Lucas’s Second Problem
In his early descriptions of the TH (see, e.g., ), Lucas pointed out the possibility of starting with an arbitrary distribution of n discs among three pegs, i.e. allowing for discs lying on a smaller one. The task is again to arrive at a perfect state on a preassigned peg, while still obeying the divine rule. This, in Lucas’s opinion , will vary the conditions of the problem of the TH “to infinity”. We may even go beyond by prescribing an arbitrary, albeit regular, state as the goal. We will approach this problem in the next section and round this chapter off with a section on an algorithmic solution to Lucas’s second problem.
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