Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

Angus gives a very good account of how matrices, probability and graph theory are used in his solution.

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.