Let's place a cube on a table and flip it around a bit. In fact, flip it according to the following instructions:
- Flip forward twice.
- Flip left twice.
- Flip backward twice.
- Flip right twice.
Assuming no sliding has occurred (e.g. your flips were perfect along the edge), the cube will have ended its traversal with the same position and orientation it started with. Unfortunately, the perfectionist in me wants to press this further, so repeat the same process, but this time track the right face of the cube. Notice that it never touches the table?
What is the minimum number of flips required to ensure that every face touches the table at least once before returning the cube to its original position and orientation?
This puzzle is fun, and it inspired this one; be sure to show it some love!