An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
The diagram shows two rectangles which enclose five regions.
What is the largest number of regions which can be enclosed by any two rectangles drawn on a sheet of paper?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.