We consider the problem of unfolding lattice polygons embedded on the surface of some classes of lattice polyhedra. We show that an unknotted lattice polygon embedded on a lattice orthotube or orthotree can be convexified in O(n) moves and time, and a lattice polygon embedded on a lattice Tower of Hanoi or Manhattan Tower can be convexified in O(n) moves and time.

We study generalizations of the Tower of Hanoi (ToH) puzzle with relaxed placement rules. In 1981, D. Wood suggested a variant, where a bigger disk may be placed higher than a smaller one if their size difference is less than k. In 1992, D. Poole suggested a natural diskmoving strategy, and computed the length of the shortest move sequence (algorithm) under its framework. However, other strateg...

The multipeg Towers of Hanoi problem consists of k pegs mounted on a board together with n disks of different sizes. Initially these disks are placed on one peg in the order of their size, with the largest at the bottom. The rules of the problem allow disks to be moved one at a time from one peg to another as long as a disk is never placed on top of a smaller disk. The goal of the problem is to...

We give new algorithms for generating all n-tuples over an alphabet of m letters, changing only one letter at a time (Gray codes). These algorithms are based on the connection with variations of the Tower of Hanoi game. Our algorithms are loopless, in the sense that the next change can be determined in a constant number of steps, and they can be implemented in hardware. We also give another fam...

Tower of Hanoi has become a popular tool in cognitive and neuropsychology to assess a set of behaviors collectively referred to as executive functions. Substantial variability in performance on the Tower of Hanoi (TOH) disk-transfer task among normally functioning young adults, and potential contributions to these individual differences, were examined. In this expanded 60-problem version of the...

ing the Tower of Hanoi Craig A. Knoblock School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 [email protected] Abstract This paper describes an automated approach to generating abstractions for the Tower of Hanoi and analyzes the use of these abstractions for problem solving. The analysis shows that the learned abstractions produce an exponential reduction in the size of the...

The Frame-Stewart algorithm for the 4-peg variant of the Tower of Hanoi, introduced in 1941, partitions disks into intermediate towers before moving the remaining disks to their destination. Algorithms that partition the disks have not been proven to be optimal, although they have been verified for up to 30 disks. This paper presents a dynamic programming approach to this algorithm, using tabli...

The Tower of Hanoi puzzle consists of n disks of distinct sizes distributed across 3 pegs. We will refer to a particular distribution of the disks across the pegs as a state and call it valid if on each peg disks form a pile with the disk sizes decreasing from bottom up. Since each disk can reside at one of 3 pegs, while the order of disks on each peg is uniquely defined by their sizes, the tot...

The aimof this paper is to investigate performance in a collaborative human–robot interaction on a shared serious game task. Furthermore, the effect of elicited emotions and perceived social behavior categories on players’ performance will be investigated. The participants collaboratively played a turn-taking version of the Tower of Hanoi serious game, together with the human and robot collabor...