Tower of Hanoi Variants with Restricted Disc Moves
In Chapter 6 we have introduced the concept of a TH variant and presented several such puzzles: the Black and white TH, additional variants with colored discs, and the Bottleneck TH. We continued in Chapter 7 where the TL (and its variations) were treated in detail. In this chapter we turn our attention to the TH with resticted disc moves. These restrictions may consist of disallowing moves between certain pegs or either of imposing a direction of moves. (Note that Variants A, B and C of the Black and white TH introduced on p. 288ff are also defined prohibiting certain moves depending on disc colors.) The variants are pretty well understood if only three pegs are present as we will see in Section 8.2. It will turn out that for these, exactly five, puzzles a unified algorithm to generate their, respectively unique, optimal solutions can be constructed. To make things precise, we will discuss solvability of a variant in Section 8.1.
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