Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?
Instant Insanity
Age 11 to 18 Challenge Level:
These are the nets of 4 cubes. Build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.