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 numbers along the leading diagonal total 58, which is
therefore the sum of each row and each column. We can now calculate
that the number to the left of 10 must be 20 and below that must be
7. Hence x=21
This problem is taken from the UKMT Mathematical Challenges.