More than a century after its proposal, the Towers of Hanoi puzzle with 4 pegs was solved by Thierry Bousch in a breakthrough paper in 2014. The general problem with p pegs is still open, with the best lower bound on the minimum number of moves due to Chen and Shen. We use some of Bousch’s new ideas to obtain an asymptotic improvement on this bound for all p > 5.

Polyethylene glycols (PEG 200-7(0) are used as solvents in various pharmaceutical preparations meant for both internal and external use (1,2). PEGs are incompatible with iodine, potassium iodide, sorbitol, tannic acid, metallic salts like bismuth, mercury and silver salts (2). Their systemic absorption in certain conditions may result in renal failure and CNS depression (3). Morbidity has been ...

The objective of this study was to develop vaginal suppository containing lactobacillus. Four kinds of vaginal suppositories containing Lactobacillus paracasei HL32 were formulated: 1) a conventional suppository with Witepsol H-15 as a base, 2) a conventional suppository with mixed polyethylene glycols (PEGs) as a base, 3) a hollow-type suppository with Witepsol H-15 as a base and 4) a hollow-t...

It is suggested that homotaxial biostratigraphic units are an unsuitable basis for the definition of a New Zealand Tertiary geological time scale. Three other possible ways of setting up a time scale are discussed, and it is concluded that stratigraphic marker pegs offer the best basis for a rigorously defined time scale. In order to avoid the disadvantages of a hierarchical system of naming it...

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...

A tromino tiling problem is a packing puzzle where we are given region of connected lattice squares and want to decide whether there exists the using trominoes with shape an L. In this work study slight variation some positions have pegs each comes hole that can only be placed on top pegs. We present characterization flow networks show (i) linear-time parsimonious reduction maximum-flow problem...

We investigate a version of the Mastermind game, where the codebreaker may only store a constant number of questions and answers, called Constant-Size Memory Mastermind, which was recently introduced by Doerr and Winzen. We concentrate on the worst case, where the codebreaker may store only one question and one answer, called Size-One Memory Mastermind. We consider two variants of the game: the...

OBJECTIVE To translate, adapt, and evaluate the applicability of the perceived efficacy and goal setting system (PEGS) for use in Sweden. METHOD Based on guidelines for cross-cultural adaptation of self-reports, the study was performed in several phases involving (i) translation and back-translation, (ii) pre-testing of the translated version, (iii) development of adjusted items and, finally,...