Amendments

Second edition (2018)

Errata:
Corrigenda:
• p. 79, l.8: replace “${\rm d}(s)$” by “${\rm d}(s)^2$”.
• p. 79, l.10: replace “$(2^n-1-{\rm d}(s))$” by “$(2^n-1-{\rm d}(s))^2$”.
• p. 79, l.11: replace “$\ell_{n-1}$” by “$\ell_{n-1}^2$”.
• p. 79, l.13: replace “$260\,951$” by “$232\,221$”.

First edition (2013)

After the release of the second edition we do not make corrections to the first edition anymore.

Errata:
Corrigenda:
• p. 3, l. 5: replace “emminent” by “eminent”.
• p. 56, l. 3: replace $\mathbb{N}$ by $\mathbb{N}_0$.
• p. 57, l. 5: replace “4 off” by “5 off”.
• p. 64, l. 9: insert “positive” between “smallest” and “integer”.
• p. 84, Algorithm 9, l. 5: for parameter $s$ delete “on the optimal path”.
• p. 125, l. -13: “$\beta_\delta =1$”
• p. 135, l. -18: replace the text in this line by: “moves of disc $n$ eventually leading to the same peg would be a waste. An analogous argument holds for the last”.
• p. 147, move “called the . . . chain)” from line 3 to line 7 after “inverse” and put it between commas. Delete line 3 and replace comma in line 2 by full-stop.
• p. 151, beginning of line 11: $s_{n+1}j^n$.
• p. 174, l. 5: replace small $n$ with capital $N$.
• p. 195, l. -4: change $\geq$ into $\leq$.
• p. 198, central paragraph: delete the sentence “The resulting graph is then a ${p\choose 2}$-regular graph.” Instead, the sentence before should end “. . . vertices of $H_p^n$ such that each of them has ${p\choose 2}$ incident edges, thus making the resulting graph more regular.”
• p. 232, l. 3: replace “$s_{n+k}$” by “$s_{n+k}-1$”.
• p. 241, l. 15: replace “that” by “than”.
• p. 249, l. 2: replace “Section 2” by “Theorem 2.1”.
• p. 272, right column, l. -1: replace “$y_8$” by “${\rm d}(s,2^8)$”.
• p. 273, left column, l. 2: replace “from $(01)^4$ to $2^8$” by “from $(02)^4$ to $1^8$”.
• p. 279, right column, l. 22: replace “cover four vertices” by “covers $p+1$ vertices”.
• p. 294, entry “edge coloring”: replace “incident” with “adjacent”.
• p. 335, third entry: replace “order” by “size”.
• p. 44, l. -9.: After “assumption” the following footnote should be inserted:
This point had already been made in 1974 in an utmost clear statement by C. Becquaert published in an unfortunately virtually inaccessible local journal [Becquaert, C., Les tours de Hanoi, Le Pentamino 2 (1974) 73-84; p. 74]. Her minimality proof appeared in a somewhat more elaborate form in [Becquaert, C., Les tours de Hanoi, Pentamino 3 (1977) 55-71; p. 59f]. Our proof is a slightly improved rendering of Becquaert's and Wood's arguments.
• p. 45, l. -7.: Replace “in 1982 in [317]” by “in 1972 in [Jullien, P., Trois jeux, in: E. Galion, La mathÃ©matique et ses applications, CEDIC, Paris, 1972, 23-43; p. 34]” and omit reference [317].
• p. 56: note that $\widetilde{\beta}_n$ is OEIS A051049.
• p. 141: l. 8 (of text): Replace “$p\in\mathbb{N}$” by “with base $p\in\mathbb{N}$ and exponent $n\in\mathbb{N}_0$”.
• p. 199: insert in l. -10 after “obtain”: (cf. [112, Theorem 1, Theorem 2]).
• p. 270: left column, line -1: “for $k$ from $1$ to $n$ . . . ”.
• p. 277: in the solution for Exercise 3.5 one might add the following. Disregarding discs $1$ to $n-2$, there are $4!/2=12$ arrangements of the two bars and the two largest discs in a state $\sigma\in\mathfrak{T}^n$ (the order of the bars being irrelevant), Only one of these, namely $\,|\,|\,n (n-1)$, has disc $n-1$ underneath disc $n$ on goal peg $j=2$. Cf. also $\overrightarrow{{H}_3^{2}}$ in Figure 3.2.
More on the average distance to a perfect state in $\overrightarrow{{H}_3^{n}}$ can be found in [1].
• p. 299: Ref. [31] has meanwhile appeared on pages 81-90.
• p. 306: Ref. [150] has meanwhile appeared in volume 11 (2013) 1153-1157.

Bibliography:
1. Schwarz, M. A., The average distance in Lucas's Second Problem, Bachelor thesis, Ludwig-Maximilians-Universität, München, 2012.