Year 1966 - Volume 3
2020 - Present

N. Smythe

Two of the most important branches of modern mathematics are the fields of Algebra and Topology.

G. Szekeres

From the earliest times of its development, geometry has offered a number of difficult and quite puzzling problems which remained unanswered until comparatively recent times.

J51 Prove that a number which consists of 3n equal digits is divisible by 3n.

J31 Prove that, given five consecutive integers, it is always possible to find one which is relatively prime to all the rest.

J. D.
Dixon Before reading the rest of this article try to prove the following statements.
If a drawer contains a large number of socks of the same colour but two different sizes, and I take out three of the socks, then two of these will make a pair.

J61 A strip of pasture land is divided into three paddocks whose areas are 35 acreas, 10 acres and 65 acres.

J51 Prove that a number which consists of 3n equal digits is divisible by 3n.

The front tyres of a car last for 25,000 miles, the back tyres for 15,000 miles. After a number of miles the front and back tyres are interchanged. What is the maximum mileage obtainable without buying new tyres?

In 1782 the Swiss mathematician, Leonard Euler, perhaps the greatest mathematician of the eighteenth century, published a paper bearing the title "On a New Type of Magic Square".

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.

J61 A strip of pasture land is divided into three paddocks whose areas are 35 acreas, 10 acres and 65 acres.

Let a,b,c,d,e,f represent the integers 1 to 6 in some order. If a+b