The Magnetic Tower of Hanoi



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. (1)
Disk numbering is done of course from bottom to top and as Equation 1 states - the smallest disk (), like the least significant bit in a "binary speedometer", makes the largest number of moves.

The total number of moves is given by the sum -
. (2)
Table 1 lists the (minimum) number of moves of each disk (Equation 1) and the total (minimum) number of moves required to solve the classical ToH puzzle (Equation 2) for the first eight stack heights.



k

N

1

2

3

4

5

6

7

8

SUM

2N - 1

1

1






















1

1

2

1

2



















3

3

3

1

2

4
















7

7

4

1

2

4

8













15

15

5

1

2

4

8

16










31

31

6

1

2

4

8

16

32







63

63

7

1

2

4

8

16

32

64




127

127

8

1

2

4

8

16

32

64

128

255

255


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