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Puzzle Games (Games) News

Rubik's Cube World Championships 202

Posted by samzenpus from the the-thrill-of-athletic-competition dept.
cadaeibfed writes "Coinciding with the 25th anniversary of the iconic puzzle's introduction to the world was the second Rubik's world championship, held in Orlando, FL this weekend. Competing under official World Cube Association rules, competitors from around the world vied for recognition in this nerd olympiad. Some new world records set include the 4x4 solve, solving using only feet, and blindfolded solving. The winner, Jean Pons of France, finished with an average solution time of 15.10 seconds on a standard 3x3 cube. Here are the full results."
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Rubik's Cube World Championships More

Rubik's Cube World Championships

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  • Wow. (Score:5, Insightful)

    by Capt'n Hector ( 650760 ) on Thursday November 10, 2005 @06:41AM (#13996422)
    15 seconds is rather insane. Yes, I know there are tricks and that there is a technique that will produce a solution. But they require quite a number of steps, all of which take time. Not to mention the need to recognize, store and process the locations of 27 color/point pairs for the win. Just... wow.

    • Re:Wow. (Score:5, Funny)

      by slack0ne ( 902749 ) on Thursday November 10, 2005 @06:46AM (#13996430)
      I found it easier to peel the stickers off. It took me weeks to actually solve one back in the day...

      • Re:Wow. (Score:5, Funny)

        by metricmusic ( 766303 ) on Thursday November 10, 2005 @06:53AM (#13996453) Homepage Journal
        pfftt. I remove the cover and unscrew the thing. Haven't made it under 15 seconds yet putting it back together *looks at mess in the corner*
        • What's really fun is taking someone's cube apart and putting it back in a situation that is unsolvable. Like just rotating one corner. Then, mix it back up again, so they don't see that's it's messed right away. If they don't catch on, they could be trying to solve it forever.
        • pfftt. I remove the cover and unscrew the thing.

          Am I the only one to apply the brute force tactic? With enough force you can expand the gaps of most cubes to the point that a corner peice can be removed, from then on they dismantle easily.

          I did eventually get a guide and solve it with instructions.

      • Re:Wow. (Score:4, Funny)

        by Funakoshi ( 925826 ) on Thursday November 10, 2005 @09:01AM (#13996749)
        average solution time of 15.10 seconds on a standard 3x3 cube

        If I could move my hands that fast I'd never leave the house...
      • Everyone's dad has made the 'peel the stickers off and put them back' joke on seeing a Rubik's cube, usually more than once. Among other things, it's not usually possible. On most cubes, the stickers tear or come up in layers or lose their adhesion.

        If you want to get a cube in order, the sub-cubes actually pop out quite easily if you twist it right, and you can without difficulty fit it back together in the proper order.
      • One word: Spraypaint.

    • Re:Wow. (Score:2, Interesting)

      by Anonymous Coward
      I looked about resolution techniques a while ago. Besides the different algorithms, some of them even grease the cube so it turns faster!

    • Re:Wow. (Score:3, Informative)

      by fm2503 ( 876331 )
      Found some videos at http://www.solvethecube.co.uk/ [solvethecube.co.uk]
      Follow the "videos" link at the top, towards the bottom
      of this page is a 13.86 second solve.

    • Re:Wow. (Score:2, Interesting)

      by ockegheim ( 808089 )
      Back in the day, when I memorised a particular method, it only fixed one or two of the cubes at once. Can these guys (and girls?) just look at the cube and work out what's necessary to solve it in one big conceptual tour de force? Or do they still have (albeit more sophisticated) intermediate steps?
      • Basically they figure out the whole thing and do it all at once. You get to look at it for quite a long time before you actually start moving the pieces around. They only time you from when you actually start moving pieces. I think the competition would be much more of a real competition if they timed from when you first saw it. It mostly comes down to who can manipulate it the fastest, and not who can actually solve it the fastest.
    • Check it out [speedcubing.com]. It's pretty unsettling watching someone solve the cube that fast.
    • If you want something hard then try a 20x20x20 cube
      http://www.speedcubing.com/chris/20cube.html [speedcubing.com]
      • I've tried a 4x4x4 cube after I got bored with the 3x3x3. Once you figure out the patterns (or look them up online) it gets really easy, and you can do it in about 5 minutes, without even trying to go fast. The 4x4x4 is much harder, and doesn't really work the same way as a 3x3x3. I've decided that i'm not going to look up the answers with the 4x4x4, so it's taken me a long time, and I still haven't figured it out actually, and it has been a few months.
    • Yes, but can they do it blindfolded... dun dun dun!

