Here is your next brain basher: the iQube!
The iQube can be described as the fusion between two of the most popular puzzles: the 130 years old Sliding Tile Puzzle and the 30 years old Rubik's cube. It was created by a Swiss mathematician, Dr Mayoraz, to be as elegant and conceptually simple as its illustrious ancestors, while remaining a very challenging puzzle. It consists of 8 rolling cubes on a 3-by-3 grid that need to be placed in a specific position and orientation.
The iQube basics
Imagine a single cube. It can be oriented in 24 ways: 6 ways to pick the top face, and 4 ways to pick the front face for each top face. Playing with a dice on a table, you will find out that only 12 of these 24 orientations can be reached by pivoting the dice on the table and bringing it back to the starting location. For each orientation, the one that would be obtained by turning the dice by 90 degree leaving two opposite faces unchanged, cannot be reached by rolling moves.
How many possible configurations does the iQube have?
The number of possible configurations of a 3-by-3 iQUBE is:
9! * 12^8 / 2 = 78,015,878,922,240 = 7.8 * 10^13 or 78 trillions!
This number of configurations grows quite rapidly with the size of the game. A 4-by-4 iQUBE takes
16! * 12^15 / 2 = 161,178,937,602,476,749,086,523,392,000 = 1.6 * 10^29
configurations, in other words 161 octillions, 161 thousand quadrillions, or 161 quadrillards.
However, the number of configurations is not the main criterion to determine the difficulty of a puzzle. A puzzle can have a very simple algorithm to find, at each step, a move that brings it closer to the solution. Hence, the total number of configurations is not a barrier for an easy resolution of the puzzle.
The beauty of the iQube is that even a 2-by-3, with 5 cubes (i.e. 5 moving pieces only), has "only" 6! * 12^5 / 2 = 89,579,520 configurations, but is already very challenging to solve.
Unscramble the iQube for lots of fun! Challenge your friends to win the Grand Master title and enter the Hall of Fame!