1.

There are two versions of Straightline Towers of Hanoi (STOH), first discussed in [5 6, Section 2.4]. In one version you must move the tower between endpoles. In the other you must move it only from one end to the middle, or vice versa. Let us call the former LSTOH (L for long trip) and the latter S1STOH (S for short trip and 1 representing a move from the middle to the end) and S2STOH (2 for a move from the end to the middle).

1. Prove by induction that LSTOH can be won, but use only knowledge of previous cases of LSTOH, not any knowledge of S1STOH or S2STOH. More specifically for n rings let P(n) be the statement that LSTOH can be won, let Q(n) be the statement that S1STOH can be won, and let R(n) be the statement that S2STOH can be won. Then the inductive step for P(n) should use only earlier cases of P and not any earlier cases of Q or R. (In principle, it s perfectly legitimate, say, to first prove Q(n) and R(n) for all n and then use them in the inductive step of P(n), but keeping the two versions completely...