Consider a 2 unit cube being composed of 8 unit cubes but with one removed. The blue circles are the centres of where the unit cubes may be placed. The unlabelled circle is the centre of the unoccupied space.
Any cube that is horizontally or vertically adjacent to the void (ie, connected by a straight line) may be moved into it (ignore gravity).
Your task is to report on three challenges:
1. The least number of moves to return the left graphic to that shown on the right, the "home" position.
After setting the HOME position:
2. The least number of moves to create a reflection of the shown left cube, ie, exchange the 2 with the 4 and the 6 with the void.
3. The least number of moves so that the sums of opposing vertices on the four major diagonals (red) is 9; allow the blank to be 8.
Having played with the interactive, have you found another challenge we could share in Comments?
Note: Please exercise the utmost of care with the interactive as programming does not trap careless entries, so on browser freeze you may need to wait about 30 secs for a pop-up dialog advice.