Showing what's behind the curtain

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

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

How many circular primes are there below one million?

Find the sum of all numbers less than one million, which are palindromic in both base 10 and base 2.

Find the sum of all eleven primes that are truncatable from both left to right and right to left.

What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, … ?

Find the sum of all pandigital numbers with an unusual sub-string divisibility property.

Find the first four consecutive integers to have four distinct primes factors.