  • Cube Theory = Group Theory (Score:5, Interesting)

    by ankarbass ( 882629 ) on Thursday November 10, 2005 @06:53AM (#13996449)
    While just solving the cube quickly may be interesting. I think it's far more interesting that the cube movements can be thought of elements of a subgroup of a very large permutation group, S48 to be precise. If you have some math background and like abstract things you might want to take a look at Adventures in Group Theory : Rubik's Cube, Merlin's Machine, and Other Mathematical Toys [amazon.com] which, despite the title is a fairly serious little math book.
    • Damn.
      SO3 groups for quantum mechanics were nasty enough, i dont really want to touch a S48, even if its disguised as a toy :D
    • While just solving the cube quickly may be interesting. I think it's far more interesting that the cube movements...


      Yeah, that's what all the slow cubers say...
      • Well, you do deserve a couple of funny mods, if I had one I'd give it to ya. Well, I suppose not since I already posted.

        Never the less. I was really just being polite. I don't think solving the cube quickly is interesting at all. I only think the cube is interesting in any sense because it lends insight into group theory. Developing theorems and proving them takes work and has depth. Twiddling the puzzle quickly is a bit like masturbation, it has its own reward but there's nothing particularly special about

  • Friend of mine can do this (Score:5, Interesting)

    by raoul666 ( 870362 ) <pi@rocks.gmail@com> on Thursday November 10, 2005 @06:54AM (#13996454)
    Young guy, mid teens. I first saw him do it at a poker tournament I was running. We were using the cube as the dealer button, so whenever it go to him, he'd start working on it. By the time the next hand had started, even if we hadn't even seen the flop, it'd be solved and back on the table. He was probably doing it in 35-45 seconds, but still, it was amazing to watch.

    • Re:Friend of mine can do this (Score:5, Informative)

      by gkhan1 ( 886823 ) <oskarsigvardsson@@@gmail...com> on Thursday November 10, 2005 @07:55AM (#13996580)
      It's really not that hard to solve a cube in around a minute. You can learn the basic, layer by layer method in about a day, and after a few more, you've got it down to under two minutes. Then you just keep doing it to get it too about a minute, and all your friends will be amazed!! (it's seriously fun to do it on a subway, everybody looks in amazement :D) Too get a time consistantly under a minute, you probably need to learn more advanced methods, like for instance the petrus system [lar5.com] or the friedrich system [binghamton.edu]. Variations on the latter is what all the pros use, but it is murder to learn, you have to memorize around 100 algorithms!!! Myself, I've gotten down to about 30 secs using the standard, layer-by-layer and some of friedrich's algorithms. It really is alot of fun.
      • The fact that there are multiple different "systems" to solve it just scares me. For me, the only "system" that consistantly works is to peel the stickers off and put them back on. But even then I occasionally can't solve it.
      • I have a problem that I'd like to see solved - the standard Rubik's cube you get at a toy store is pretty cheap - the stickers come off too easily. I started solving the cube a few months back, and I'm still nowhere near good yet, but my stickers have fallen off already. Do you get your cubes from a certain place, or do you just spend the $5 every few months?
        • Yeah, the stickers wear out pretty fast, and you have to replace them if you do any semi serious cubing.

          I do mine myself, but if you're not DIY inclined and/or want professional quality stuff, you can order from Cubesmith [cubesmith.com].

  • Second prize (Score:5, Funny)

    by jurt1235 ( 834677 ) on Thursday November 10, 2005 @07:00AM (#13996462) Homepage
    The second prize is an all day massage to get the RSI down a bit.

  • Amateurs. (Score:2, Funny)

    by Quaoar ( 614366 )
    None of them are up to the challenge of the 1x1 cube!
  • I'm disappointed that my favorite solver, Shotari Makisumi, only placed third. Them's the breaks. I've seen him solve, and as is true for anyone in his league, it's incredible.

