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.

Investigating the numbers which are equal to sum of their digits raised to some power.

Find the value of the first triangle number to have over five hundred divisors