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 golden ratio.
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 versa).
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.