  • Save this one for your next party (Score:3, Funny)

    by gringer ( 252588 ) on Thursday November 10, 2005 @07:08AM (#13996477)
    For those folks who are interested in dressing up all nerdy, you could try making your own functional Rubik's Cube Costume [flickr.com]. It appears to only have one axis of rotation, but I'm sure someone could work a way to get the other axis rotation working as well.

  • Here's something on the origins of the thing, and (Score:5, Interesting)

    by putko ( 753330 ) on Thursday November 10, 2005 @07:11AM (#13996485) Homepage Journal
    http://inventors.about.com/library/weekly/aa040497 .htm [about.com]

    The history of it is interesting. It seems multiple folks developed similar items around the same time.
  • I remember the craze. I got one cube, my brother too, my friends too, almost every pupil had one. I never could do more than two lines but some could in 1'30. There was different types, the official and some imitations of quite bad quality. There was also similar games (cylinders, ...). Fun to see the competition continues.

    • Re:So 1980 (Score:2, Interesting)

      by CortoMaltese ( 828267 )

      I remember the craze. I got one cube, my brother too, my friends too, almost every pupil had one. I never could do more than two lines but some could in 1'30.

      My observation was that most people eventually learned how to solve it - one way or the other. In general, the boys usually used a screwdriver, while the girls just moved the stickers.

      In fact, I came across a dusted 20-year-old cube this summer, and finally learned to solve it the right way for the first time. It was actually quite satisfying no

      • > ...boys usually used a screwdriver, while the girls just moved the stickers...

        What a profound observation about the nature of the universe.

      • My observation was that most people eventually learned how to solve it - one way or the other. In general, the boys usually used a screwdriver, while the girls just moved the stickers.

        I have one where the colors are printed on it. Nothing for girls, I guess.

  • how... (Score:1, Interesting)

    by drewxhawaii ( 922388 )
    ...exactly, does one solve a rubiks cube while blindfolded?

    braille, perchance?

    enlighten me

    • Re:how... (Score:5, Informative)

      by kylemonger ( 686302 ) on Thursday November 10, 2005 @07:23AM (#13996513)
      You are given the scrambled cube to study for a time and then are blindfolded. You have to perform all the moves to solve the cube while blindfolded.
      • If you're one of the guys solving it in 15 seconds (unblindfolded) I'd assume you've effectively memorized and mapped out all the necessary moves before they put the cube in your hand.

        But I think you impress more chicks by saying you can do it blindfolded

        • Re:15 seconds (Score:3, Interesting)

          by dim5 ( 844238 )
          Actually, the Fridrich method (which is what most people with times under 30 seconds use), requires 4 looks, and only the first step requires on-the-spot thinking to plan out:
          1. Get the edge pieces of the top layer in place (7-10 moves, different every time)
          2. Put the corner pieces of the top layer and edge pieces of the middle layer in place (1 of 22 algorithms, all memorized)
          3. Get all of the bottom layer to be one color (1 of 41 memorized algorithms)
          4. Get all of the pieces of the bottom layer into the right po
    • You look at it before for X seconds to try and memorize the position of everything, then blindfold and go!
    • Blindfolded solving involves studying the cube first, memorising the layout, then being blindfolded and solving the cube. Must require a damn good memory as long as a fair whack of logic!
    • my guess is that at first you look at the cube and memorise it. then you put the blindfold on and start solving it. so you have to keep track of all the colors in your head
    • Its all about memorizing a routine. I bought a book and learned what to do. You set one corner up correctly and then every move after that is performed in sequence until it is solved. Don't remember how long it took to solve it but I would say maybe about a minute. Once you solve it though, it got boring. I've still got the cube, but I don't have the book anymore. So without the book, its taking me 20+ years and I still haven't solved it.
    • Watch and learn [collegehumor.com] :-)

  • Fun with Rubik's Cube geeks... (Score:5, Interesting)

    by Geeky ( 90998 ) on Thursday November 10, 2005 @07:32AM (#13996535)
    1. Take cube apart.

    2. Put back together in random order so it can't be solved.

    3. Give to cube geek.

    4. Watch them sweat as their moves don't work.

    5. .. er, profit?

    Of course, these serious cubers would probably take one look at the cube and immediately tell you it had been tampered with.

