Volume 2


This article is concerned with the decimal expansions of numbers of the form $\frac{a}{b}$, where $a$ and $b$ are positive integers with no common factor except $1$, and $a$ is less than $b$.

Each answer is the recurring block of digits in the "decimal" expansion of a rational number $\frac{a}{p}$, using $S$ as the base of the number system.

The theory of combinatorial configurations abounds in unsolved problems, some of which can be stated in simple non-technical terms.

The word induction is used to describe two quite different processes for reaching conclusions.

J41 In the following equation: - $$ 29+38+10+4+5+6+7 = 99 $$ the left hand side contains every digit exactly once. Either find a similar expression (involving only $+$ signs) whose sum is $100$, or prove that it is impossible to do so.

J31 This is set again in the Problems Section.

Q.1 As for the Junior Section - see Parabola Vol. 2, No. 1.