A standard 3x3x3 Rubik's cube has 43 trillion possible scrambles!

And any 3x3x3 cube can be solved in 18 or less moves. The minimum number of entries to have pre-filled in a Sudoku such that there is only one solution to it is 17. As an application of the Borsuk-Ulam Theorem, given any two finite, closed, two-dimensional shapes, there exists a straight line which bisects both of them. Given any three finite, three-dimensional objects, there exists a plane which bisects all three. Two of the most difficult open problems in mathematics are as simple as:

Partition Problem: How many ways can an arbitrary integer be written as the sum of positive integers? (i.e. 4 = 1+1+1+1, 1+1+2, 1+3, 2+2, 4). The answer has been shown to strongly correlate to fractal geometry.

Collatz Conjecture: Take any positive integer. If it's odd, divide it by 2. If it's even, multiply it by 3, and then add 1. Continue doing this, depending on whether or not it's even or odd at each successive step. The conjecture is that yes, eventually this algorithm will reduce the number to 1. Paul Erdos, considered by many to be the greatest mathematician of the 20th century, considered it to be the most difficult problem ever conceived.

Some random facts:

Edison did not invent the light bulb.

Morse did not invent the telegraph.

Darth Vader never said, "Luke, I am your father."

The evil queen never said, "Mirror, mirror, on the wall."

Sherlock Holmes never said, "Elementary, my dead Watson."

Captain Kirk never said, "Beam me up, Scotty."

Possibly well-known on this board, but Franz Liszt was Richard Wagner's stepfather.

Anybody who is a member of a piano forum and believes that Saint-Saens is an obscure composer is an idiot.