Let τ be the 2-cycle (12) and σ the n-cycle (12ëëën). These two cycles generate the symmetric group Sn. Let Gn denote the directed Cayley graph Cay({τ,σ}:Sn). Based on erroneous computer calculations, Nijenhuis and Wilf give as an exercise to show that G5 does not have a Hamiltonian path. To the contrary, the authors show that G5 is Hamiltonian. Furthermore, they show that G6 has a Hamilton path. The present results illustrate how a little theory and some good luck can save a lot of time in backtracking searches.
