The Magnetic Tower of Hanoi



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Figure 12: Duration ratio curves for the "SF" Algorithm, the "67" Algorithm, and for the "62" Algorithm. The limits are 3/4, 2/3, and 67/108 respectively.
We can see now the effect of "freedom" on solution "efficiency":
(21A)

(21B)

(21C)
The (fully) Colored MToH has the lowest efficiency defined as 1 [], the SemiFree MToH is next with efficiency of 3/4, and for the (completely) Free MToH we have found two algorithms – "67" and "62" with efficiencies of 2/3 and 67/108 respectively.

The three "duration-ratio" curves are shown in Figure 12.

Next is a set of recursive equations showing again the "starring" role of the number "3".



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