Volume 30
, Issue 1

1994

The diagram on the cover of this magazine illustrates the reflecting property of the parabola: light rays which are parallel to the axis of the parabola are reflected by the parabola in such a way that they pass through a common point.

We'll look at a few two-player games, each of which can be broadly described as follows:

Mathematics can at times appear fairly dull and routine. Solving 30 quadratic equations, finding the hypotenuse of seemingly endless right triangles and differentiating even more functions can be downright boring!

Q.913 $S$ is a collection of numbers. At least half of the numbers in $S$ are even, at least two thirds are multiples of $3$, and at least six sevenths are multiples of $7$. Prove that at least one of the numbers in $S$ is a multiple of $42$.

Q.903 Find all positive integers $n$ such that $1+2+3+\cdots + n$ is a factor fo $1\times 2 \times 3 \times \cdots \times n$.