This article explores the concept of epistemic actions in the Tower of Hanoi (ToH) problem. Epistemic actions (Kirsh & Maglio, 1994) are actions that do not traverse the problem space toward the goal but facilitate subsequent problem solving by changing the actor’s cognitive state. We report an experiment in which people repeatedly solve ToH tasks. An instructional manipulation asked participan...

When speakers gesture, their gestures shape their thoughts, but how this happens remains unclear. What kinds of feedback from gesture—visual, proprioceptive, or both— drive these cognitive effects? Here we address this question using a test bed previously employed to explore gesture’s cognitive effects (Beilock & Goldin-Meadow, 2010). Participants solved the Tower of Hanoi puzzle, explained the...

The approach to teaching recursion in introductory programming courses has changed little during the transition from procedural to object-oriented languages. It is still common to present recursion late in the course and to focus on traditional, procedural examples such as calculating factorials or solving the Towers of Hanoi puzzle. In this paper, we propose that the shift to object-oriented p...

We examine Generalized Towers of Hanoi, Generalized Spin-Out, and the Combination Puzzle, and continue to describe the puzzles and their properties. We introduce Finite State Transducers (FSTs) that compute the shortest sequence of winning moves for each of these puzzles for all dimensions, and show that the solution sequence for Spin-Out is not finite-state computable when going from configura...

We present an advanced Bidirectional A* algorithm featuring an application of Frontier Search and a strategy for the performance-efficient utilization of External Memory. We present the results of an experimental evaluation demonstrating that this algorithm is capable of tackling exceptionally large state spaces while consuming significantly less time and space than its A* counterpart. For inst...

In the Twin Towers of Hanoi version of the well known Towers of Hanoi Problem there are two coupled sets of pegs. In each move, one chooses a pair of pegs in one of the sets and performs the only possible legal transfer of a disk between the chosen pegs (the smallest disk from one of the pegs is moved to the other peg), but also, simultaneously, between the corresponding pair of pegs in the cou...

Goal-directed cognition is often discussed in terms of specialized memory structures like the “goal stack.” The goal-activation model presented here analyzes goal-directed cognition in terms of the general memory constructs of activation and associative priming. The model embodies three predictive constraints: (1) the interference level, which arises from residual memory for old goals; (1) the ...

Sierpiński graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpiński gasket graphs Sn are the graphs naturally defined by the finite number of iterations that lead to the Sierpiński gasket. An explicit labeling of the vertices of Sn is introduced. It is proved that Sn is uniquely 3-colorable, that S(n, 3) is uniquely 3-edgecolorable, and that χ′(Sn) = 4, thus answering ...

The famous Towers of Hanoi puzzle consists of 3 pegs (A, B, C) on one of which (A) are stacked n rings of different sizes, each ring resting on a larger ring. The objective is to move the n rings one by one until they are all stacked on another peg (B) in such a way that no ring is ever placed on a smaller ring; the other peg (C) can be used as workspace. The problem has tong been a favourite i...

Given is a problem sequence and a probability distribution (the bias) on programs computing solution candidates. We present an optimally fast way of incrementally solving each task in the sequence. Bias shifts are computed by program prefixes that modify the distribution on their suffixes by reusing successful code for previous tasks (stored in non-modifiable memory). No tested program gets mor...