    Sad news. I'm old enough to remember these when they first came out. I feel very, very old. Anyone remember Rubik's snake?

    • The snake was more fun the the cubes. And then they came out with all these silly things in different polygons, cylinders, spheres. It got old pretty fast.

      Pocketeers were a much better toy craze :-)
    • Even non-serious solvers who just solve using the simple method (which ANY serious slashdotter could easily learn in an hour or two) would recognize it as unsolvable after only a couple of moves.
      • Back in the day, I used to be the local cube geek (although with times around the 1:30 mark I'd be toast nowadays). One day I was at my cousin's house, and she gave me her cube to solve. I got about three moves into it when I realized something was very, very wrong.

        Turns out her parents had bought her a cheap knockoff cube, and the colors were all off--blue opposite red, etc. It took me a good five minutes to solve the damned thing.
    • If you put it together in random order, you'll still have a chance of 1/6 to get a solvable cube. A better way is to just take the normal (solvable) cube, take one piece (edge or corner) out, and put it back turned around. This will give you a guaranteed unsolvable cube.
    • The snake is fun - I still have my original, and also about a dozen very recent knockoffs that I picked up while at a dollar store.

      My favorite was the pyramid. I got to where I could solve that one in about 15-20 seconds. Not nearly as tricky as the cube to do, but it was good for winning beers back in college :)
    • Snakes ruled. How else would I have learned what a rhombicuboctahedron was? Which led me to other shapes, including the granddaddy of them all: the rhombitruncatedicosododecahedron. [rhombitrun...hedron.com]. (Warning: audio.)

      Pyramynx was also fun and much easier to solve. I could never wrap my head around the cube.
    • Put back together in random order so it can't be solved. Watch them sweat as their moves don't work.

      Sweat? I always laughed. You wouldn't believe how many screwed up cubes people gave me. I'd say, "You swapped some stickers didn't you?" and they'd always lie. Sometimes more than once. Then I showed them how the cube is made out of solid peices with once peice having the same color on two sides and they'd admit they swapped stickers because they just wanted to finish one side. Messed peices was rar
    • No need to know how to solve a cube or even try a single move before spotting a problem.

      The central squares on each face of the cube cannot be moved, only rotated. So, for example, if two of them are same color, the cube has been tampered with.

      Anyway the surest way is to look at those "opposing" colors. IIRC most cubes had the green face opposed to the blue one, white face to yellow, orange to dark red...
      anyway one can just look at the cube's central squares and see what the opposite colors should be if the

  • the timing system... (Score:5, Informative)

    by ragahast ( 879945 ) on Thursday November 10, 2005 @07:36AM (#13996539)
    ...is pretty awesome. They have each of the competitors solve their cubes, then follow the same steps to mix it up. Then each of the competitors places their cube on a central pad and their hands on two pads to either side. Each person has a their own digital timer, which will be activated when they lift their hands from the pads. A ref blows a whistle, the competitors lift their cubes and solve and then stop their timers by dropping the solved cube on the central pad. The best time I've seen is 12.3 seconds. Frickin' ridiculous. (I was working during the Caltech winter 2005 competition)

  • Videos (Score:3, Informative)

    by vagabond_gr ( 762469 ) on Thursday November 10, 2005 @08:17AM (#13996637)
    Take a loot at the videos on the following page [cubewhiz.com]. 3x3x3 in 20.55, still amazing!

  • Cube can be solved in 29 moves or less (Score:4, Interesting)

    by richieb ( 3277 ) <richieb@gmai l . com> on Thursday November 10, 2005 @08:21AM (#13996651) Homepage Journal
    The cube can be solved in 29 or less moves. Here is a reference [wolfram.com].

    I originally worked out the solution to the cube when the Scientific American article by Douglas Hosfstader appeared. I never got my speed much below one minute. I did manage to win a T-Shirt at a Cube contest though - a contents with several hundreds of participants...

