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.

Investigate the optimum polynomial function to model the first `k` terms of a given sequence.

Determine if the origin is contained inside a triangle.

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.