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.

Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed 4 million.

Find the largest prime factor of a composite number.

Find the largest palindrome made from the product of two 3-digit numbers.

Find the smallest number divisible by each of the numbers 1 to 20.

Find the difference between the sum of the squares and the square of the sum.

Find the 10001st prime.

Discover the largest product of thirteen consecutive digits in the 1000-digit number.

Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.