The 2×2 Rubik’s Cube, also known as the Pocket Cube, has a total of 3,674,160 possible combinations.
To understand how this number is derived, it’s important to consider that a 2×2 cube consists of 8 corner pieces, each of which can be oriented in 3 different ways. However, not all orientations are possible when the cube is fully assembled. The total possible arrangements can be calculated by taking into account both the permutations of the corner pieces and their orientations.
Specifically, the formula for finding out the number of unique positions for a 2×2 cube is:
Total Combinations = 8! / 1 * 3^7
Where:
- 8! (factorial) accounts for the arrangement of 8 corners.
- 3^7 represents the orientation possibilities for these pieces, with the orientation of the last piece being dependent on the first seven.
When you calculate this, you get to the total of roughly 3.67 million combinations. This vast number means that even though the 2×2 cube is a simpler version of the classic Rubik’s Cube, it still poses a significant challenge to those trying to solve it!