  • True Story (Score:5, Informative)

    by krygny ( 473134 ) on Thursday November 10, 2005 @08:25AM (#13996657)
    I was fortunate to be one of the first people in the world to play with a Rubik's Cube. In the late '70s, I worked with a woman who's husband worked for the Ideal Toy Co. in Jamaica, NY (that's Queens). She brought a secret prototype into work and all the engineers and technicians couldn't stop fighting over this thing; trying both to solve it and to figure out the mechanism. It was supposed to be hush-hush and she could have gotten her husband in trouble, but when she realized how obsessed we all were with it, she was afraid it would disappear.

    It was only a few months later that they hit the market and I couldn't wait to get my hands on one. I eventually got to the point of being able to solve it consistently within a half hour or less. Then I lost interest in the challenge.

    I also remember a Scientific American cover story (c. 1980), where I finally learned about the mechanism, disassembly and reassembly. Of course, they also discussed algorithms, but I wasn't interested in that. I never use cheats. Takes most of the fun out.

    • Re:True Story (Score:3, Insightful)

      by imsabbel ( 611519 )
      Cheats? Solving via algorithms isnt cheating, its using your brain.
      Solving WITHOUT algorithms (even unconscious) is just the 100k monkeys approach...

      • Re:True Story (Score:3, Interesting)

        by Council ( 514577 )
        Solving WITHOUT algorithms (even unconscious) is just the 100k monkeys approach...

        Last time I checked, which was a couple years ago, I could solve any rubik's cube in roughly 1:30 or less.

        That said, one thing I've never really understood was people who say "oh, yeah, took me weeks and I only ever solved it once or twice."

        Trial-and-error, with a very few exceptions for very clever people, just doesn't seem realistic. When you get it to the point where you have nearly every piece done, there are generally lo

        • Re:True Story (Score:3, Informative)

          by 2short ( 466733 )
          "one thing I've never really understood was people who say 'oh, yeah, took me weeks and I only ever solved it once or twice.'"

          They are lying. They never spent a fantastic amount of time doing the cube, but it was a big deal back when, and everyone had one and probably many of their friends could solve it (having read the solution in a book). The idea of having solved it "once" seems plausible, not terribly baostful, a perfectly innocent little white lie. But serious cubers know it's BS. Claiming to have

        • Re:True Story (Score:2, Informative)

          by Kaki Nix Sain ( 124686 )
          I solved it in a few days --four , I think--.

          It happened after I first watched the movie Pi one night. I was walking around wondering how much brain-time I've wasted, what I could do if I tried, etc. I saw that someone in the apartment complex had a cube. I asked nicely and borrowed it.

          First, I did an algorithm for one layer, that was done and written out before I slept that night. The next couple of days I fiddled around with it constantly (carried it around everywhere) and came up with various notat

      • ... I apparently had developed my own algorithm, sub-consciously. Maybe not very efficient, or perhaps PROficient, and I couldn't express it in a formula, but it was reproduceble. I just didn't want to learn somebody else's algorithm. That's what I meant by "cheat". No fun, or adventure, or mental exercise in it.

  • actually (Score:2, Insightful)

    by AntiNeutrino ( 63802 )
    don't you mean ... a 3x3x3 and a 4x4x4 cube?
    • If it's a cube, you only have to specify one dimension. But it sounds silly & confusing to say a "3 cube," so people say "3 by 3 cube," and notate as 3x3 cube.

  • Speed cubing pioneer (Score:2, Interesting)

    by Anonymous Coward
    Jessica Fridrich has kindly published her notes on the process of speed cubing: http://www.ws.binghamton.edu/fridrich/cube.html [binghamton.edu]

    Watch her solve cubes!
    http://www.ws.binghamton.edu/fridrich/video.html#l ast [binghamton.edu]

  • Been There, Done That (Score:4, Interesting)

    by ajs318 ( 655362 ) <sd_resp2@@@earthshod...co...uk> on Thursday November 10, 2005 @09:13AM (#13996802)
    I remember the Rubik's Cube from first time around. I knew a few different "complete solutions" -- depending on the initial state, one might be significantly faster than the others. I rarely needed longer than a minute. My friend and I built a fake "cube solving machine" from an old washing machine box, with a hatch tor loading the "scrambled" cube, a drawer for removing the "solved" cube -- and me inside with a bicycle lamp, and a cassette recorder for sound effects!

