Tower Of Hanoi Research Articles

Performance of Children With Developmental Dyslexia on Two Skill Learning Tasks—Serial Reaction Time and Tower of Hanoi Puzzle

Among the various theories proposed to explain developmental dyslexia (DD), the theory of specific procedural learning difficulties has gained certain support and is the framework for the current research. This theory claims that an inability to achieve skill automaticity explains the difficulties experienced by individuals with DD. Previous research on automaticity and DD has exhibited methodological issues such as a failure to test a range of skills. The current study broadens previous findings by delineating various reading skills correlated with several aspects of skill acquisition. Furthermore, the study utilizes two nonverbal tasks that reflect distinct types of skills: Serial Reaction Time (SRT) and the Tower of Hanoi Puzzle (TOHP). A total of 53 children aged 11 to 13 participated in the study, of whom 23 were children with DD and 30 were controls. Participants completed a test battery that consisted of reading tests, the SRT, and the TOHP. Results show no differences in learning rate between individuals with or without DD, although individuals with DD performed both tasks at a slower rate. Correlations were identified between a number of reading measures and measures of skill acquisition, expressed primarily in individuals with DD. Implications are examined in the discussion.

The Tower of Hanoi--myths and maths

This is the first comprehensive monograph on the mathematical theory of the solitaire game The Tower of Hanoi which was invented in the 19th century by the French number theorist douard Lucas. The book comprises a survey of the historical development from the games predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiski graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the Tower of London, are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

The Tutte polynomial of the Sierpiński and Hanoi graphs

Abstract We study the Tutte polynomial of two infinite families of finite graphs: the Sierpi´nski graphs, which are finite approximations of the well-known Sierpi´nski gasket, and the Schreier graphs of the Hanoi Towers group H(3) acting on the rooted ternary tree. For both of them, we recursively describe the Tutte polynomial and we compute several special evaluations of it, giving interesting results about the combinatorial structure of these graphs.

The effects of cognitive function training on motor and executive functions after basal ganglia stroke

Objective To observe the effect of cognition training on the motor and executive functioning of patients after a basal ganglia stroke.Methods Thirty patients with basal ganglia stroke were randomly divided into a treatment group and a control group.The control group received standard stroke rehabilitation training,while the treatment group received in addition 2 months of cognitive function training.The executive and motor functions of all of the subjects and their facility in the activities of daily living (ADL) were tested using the Tower of Hanoi,the Wisconsin card sorting test,a Stroop-3 test and the Fugl-Meyer assessment,the Berg balance scale and the modified Barthel index before and at the end of treatment.Results After two months of training,both within-group and between group comparisons showed that the treatment group had improved significantly more in executive function,cognition and motor function.Conclusion Cognition training can improve executive function,motor function and ADL performance after a basal ganglia stroke. Key words: Cognition training; Executive function; Motor function; Stroke

Executive Dysfunction and Processing Speed Predict Nonverbal Problem Solving Deficits in a Substance Use Disorder Population

Individuals with chronic substance use disorders have demonstrated various types of executive dysfunction, including nonverbal planning and problem solving. Prior studies that have examined the cognitive abilities that support performance of the Tower of Hanoi, a measure of nonverbal planning and problem solving task, have predominately been investigated in healthy adult populations. The present study examined how executive functions such as concept formation and cognitive flexibility, as well as information processing speed, and memory contribute to the performance of the Tower of Hanoi within a sample of 191 individuals with a substance use disorder. Results indicated that concept formation, cognitive flexibility, and information processing speed, but not memory significantly predict performance of Tower of Hanoi.

The worst Hanoi graphs

The “Towers of Hanoi” is a problem that has been extensively studied and frequently generalized. We are interested in its generalization to arbitrary directed graphs and ask how many moves are required in a given graph to move n disks from the starting peg to the destination peg. Not all directed graphs allow solving this problem; we will call those graphs that do Hanoi graphs. We settle the question of what are the Hanoi graphs that require the largest number of moves.

