Year 1967 - Volume 4
2020 - Present

We are all familiar with the fact that every real number can be expressed as a decimal (or has a decimal expansion). Such expansions are of course useful in allowing an easy comparison of the size of numbers, convenient addition, and so forth.

J81 The lengths of the sides of a right angled triangle are natural numbers. The length of one side is 14. Find the lengths of the other sides.

J71 Find a four digit number which on division by 149 leaves a remainder of 17 and on division by 148 leaves a remainder of 29.

To grasp the nature of the contents of this article, consider the four figures in the diagram.

J91 (i) Find all whole numbers such that when the third digit is deleted, the resulting number divides the original one.

J81 The lengths of the sides of a right angled triangle are natural numbers. The length of one side is 1414. Find the lengths of the other sides.

Two runners start on a straight one mile race track. The slower runner S is given a handicap and starts first.

A theorem of twentieth century mathematics which must surely earn a place in any list of the great theorems of mathematics, is the theorem of Kurt Gödel concerning the existence of undecidable statements in formalised arithmetic.

J101 In n is a positive integer other than 2,32,3 or 55, any square can be dissected into n smaller squares.

J91 (i) Find all whole numbers such that when the third digit is deleted, the resulting number divides the original one.

If a,b,c, are any three numbers show that

${a}^{2}+{b}^{2}+{c}^{2}\ge ab+bc+ca$