For the multi-peg Tower of Hanoi problem with k ≥ 4 pegs, so far the best solution is obtained by the Stewart’s algorithm [15] based on the the following recurrence relation: Sk(n) = min 1≤t≤n � 2 · Sk(n− t) + Sk−1(t) � , S3(n) = 2 − 1. In this paper, we generalize this recurrence relation to Gk(n) = min 1≤t≤n � pk · Gk(n− t) + qk · Gk−1(t) � , G3(n) = p3 · G3(n− 1) + q3, for two sequences of a...

This is the general idea of the problem space hypothesis. The part icular detai ls of the construct ion of a space and the search through it depends on the task and on the person who solves i t . For instance, if the task is simple, as in the item-recognition task <16> and the three-term ser ies task <8>, the process of constructing a problem space is t r i v i a l . The task is easi ly assimil...

Interruption interference is a significant decrease in performance that follows task interruption. This interference is often studied using a primary and interrupting task pair. Evidence suggests that interruption interference can be reduced through practice by exposing individuals to many interruptions. However, the evidence that this skill transfers beyond the tasks being trained is less clea...

It is known that in the Tower of Hanoi graphs there are at most two different shortest paths between any fixed pair of vertices. A formula is given that counts, for a given vertex v, the number of vertices u such that there are two shortest u, v-paths. The formula is expressed in terms of Stern’s diatomic sequence b(n) (n ≥ 0) and implies that only for vertices of degree two this number is zero...

The proposed distinction between perceptual and conceptual skill-learning tasks was tested. Eighty participants were administered a cued recall task and two priming tasks, one perceptual (partial word identification) and one conceptual (category production). Two skill-learning task were administered as well, one putative perceptual (mirror reading) and the other putative conceptual (Tower of Ha...

Past research on the Tower of Hanoi problem has provided clear evidence for the importance of goal-subgoal structures in problem solving. However, the nature of the traditional Tower of Hanoi problem makes it impossible to determine whether there is any special cost associated with storing or retrieving goals. A variation of the Tower of Hanoi problem is described that allows one to determine s...

The Tower of Hanoi is a tool used to evaluate executive functions. However, few studies describe what functions are evaluated in this test. This study investigates the executive functions, evaluated by the Tower of Hanoi (ToH), and the influence of gender, age and its relationship with intelligence. We evaluated 55 children and adolescents, between the ages of ten and 16, without diagnosed neur...

The aim of the present study was to investigate executive functions in adults with intellectual disability, and compare them to a closely matched control group longitudinally for 5 years. In the Betula database, a group of adults with intellectual disability (ID, n=46) was defined from measures of verbal and non-verbal IQ. A control group, with two people for every person with intellectual disa...

The classical Tower of Hanoi puzzle, invented by the French mathematician Édourd Lucas in 1883, consists of 3 wooden pegs and n disks with pairwise different diameters. The n disks are initially stacked on a single peg in order of decreasing size, from the largest at the bottom to the smallest at the top. (See Figure 1.) The goal is to move the tower of disks to another peg, moving one topmost ...