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 ten numbers in the star total 75.
Each number appears in two "lines".
And there are five lines, making a total of 150. Which implies
the total for each line is 30.
This means that R+I=24 and therefore R=11 and I = 13 (or vice
If R=11 then N=12, H =10 and C=11 which is impossible.
If R=13 then N = 10; H = 12 and C= 9, which is correct.
This problem is taken from the UKMT Mathematical Challenges.