The problem of stack sorting was introduced by Knuth in the 1960s. He described the stack sorting operation as the movement of railway cars across a railroad switching network. The problem is also similar to the childhood game of Hanoi Towers, in which the player is supposed to move concentric discs of varying sizes from one side across to another without placing a bigger disc above a smaller o...

Many questions regarding the Tower of Hanoi problem have been posed and answered during the years. Variants of the classical puzzle, such as allowing more than 3 pegs, and imposing limitations on the possible moves among the pegs, raised the analogous questions for those variants. One such question is: given a variant, and a certain number of disks, find a pair of disk arrangements such that th...

We show how our previously described system model of the primate neocortex can be extended to allow the modeling of problem-solving behaviors. Speci+cally, we model di-erent cognitive strategies that have been observed for human subjects solving the Tower of Hanoi problem. These strategies can be given a naturally distributed form on the primate neocortex. Further, the goal stacking used in som...

In contrast to the widespread interest in the Frame-Stewart Conjecture (FSC) about the optimal number of moves in the classical Tower of Hanoi task with more than three pegs, this is the first study of the question of investigating shortest paths in Hanoi graphs H p in a more general setting. Here p stands for the number of pegs and n for the number of discs in the Tower of Hanoi interpretation...

This paper presents a study of an auditory version of the game Towers of Hanoi. The goal of this study was to investigate the nature of continuos presentation and what this could mean when implementing auditory direct manipulation. We also wanted to find out if it was possible to make an auditory interface that met the requirements of a direct manipulation interface. The results showed that it ...

The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of spanning trees and the study of their properties remain a challenge, particularly for large networks. In this paper, we study the number and degree distribut...

We establish some rank and crank analogs for partitions into distinct colors and give combinatorial interpretations for colored partitions such as partitions defined by Toh, Zhang and Wang congruences modulo 5, 7.

We compute the complexity of two infinite families of finite graphs: the Sierpiński graphs, which are finite approximations of the well-known Sierpiński gasket, and the Schreier graphs of the Hanoi Towers group H(3) acting on the rooted ternary tree. For both of them, we study the weighted generating functions of the spanning trees, associated with several natural labellings of the edge sets.

This research used a real and a virtual Tower of Hanoi puzzle to examine performance differences between virtual and real environments. The puzzle was solved twice in the real environment and twice in the virtual environment by each of the participants. A one-way ANOVA was performed for each of the four trials to compare the performance difference between the two environments. Comparisons were ...

Pattern databases are among the strongest known heuristics for many classical search benchmarks such as sliding-tile puzzles, the 4-peg Towers of Hanoi puzzles, Rubik’s Cube, and TopSpin. Min-compression is a generally applicable technique for augmenting pattern database heuristics that has led to marked experimental improvements in some settings, while being ineffective in others. We provide a...