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
Four wiggles are the same as three woggles; two woggles are the same as five waggles, and six waggles are the same as one wuggle. Which is the smallest:
1 wuggle, 2 woggles, 3 waggles or 4 wiggles, or is there more than one with the same value?
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.