There is a famous puzzle called the Towers of Hanoi that consists of three pegs and n...
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There is a famous puzzle called the Towers of Hanoi thatconsists of three pegs
and n circular disks, all of different sizes. The disks start onthe leftmost peg, with the largest disk
on the bottom, the second largest on top of it, and so on, up tothe smallest disk on top. The goal
is to move the disks so that they are stacked in this same orderon the rightmost peg. However,
you are allowed to move only one disk at a time, and you arenever able to place a larger disk on
top of a smaller disk. Let tn denote the fewest moves(a move being taking a disk from one peg
and placing it onto another) in which you can accomplish thegoal. Determine an explicit formula
for tn.
There is a famous puzzle called the Towers of Hanoi thatconsists of three pegs
and n circular disks, all of different sizes. The disks start onthe leftmost peg, with the largest disk
on the bottom, the second largest on top of it, and so on, up tothe smallest disk on top. The goal
is to move the disks so that they are stacked in this same orderon the rightmost peg. However,
you are allowed to move only one disk at a time, and you arenever able to place a larger disk on
top of a smaller disk. Let tn denote the fewest moves(a move being taking a disk from one peg
and placing it onto another) in which you can accomplish thegoal. Determine an explicit formula
for tn.
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