Sunday, January 22, 2017

Abstracts of the papers in “Journal of Recreational Mathematics” Volume 10, Number 4, 1977-78

Abstracts of the papers in “Journal of Recreational Mathematics” Volume 10,  Number 4, 1977-78

 Given the elapsed time since these papers appeared and that there were no abstracts with the originals, nearly all of the items in this list were written by Charles Ashbacher.

“The Six-Piece Burr,” by William H. Cutler
 A burr is described as a interlocking geometrical puzzle with a great deal of symmetry that is composed of notched rods of wood. The best known such puzzle is the burr made of six pieces. Individual pieces are said to be either notchable or saw-cut. A notchable piece is one where there are notches cut that are perpendicular to the axis of the rod.
 With six pieces, each of which can or cannot be notched, there are 26 different ways the pieces can be constructed. Furthermore, for any specific selection of the form of the pieces, there is the potential for many different configurations. In this paper, that problem is examined and the number of solutions given.

“The Games of Ham,” by Bernardo Recaman S.
 Mathematician Sir William Hamilton created what is known as the “Around the World” problem of graph theory. It is a graph with 20 nodes connected in a specific way and the goal was to find a tour that starts at one node, visiting each node exactly once and then returning to the node of origin. This specific problem is demonstrative of the general one of determining if such a tour of a graph exists.
 The first game of Ham starts with a set of completely disconnected nodes and two players with markers of a different color and the players are called the attacker and the defender. They alternate plays with the goal of the attacker to create a Hamiltonian tour of the nodes and the goal of the defender is to prevent that. In the second game of Ham it is the goal of both players to construct a tour. The purpose of this paper is a brief analysis of the games based on the small numbers of nodes. 

“Number Patterns in More Than One Dimension, Part II,” by Doug Engel
 This abstract is a paraphrase of the first paragraph of the paper.
  In a previous issue of JRM, 10(3), a method of labeling 2k × 2k boards with binary colored patterns was discussed, along with some uses of the binary number patterns. This discussion will reveal some more applications of binary number patterns and discuss some further implications of those patterns.

“The 30/36 Problem With Pentominoes/Hexiamonds,” by Jean Meeus and Ir. P. J. Torbijn
 This abstract is a paraphrase/abbreviation of the opening section of the paper.
 The 30-problem for pentominoes is arranging the twelve pentominoes into two congruent regions of six pieces each and the 36-problem for hexiamonds is arranging them into two congruent pieces of six pieces each. In the case of the pentominoes, the region is made up of 30 squares and for the hexiamonds the regions each have 36 triangles. In this paper, the cases of regions where the number of holes is zero or one are examined.

“A Note on Digital Products,” by Stewart Metchette
 Digital products are multiplications where the factors and products together contain 9 or 10 unrepeated digits. There are seven different forms of such problems and this paper is a report of a computer search for solutions.

 “Some Oddities Among 7-Place Logarithms,” by Leslie E. Card
 This paper reports on an examination of the mantissas of the 7-place logarithms of the 5-digit numbers, where the search was for digit duplications as well as perfect squares and perfect cubes.

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