Showing what's behind the curtain

Find the sum of all the natural numbers that are multiples of 3 or 5 using the inclusion-exclusion principal.

Calculate the sum of all the primes below two million.

Finding the number of blue discs for which there is 50% chance of taking two blue.

Find Fibonacci numbers for which the first and last nine digits are pandigital.

Find the greatest product of four adjacent numbers in the same direction in a grid.

Investigating the density of “bouncy” numbers.

Count how many numbers below a googol (10**100) are not “bouncy”

Count the ways a row measuring fifty units in length could be filled with blocks three units long. The blocks must be separated by at least one empty space.

Fill an empty row with blocks, a minimum length of 50 units, until the size of the row exceeds 1,000,000 units. The blocks must be separated by at least one empty space.

Count the number of ways a space 50 units long could be filled by tiles, homogeneously, measuring 2, 3 or 4 units long.