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 number may be divided up into 400 blocks of '12345'. The sum
of the digits in each block is 15 and there are 400 blocks. Hence
the sum of all 2000 digits is 400 x 15 = 6000.
Alternatively, the mean of each group of five digits is 3 and so
the mean of the digits making up the number is 3. Therefore the sum
is 2000x3 = 6000.
This problem is taken from the UKMT Mathematical Challenges.