Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
How many right-angled triangles are there with sides that are all
integers less than 100 units?
Two trains set off at the same time from each end of a single
straight railway line. A very fast bee starts off in front of the
first train and flies continuously back and forth between the two
trains. How far does Sidney fly before he is squashed between the
Each edge of a cube is coloured either red or black. If every face of the cube has at least one black edge, what is the smallest possible number of black edges?
This problem is taken from the UKMT Mathematical Challenges.