According to Davis: Connecting principles and practices

In this article, the author allows Robert B. Davis to state for himself his own Principles concerning how children learn, and how teachers can best teach them. These principles are put forward in Davis’ own words along with detailed documentation. The author goes on compare Davis’ words with his practices. A single Davis video (Towers of Hanoi) is analyzed to determine if, and to what extent, his principles are evident in his teaching of this lesson.

Multi-Peg Tower of Hanoi

SummaryA simple algorithm for the multipeg Tower of Hanoi is proven to generate optimal Frame/Strewart partitions.

A Tale of Two Puzzles: Towers of Hanoi and Spin-Out

A Tale of Two Puzzles: Towers of Hanoi and Spin-Out

A Tale of Two Puzzles: Towers of Hanoi and Spin-Out

A Tale of Two Puzzles: Towers of Hanoi and Spin-Out

Solving the Towers of Hanoi – how an amoeboid organism efficiently constructs transport networks

Many biological systems require extensive networks to transport resources and information. Biological networks must trade-off network efficiency with the risk of network failure. Yet, biological networks develop in the absence of centralised control from the interactions of many components. Moreover, many biological systems need to be able to adapt when conditions change and the network requires modification. We used the slime mould Physarum polycephalum (Schwein) to study how the organism adapts its network after disruption. To allow us to determine the efficiency of the constructed networks, we used a well-known shortest-path problem: the Towers of Hanoi maze. We first show that while P. polycephalum is capable of building networks with minimal length paths through the maze, most solutions are sub-optimal. We then disrupted the network by severing the main connecting path while opening a new path in the maze. In response to dynamic changes to the environment, P. polycephalum reconstructed more efficient solutions, with all replicates building networks with minimal length paths through the maze after network disruption. While P. polycephalum altered some of its existing network to accommodate changes in the environment, it also reconstructed large sections of the network from scratch. We compared the results obtained from P. polycephalum with those obtained using another distributed biological system: ant colonies. We hypothesise that network construction in ants hinges upon stronger positive feedback than for slime mould, ensuring that ants converge more accurately upon the shortest path but are more constrained by the history of their networks in dynamic environments.

Paying the price works: Increasing goal-state access cost improves problem solving and mitigates the effect of interruption

The aim of this paper was to investigate whether it was possible to induce more internal planning in the four-disk Tower of Hanoi (ToH) in order not only to produce more efficient problem solving but also to make it more resistant to the negative effect of interruption. The theoretical frameworks of soft constraints and the memory for goals model underpinned Experiments 1 and 2. In both experiments, three goal-state access cost conditions were used: high (mouse movements and 2.5-s delay), medium (mouse movements) and low (goal state always available). In Experiment 1, more memory-based planning was induced by the high cost condition, which resulted in fewer moves to solution and the gradual development of an efficient subgoaling strategy, resulting in more perfect solutions. In Experiment 2, the same condition protected performance against a 10-s interruption irrespective of the interrupting task (blank screen, mental arithmetic, or three-disk ToH). The more memory-based planning strategy, induced by high access cost, presumably strengthened participants' goals during planning and problem solving, making them less susceptible to decay and interference from interruption. These novel results are discussed in the context of other recent studies.

Performance in neurocognitive tasks in obese patients. Does somatic comorbidity matter?

The aim of the present study was to examine if obese individuals with obesity-related somatic comorbidity (i.e., hypertension, diabetes, sleep apnea, dyslipidemia, pain disorder) perform worse in neurocognitive tasks compared to obese individuals without any somatic disorder. Neurocognitive functioning was measured by a computerized test battery that consisted of the following tasks: Corsi Block Tapping Test, Auditory Word Learning Task, Trail Making Test-Part B, Stroop Test, Labyrinth Test, and a four-disk version of the Tower of Hanoi. The total sample consisted of 146 patients, the majority (N = 113) suffered from obesity grade 3, 26 individuals had obesity grade 2, and only 7 individuals obesity grade 1. Ninety-eight participants (67.1%) reported at least one somatic disorder (Soma+-group). Hypertension was present in 75 individuals (51.4%), type 2 diabetes in 34 participants (23.3%), 38 individuals had sleep apnea (26.0%), 16 suffered from dyslipidemia (11.0%), and 14 individuals reported having a chronic pain disorder (9.6%). Participants without a coexisting somatic disorder were younger [MSoma− = 33.7, SD = 9.8 vs. MSoma+ = 42.7, SD = 11.0, F(1, 144) = 23.01, p < 0.001] and more often female [89.6 and 62.2%, χ2(1) = 11.751, p = 0.001] but did not differ with respect to education, regular binge eating, or depressive symptoms from those in the Soma+-group. The Soma−-group performed better on cognitive tasks related to memory and mental flexibility. However, the group differences disappeared completely after controlling for age. The findings indicate that in some obese patients increasing age may not only be accompanied by an increase of obesity severity and by more obesity-related somatic disorders but also by poorer cognitive functioning.

