In his early descriptions of the TH, Lucas pointed out the possibility of starting with an arbitrary distribution of nψ 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
... [Show full abstract] 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.