Volume 3
, Issue 2


Before reading the rest of this article try to prove the following statements.

  1. 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 $3^n$ equal digits is divisible by $3^n$.

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?