On distances in Sierpiński graphs: Almost-extreme vertices and metric dimension

Sierpi?ski graphs Sn p form an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. An almost-extreme vertex of Sn p is introduced as a vertex that is either adjacent to an extreme vertex of Sn p or is incident to an edge between two subgraphs of Sn p isomorphic to Snp-1. Explicit formulas are given for the distance in Sn p between an arbitrary vertex and an almostextreme vertex. The formulas are applied to compute the total distance of almost-extreme vertices and to obtain the metric dimension of Sierpi?ski graphs.

Executive functioning in anorexia nervosa patients and their unaffected relatives

Formal genetic studies suggested a substantial genetic influence for anorexia nervosa (AN), but currently results are inconsistent. The use of the neurocognitive endophenotype approach may facilitate our understanding of the AN pathophysiology. We investigated decision-making, set-shifting and planning in AN patients (n=29) and their unaffected relatives (n=29) compared to healthy probands (n=29) and their relatives (n=29). The Iowa Gambling Task (IGT), the Tower of Hanoi (ToH) and the Wisconsin Card Sorting Test (WCST) were administered. Concordance rates and heritability indices were also calculated in probands/relatives. Impaired performance on the IGT and the WCST were found in both AN probands and their relatives, although planning appeared to be preserved. The IGT heritability index suggested the presence of genetic effects that influence this measure. No evidence for genetic effects was found for the WCST. The results suggest the presence of a shared dysfunctional executive profile in women with AN and their unaffected relatives, characterized by deficient decision-making and set-shifting. Concordance analysis strongly suggests that these impairments aggregate in AN families, supporting the hypothesis that they may constitute biological markers for AN. Decision-making impairment presents a moderate heritability, suggesting that decision-making may be a candidate endophenotype for AN.

Prefrontal EEG Correlation During Tower of Hanoi and WCST Performance: Effect of Emotional Visual Stimuli

Emotional stimuli elicit changes in the electroencephalographic (EEG) activity of several brain structures. Prefrontal cortex is involved in the processing of emotional stimuli and executive functions. The correlation analysis of EEG provides information about the functional coupling between areas. It is reasonable to expect that emotional activation will modify prefrontal coupling during the performance of executive tasks such as Tower of Hanoi or Wisconsin Card Sorting Test (WCST). Determine whether the prefrontal EEG correlation during the performance of the Tower of Hanoi and WCST is affected by previous exposure to videos with sexual or aggressive content. Prefrontal EEG coupling was determined by the Pearson correlation. Valence and general arousal were evaluated by the Self-Assessment Manikin Scale and sexual arousal with a Sexual Arousal Scale. Computerized versions of the Towers of Hanoi and WCST provided data on prefrontal executive functions. EEG from the left and right prefrontal zones was recorded during the performance of the Tower of Hanoi and WCST immediately after the subjects were exposed to one of the videos (neutral, aggressive, and erotic). There was no difference between videos in the task performance parameters. Only the erotic video produced an increased prefrontal coupling in the slow bands (delta and theta) during the performance of the Tower of Hanoi, whereas a decreased coupling in the delta, theta, and alpha bands was observed during the WCST. Prefrontal coupling was changed after exposure to the erotic video, and it is likely that enhanced sexual arousal was the main cause of this change. The correlation patterns obtained could be associated with particular cognitive strategies or to functional adaptations while being sexually aroused. The results of this study may contribute to an understanding of the central nervous mechanisms underlying the cognitive effects of sexual arousal.

