Volume 20


Most of us will have a tree in our homes over Christmas. To the mathematician, a tree is a special type of graph.

Suppose you were required to find the minimum value of $$f(x) = x^4 - 15x^3 + 72x^2 - 1135x \text{ for } 1 \leq x \leq 15.$$

Mathematicians love formulae. Nothing pleases a mathematician more than to come up witha nice simple formula which solves a problem or summarises a result.

People came from all over the world to Australia to talk together and learn from each other about how best people from age 4 to infinity can learn mathematics and enjoy using it.

Q.612 From a point $P$ inside a cube, line segments are drawn to each of the eight vertices of the cube, forming six pyramids each having $P$ as the apex and a face of the cube as the base.

Q.588 We are given a set of 201 different numbers with the property that the sum of any 100 of them is less than the sum of the remaining 101. Prove that all of the numbers are positive.