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 $3^n$ 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?