John M. Blatt
Electronic Brains, i.e., high speed electronic digital computers, are producing major and far reaching challenges in our society. This article aims to tell you what an electronic computer is.
J21 In a box there is a number of balls c of different colours. What is the smallest number of balls for which we can say that, however the colours are distributed, there is at least one set of s balls of the same colour? Justify your statement.
J11 A drill squad contains mn people, arranged in m rows of n people. In each of the n columns so formed, the lightest person is noted, and the heaviest of these is found to be Smith.
C. Cox
Doubtless the above heading will be to most of our readers as cryptic as the meaning as some of the more outlandish examples of the so-called "Strine language" which have recently appeared in the newspapers.
G. Szekeres
In the October 1964 issue of Parabola, the article on the Four Color Problem called your attention to the existence of numerous unsolved mathematical problems which can be stated in quite simple non-technical terms.
J31 Prove that, given five consecutive integers, it is always possible to find one which is relatively prime to all the rest.
J21 (i) In a box there is a number of balls c of different colours. What is the smallest number of balls for which we can say that, however the colours are distributed, there is at least one set of s balls of the same colour? Justify your statement.
X is a point inside a polygon and AB is one of the sides of the polygon. Show that the perimeter of the triangle ABX is shorter than the perimeter of the polygon.
C. D. Cox
This article is concerned with the decimal expansions of numbers of the form a/b,where a and b are positive integers with no common factor except 1, and a is less than b.
Each answer is the recurring block of digits in the "decimal" expansion of a rational number a/p, using S as the base of the number system.
G. Szekeres
The theory of combinatorial configurations abounds in unsolved problems, some of which can be stated in simple non-technical terms.
M. Arbib
The word induction is used to describe two quite different processes for reaching conclusions.
J41 In the following equation: -
29+38+10+4+5+6+7=99
the left hand side contains every digit exactly once. Either find a similar expression (involving only + signs) whose sum is 100, or prove that it is impossible to do so
J31 This is set again in the Problems Section.
Q.1 As for the Junior Section - see Parabola Vol. 2, No. 1.