Great Z Cube
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The Great Z Cube is a very nice puzzle that I got in my latest Brilliant Puzzles order. Probably not so well known as the Great Y Cube, which to my knowledge is designed by Jean Claude Constantin and known simply as 25Y, but it's also equally hard - Extremely hard.
The puzzle has 25 identical Z-shaped pieces and the object is to build a 5x5x5 cube. There are also other less complex shapes that you can try to build, besides the cube and with less pieces, but I have been so immersed with the main goal that I haven't even tried those yet.
The design of the Great Z Cube is superb and the quality is very good as well. It comes in a die box with holes instead of dots and completely made of natural wood. Worth noting is that the configuration of the holes matches exactly the ones in a real die (adding opposite faces equals 7). The holes in the box have a darker contour to them, which looks great contrasting with the wood tone.
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The difficulty of this puzzle is one of the greatest that you can find in any assembly/packing puzzle. I haven't tried such a tough puzzle since Conway's Packing Box (Shipper's Dilemma). Suffice it to say, I haven't been able to solve it yet and I have little faith that I ever will. It doesn't seem so complex at first - How can 25 identical pieces be so damn hard to pack, right? - It just is... In fact, the identical nature of the pieces is what makes it so difficult, because there's literally millions of possibilities to stack the pieces the wrong way. I'm not sure the exact number of solutions, but I reckon even Burr Tools will choke trying to solve this. I have been trying to solve it, not exhaustively, for the past couple of months and the best I can do is to get all but one piece inside.
I'm sure there's a better strategy than just randomly stack pieces on top of others, and with a thorough mathematical analyses, one can easily find the right solution. I'll have to leave that to the experts, I'm afraid, as I lack the proper mathematical skills needed for this task. If by any chance someone finds the number of possible solutions, leave a message in the comments section, and I'll be sure to update the information on the post.
Update: Thanks to my fellow puzzle blogger, Kevin Sadler, I now know that the puzzle has four distinct solutions. There's still hope to find at least one... or not! Thanks Kevin ;)
Update: Thanks to my fellow puzzle blogger, Kevin Sadler, I now know that the puzzle has four distinct solutions. There's still hope to find at least one... or not! Thanks Kevin ;)
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The Great Z Cube is available at Brilliant Puzzles for about $15 USD.
Closing Comments:
Despite not having been able to solve it (...yet, hopefully), I have to say that the Great Z Cube is a fantastic puzzle. From the amazing design to the ultra challenging task, this is everything an experienced puzzler could ask for. Not for the easily frustrated casual puzzler.
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9 comments:
If the great packing puzzle genius called Gabriel can't do this one then I don't stand a chance! I have created a Burrtools file for it and it found that there are a total of 4 discrete solutions (i.e. no rotations or reflections). On my 4 year old Mac it took 25 minutes!
If you want the file then just drop me a line.
Kevin
PuzzleMad
Thanks for the info Kevin, and for the compliments, although I reckon I'm far from being a packing genius. I wish :P
Still, 25 minutes is a lot of processor power. This puzzle is a beast.
Cheers ;-)
You can use these pieces to make a much easier challenge, although you need one extra piece. Take 10 of these Z pieces, plus the 3D tetromino "screw" (which is a SOMA piece). This last piece is known as "the worm" and ideally colored green. Can you pack these 11 pieces into a 4x4x4 cube "apple" so that the worm is not visible? This is the puzzle I named "Hide the Worm", it is on puzzlewillbeplayed.com.
Sorry, you need 12 of the Z-pieces in the above puzzle. My 2 year old laptop solved the original problem in only 3.6 minutes ...
Thanks for the puzzle suggestion, George ;-)
Now, all I need is to find, within all these hundreds of puzzles, one piece with the same dimensions as the Zs :P
Or just try to leave a hole in the middle with that shape ...
That's brilliant! Why didn't I think of that?
Thanks, George ;-)
Hi, Gabriel, this puzzle you call the Great Z Cube is actually the 25 N's problem first solved by hand by David Klarner many years ago. It's built of N pentominoes. The Z pentomino looks different. So what you have here is actually the Great N Cube! And indeed, it is very, very hard.
Hi Kate,
Thank you for your info. That's very interesting. It's always good to know more about the puzzles I write. That's actually what they call it at Brilliant Puzzles, where I got it. I also saw it at Puzzle Crafthouse and they call it "Shipper's Dilemma Z". I guess at first sight, people think that it looks like a Z :P
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