Volume 36
, Issue 1


Several years ago, a friend of mine in Germany sent me a German 10-mark banknote. It was unusual in that it featured the image and the work of a mathematician.

There is a simple approximate rule of thumb used by investors and accountants to estimate the time taken in years, $n$; for an investment to double with an interest rate of $R%$; or indeed for a debt to double if left unpaid. One simply divides $72$ by $R$ to estimate the time in years.

Fairly early in your study of algebra, you meet one of the most useful of algebraic techniques, the difference of two squares which enables you to write, for example $x^2-1=(x-1)(x+1)$.

Q1064. The numbers $1, 2,\ldots , 16$ are placed in the cells of a $4\times 4$ table as shown in the left hand diagram below. One may add $1$ to all numbers of any row or subtract $1$ from all numbers of any column.

Q1057 Remember that a regular polygon has all sides equal and all angles equal.