**Abstracts of the papers that appeared in “Journal of Recreational Mathematics, Volume 1, Number 4, 1968"**

Abstracts were not included with the original papers,
so all of the abstracts were written by Charles Ashbacher.

“Compounding a
Series,” by R. Robinson Rowe

**Abstract**

In this paper, a set of infinite series constructed from the products of the terms of two infinite series are briefly examined. All the series are the infinite sums of the terms of N / n!, where N is a simple series. Two of the examples are N = n – 1 and N = n(n – 1).

“Mathematicians and Mathematics on Postage Stamps,” by
William L. Schaaf

**Abstract**

Many nations have honored mathematicians and their work via designs on postage stamps and this paper contains a list as well as many quality images of the stamps.

“VF Numbers,” by J. A. Lindon

**Abstract**

VF stands for Visible Factor and a VF number is one where the digits exhibit in a clear way what some of the prime factors are. The most obvious such numbers are those that end in an even digit or 5. The prime factors of more complex VF numbers are recognized by the patterns that they exhibit.

“The Construction of Magic Knight Tours,” by T. H.
Willcocks

**Abstract**

A magic knight’s tour on a chessboard is one where the moves are numbered 1, 2, 3, ... and placed in the target square as the tour progresses and the result is a magic square. No known magic knight’s tour is known, although some semi-magic squares are given. Some of the mathematical techniques used to search for magic knight’s tours are presented.

“Recurrent Operations on 1968,” by Charles W. Trigg

**Abstract**

In this paper, several operations are performed on the number 1968 and then repeated several times. For example, the first one is the sum of 1968 and its reversal, where the reversal of that is then added to the sum.

“Reversal
Products,” by J. A. H. Hunter

**Abstract**

There are several pairs of two-digit numbers such that the product of the two is the product of their reversals. For example, (93)(26) = (39)(62). The theoretical methods used to identify all such pairs of numbers are given.

“Additional Mathematical Theory of Think-A-Dot,” by
Sidney Kravitz

**Abstract**

“Think-a-Dot” is a simple game based on a box with three holes on the top. Each of those holes are connected to a node directly beneath it and the nodes are designated A, B and C left to right. There are two nodes in the row underneath that one, labeled as D and E. The final row has three nodes, labeled F, G and H left to right. The nodes are connected in the following way, A to D, B to D and E and and C to E. D is connected to F and G and E is connected to G and H. Marbles are dropped in the holes and the marble will then follow a path to the bottom row.

There are switches on each connection so that the
marbles that reach a node will alternate on which path they take. The states of
the switches can be represented using zeroes and ones and the analysis is
determining the original state of the switches based on the drops of several
marbles and noting the bottom node they end up in.

“Patterns in Primes – Addenda,” by Leslie E. Card

**Abstract**

This paper lists all primes of 2 through 9 digits in length where the digits are consecutive. For the purposes of this analysis 9 and 0 are considered consecutive digits. Snowball primes are sequences of prime numbers where you start with an initial prime and generate additional primes by appending a digit on the low end. A list of snowball primes is also given.

“Strings of 7 and 8 Identical Digits in 2^n,” by Edgar
Karst

**Abstract**

A computer program was written to identify power of 2 where there is a sequence of 7 or 8 identical digits. A list of all such numbers for all n < 100,000 is given.

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