The Neurocognitive Phenotype of Apathy following Acquired Brain Damage

Apathy is one of the most common neuropsychiatric sequelae of acquired brain damage. The disorder is usually defined in terms of observed deficits in motivation related behavioural, emotional, and cognitive aspects of goal directed activity. Most neuropsychological research on apathy has focused primarily on its associated neurocognitive correlates; particularly those related to executive dysfunction, or its association with other clinical syndromes like depression. Results from these studies have been mixed, probably reflecting the use of different neuropsychiatric samples and assessment tools, or reflecting the differences in the conceptualisation of apathy across studies. In this study we ask whether performance on ‘standard’ executive tests would distinguish brain-damaged patients with apathy symptoms from those without apathy. To potentially strengthen the power of the possible relationships between apathy and executive function we included brain-injured patients with varied aetiologies, and used a much broader range of ‘executive function’ tests than in previous studies. Results indicate that the Tower of Hanoi puzzle is sensitive to apathy symptoms. Patients with apathy symptoms were significantly impaired on the task compared to non-apathetic patients. Performance on the Wisconsin Card Sorting test, the Hayling and Brixton tests, and the Stroop test failed to show this distinction. We discuss these findings and their implications for treatment and rehabilitation.

Timing in Multimodal Turn-Taking Interactions: Control and Analysis Using Timed Petri Nets

research-article Free Access Share on Timing in multimodal turn-taking interactions: control and analysis using timed Petri nets Authors: Crystal Chao Georgia Institute of Technology Georgia Institute of TechnologyView Profile , Andrea L. Thomaz Georgia Institute of Technology Georgia Institute of TechnologyView Profile Authors Info & Claims Journal of Human-Robot InteractionVolume 1Issue 1July 2012 pp 4–25https://doi.org/10.5898/JHRI.1.1.ChaoOnline:28 July 2012Publication History 12citation458DownloadsMetricsTotal Citations12Total Downloads458Last 12 Months115Last 6 weeks10 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Effects of regular meditative practice on psychological measures of healthy subjects

Introduction: Meditation is described as a method for improving attention and promoting psychological and emotional stability, presenting favorable results on cognitive functions and stress tolerance as well. Recently, studies have shown differences on psychological measurements between meditators and non-meditators. The aim of this study was to investigate the influence of regular practice of meditation on psychological measures of healthy participants in basal conditions or after experimental stress-induction. Methods: Forty-four healthy participants (20 meditators and 24 non-meditators) were evaluated by inventories of life quality, anxiety, mood, sleep quality, depression, and stress. Furthermore, all participants were submitted to working memory tasks (Hanoy tower and Digit Spam) before and after two stress-induction procedures: Stroop Color-word and Serial Subtraction tests. The research protocol was approved by the institutional ethics committee (204/09 - CEP/UFRN, CAAE 0221.0.051.000-09). Results: Our results showed that meditators presented better inventories scores when compared with non-meditators in parameters such as life quality (score 15.6 versus 14.9, p = 0.04), mood (score 6.0 versus 22.5, p = 0.02), and depression (score 2.5 versus 7.0, p = 0.01). Regarding stress levels, 10 % of meditators (against 37.5% of non-meditators) presented low levels of stress (p = 0.04). Moreover, there was an improvement in performance of meditators (23.3 ± 0.8) in relation to non-meditators (19.0 ± 1.0) on digit span task and in Hanoi tower of meditators (165.2 ± 6.1 ) in relation to non-meditation (224.1 ± 13.1) after stress induction. Conclusion: These findings corroborate other studies showing that meditation can provide an improvement in general quality of life as well as the performance of practitioners in memory tasks.

Towers of Hanoi related problems

This paper presents a set of twelve problems related to Towers of Hanoi. The problems involve black and white disks and three poles. Various types of problems such as moving disks, splitting disks,...