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?
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Can you make a tetrahedron whose faces all have the same perimeter?
Each edge of the cube borders borders two faces. As there are six faces, a minimum of three black edges will be required.
The diagram on the right shows that three black edges is enough.
This problem is taken from the UKMT Mathematical Challenges.View the archive of all weekly problems grouped by curriculum topic