Solution to Rubik’s Cube Riddle.
There are 8 corner pieces each one can be in any corner => 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 possibilities.
The first 7 corner pieces can be oriented in three different directions but the last one is fixed => 3 * 3 * 3 * 3 * 3 * 3 * 3 * 1 possibilities.
There are 12 side pieces the first 10 can be anywhere but the last two are fixed => 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 1 * 1.
The first 11 sides can be oriented in any direction but the last one is fixed => 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 1.
The centers are all connected and direction does not matter since the faces are a solid color (recall that we are talking about a classic Rubik’s Cube with no logo on any face) => one possible way.
(8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) *
(3 * 3 * 3 * 3 * 3 * 3 * 3 * 1) *
(12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 1 * 1) *
(2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 1) *
1
=
8! * (3^7) * (12!/2) * (2^11) * 1
=
43,252,003,274,489,856,000 possible configurations, of which one is correct and
43,252,003,274,489,855,999 are incorrect.
As you can see the number is greater than 10,000,000 and the last three digits are the same.
(The number is 43 quintillion, 252 quadrillion, 3 billion, 274 million, 855 thousand, 999)