Showing what's behind the curtain

Investigating the density of “bouncy” numbers.

Determining the number of solutions of the equation x^{2} − y^{2} − z^{2} = n.

Find Fibonacci numbers for which the first and last nine digits are pandigital.

Investigate the game of chance involving colored discs.

Find the kth element in a sorted list of radicals.

How many reversible numbers are there below one-billion?

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