Showing what's behind the curtain

Find the sum of the digits in 100!

Evaluate the sum of all amicable pairs under 10,000.

Calculate the total of all the name scores in the file of first names.

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

Find the first term in the Fibonacci sequence to contain 1000 digits.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle.

Find a quadratic formula that produces the maximum number of primes for consecutive values of n.

Find the sum of both diagonals in a square spiral.

Find the distinct terms in the sequence generated by a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?