Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Can you work out the dimensions of the three cubes?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Two ladders are propped up against facing walls. At what height do the ladders cross?
The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
