We introduce the k-peg Hanoi automorphisms and Hanoi self-similar groups, a generalization of the Hanoi Towers groups, and give conditions for them to be contractive. We analyze the limit spaces of a particular family of contracting Hanoi groups, H (k) c , and show that these are the unique maximal contracting Hanoi groups under a suitable symmetry condition. Finally, we provide partial results...

© 1998 The International Bank for Reconstruction and Development / THE WORLD BANK Paul R. Masson, Tamim Bayoumi, and Hossein Samiei are with the Research, Asia and Pacific, and European I departments, respectively, at the International Monetary Fund. The authors are grateful to colleagues and seminar participants at the World Bank, to Klaus Schmidt-Hebbel and to David Weil for advice and commen...

More than a century after its proposal, the Towers of Hanoi puzzle with 4 pegs was solved by Thierry Bousch in a breakthrough paper in 2014. The general problem with p pegs is still open, with the best lower bound on the minimum number of moves due to Chen and Shen. We use some of Bousch’s new ideas to obtain an asymptotic improvement on this bound for all p > 5.

We present a new technique to compress consistent pattern databases without loss of information by storing the heuristic estimate modulo three, requiring only two bits per entry, or in a more compact representation only 1.6 bits. This enables us to store a pattern database with four or five times as many entries in the same amount of memory as an uncompressed pattern database. We compare both m...

The Apollonian networks display the remarkable power-law and small-world properties as observed in most realistic networked systems. Their dual graphs are extended Tower of Hanoi graphs, which are obtained from the Tower of Hanoi graphs by adding a special vertex linked to all its three extreme vertices. In this paper, we study analytically maximum matchings and minimum dominating sets in Apoll...

The weighted Tower of Hanoi is a new generalization the classical problem, where move disc between two pegs $i$ and $j$ by positive real $w_{ij}\geq 0$. This problem generalizes concept finding minimum number moves to solve Hanoi, find sequence with total cost. We present an optimal dynamic algorithm we also establish some properties this as well its relation variants that are based on restrict...

BACKGROUND The Towers of London (TOL) and Hanoi (TOH) have been viewed as equivalent measures of planning and/or problem solving, although recent evidence in adults suggests that the underlying measurement characteristics of these two tasks may differ. As tower tasks are one of the few instruments that can be used to assess executive functioning in young children, the cognitive demands for both...