, one at a time, placing no disk atop a smaller one. ( You can experiment yourself without pegs; use coins of different sizes, for example, a dime on top of a penny, on top of a nickle, on top of a quarter. It may take some patience to find the minimum number of moves re- quired.) (a) What is the minimum number of moves required if you start with 1 disk? 2 disks? 3 disks? 4?

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Towers of Hanoi There are three pegs on a board.
Start with n disks on one peg, as suggested in the draw-
ing. Move all disks from the starting peg onto another
peg, one at a time, placing no disk atop a smaller one.
(You can experiment yourself without pegs; use coins of
different sizes, for example, a dime on top of a penny, on
top of a nickle, on top of a quarter. It may take some
patience to find the minimum number of moves re-
quired.)
(a) What is the minimum number of moves required if
you start with 1 disk? 2 disks? 3 disks? 4?
Transcribed Image Text:Towers of Hanoi There are three pegs on a board. Start with n disks on one peg, as suggested in the draw- ing. Move all disks from the starting peg onto another peg, one at a time, placing no disk atop a smaller one. (You can experiment yourself without pegs; use coins of different sizes, for example, a dime on top of a penny, on top of a nickle, on top of a quarter. It may take some patience to find the minimum number of moves re- quired.) (a) What is the minimum number of moves required if you start with 1 disk? 2 disks? 3 disks? 4?
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