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
2
^{N}
- 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
Directory:
~dechter
->
courses
courses -> Ideas for projects 276-2017: Come up with your own idea. Must be relevant to the class
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