Reilly's Cube

Posted on by Gabriel | 1 comments
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(Click to Enlarge)
Puzzle Crafthouse (also known as Creative Crafthouse) make at their Florida shop, extremely high quality wooden puzzles. From these designs, some are unique to them, so you won't find them anywhere else. The Reilly's Cube, invented by Mike Reilly is one of such puzzles.

The cube is comprised of eight pieces and each one has three faces with a diagonal combination of a pin and a hole. You have to match the pins and holes of all pieces to assemble the cube. The puzzle is made from Raintree hardwood and it's beautifully crafted with round edges. The outside surface of the cubes is also very smooth to touch, product of a high quality finish work.

(Click to Enlarge) - Pieces Grouped by  Identical Pairs  and Unique
I was very curious about this design when I first saw it, because I already had in my collection a similar puzzle, but less complex. The main difference is that the Reilly's Cube has a set of hole and pin in three faces, and the other one I have has only a pin or a hole in each of those faces. This one's definitely a lot more complex.

Knowing that I was before a much harder puzzle, I was expecting to spend a not so reasonable amount of time working on its solution. Not quite... It took me around 15 minutes or so to find the correct solution. Whether I had the help of lady luck or not, I'm not certain, but I might have to try and solve it again just to be sure. I did found a couple of times, partial solutions with just one piece left, though. This can be rather frustrating if it happens multiple times in a row.

(Click to Enlarge) - Half Disassembled
Despite having just eight pieces, and if you think about it, they are all corner pieces, it doesn't look too difficult. Just grab two pieces and see if they match. If not, grab another and repeat the process until you succeed, as there's now only seven pieces left to check. Simple, right? - Wrong. There's more to it than just meets the eye. The common mistake I found myself making, shortly after starting to solve it, was that I was only checking one of the faces as a possible match. Then it hit me: "If I rotate the piece around its corner vertex, there's a total of three possibilities for it to match the other piece". This may sound like an obvious assumption, but believe me, it's not that simple. Considering this, it comes to a total of several thousand possible combinations. I came to the total number of 6561 by considering three possibilities for each of the eight pieces (38). I could be wrong with my interpretation of the possibilities, so take this with a grain of salt, but I know the possibilities are in the several thousands.

In case you're wondering if the puzzle has more than one solution, which would explain the easiness to find one, according to the inventor himself, it's only one, therefore the question of luck might be valid. To consider that one solution, we have to carefully analyze the puzzle. One known fact is that there are three pairs of identical pieces and the remaining two are unique, so in total, there's five unique face patterns. To consider a unique solution we can't count as different, swapping places with two identical pieces, as the interlock pattern of pins and holes wouldn't suffer a change per se. Many possibilities, but only one correct.

Update: My fellow puzzle blogger, Brian Pletcher run this puzzle with Burr Tolls and found 3 unique solutions, so it might not be so difficult to find a solution after all, although it's still far from easy. Thanks Brian ;)

(Click to Enlarge) - Solved
Closing Comments:

The Reilly's Cube is a worthy addition to any puzzle collection. Its high quality alone is enough to convince anyone who appreciates a good puzzle, but the challenge involved is what makes it so special and appealing. Yes, it took me only 15 minutes to solve (with a bit of luck), and you know how I feel about puzzles that take so little time to be solved, but this is considered a hard puzzle (level 4/5), so I might not be so lucky next time. If you're into assembly puzzles, go for it, it's really worth it.

The Reilly's Cube is available at Puzzle Crafthouse for $17 USD.



Brian Pletcher said...

Indeed, finding one of the 3 solutions is still quite a feat with all the possible combinations. It took me quite a bit longer!

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