    Obviously you cannot have just five faces "solved", but it is also not possible to have just four faces "solved". You can render a cube insoluble by reversing one of the two-sided pieces, or rotating one of the three-sided pieces. The easiest way to split a cube apart is to rotate one side by 45 degrees, and push the protruding corner piece until its latch pops out. Reassembly is done by inserting one of the two-sided pieces last. I have also seen evidence of very bad sticker-peeling, where one of the two-sided pieces carried the colours of opposite centres and one of the three-sided pieces carried the same colour on each face!

    Rubik's Snake was boring: all you could really make with it was a dog and a football.

    Rubik's Magic was a little better, because there were two different puzzles on the go: arranging the eight hinged squares to create a shape {4 x 2 rectangle, 3 x 3 square with corner missing, or various solids} and orientating the components of the shape to produce a picture {three separated rings on the rectangle, or three linked rings on the 3-3-2}.

    I remember Rubik's Clock best of all. I was given one of the first ones in the country, which my parents got from a toy shop in Yorkshire. It took me nearly two days to crack it -- and then I could not believe just how daft I had been in not spotting it sooner. The secret is to ghea gur pbeare onpxjneqf, ratntr vgf ohggba naq ghea rirelguvat sbejneqf gbtrgure.
    • I remember the Rubik's Cube from first time around. I knew a few different "complete solutions" -- depending on the initial state, one might be significantly faster than the others. I rarely needed longer than a minute.

      I never managed to get much faster than two minutes, since I could only easily think a few moves ahead; most of the people I know that are much faster than me pretty much have the whole series of moves figured out in their head right away.

      Still, I had to prove to my coworkers a few weeks

    • Re:Been There, Done That (Score:2, Informative)

      by DavidB ( 23006 )
      > Obviously you cannot have just five faces "solved", but it is also not possible to have just four faces "solved".

      Not true. There are many examples, but here are a couple examples sequences that leave only two faces scrambled:

      1) F2 R2 F2 R2 F2 R2
      2) R2 U' F2 R2 F2 U2 R2 F2 R2 U' R2

      > The easiest way to split a cube apart is to rotate one side by 45 degrees, and push the protruding corner piece until its latch pops out.

      That's a pretty rough way to do it. You're better off turning the top face by 45 de
    • The secret is to ghea gur pbeare onpxjneqf, ratntr vgf ohggba naq ghea rirelguvat sbejneqf gbtrgure.

      Crap, does anyone know Welsh?

  • 14 seconds pfft? (Score:3, Funny)

    by AviLazar ( 741826 ) on Thursday November 10, 2005 @10:18AM (#13997158) Journal
    I've been working on it for 15 years! Now that's amazing.
  • Wonder what happened to that Japanese kid who solved it in 12 seconds in 2003 (2004?) There's a really cool video of it here somewhere. http://cubefreak.hp.infoseek.co.jp/ [infoseek.co.jp]
    • He's ended up third in the big competition, and placed high in several of the others. Search for Shotaro on the result page.I doubt it helped to have one (or more) film teams following your every action and word during the entire weekend...
  • The 3x3 cube is a reasonable challenge, but anyone can learn to solve it without having to memorize any special "moves". I can solve it consistently in about 5-7 minutes just by working through it. (There are many, many methods.) It's one of those things that can look quite difficult at first, but when shown how to do it, you are quickly surprised at how easy it really is. I'd compare it to juggling 3 balls at once -- just about anyone can do it with a bit of practice.

    The guys that solve the cube in mere se

  • 3x3 in 10.95 sec (Score:4, Informative)

    by SpinyNorman ( 33776 ) on Thursday November 10, 2005 @12:57PM (#13998710)
    Check this video out - solved in 10.95sec

    http://www.xpert.co.kr/1enjoy/2game/cube/pds/1095. wmv [xpert.co.kr]

    Some amusing well-deserved gleeful cackling at the end!

    Link posted in the "chatter" section of Macky's page:

    http://cubefreak.hp.infoseek.co.jp/ [infoseek.co.jp]

  • Obligitory disclaimer: I work for an extremely famous toy store mentioned in this post. I link there because I want to; they don't know about this post.

    The snake is really the most fun toy out of all the Rubik's toys. You can give that to a very small kid and it'll be fun for hours as they manipulate it in various ways. Once you're a bit older, you can start to work on the "puzzle shapes," like the eagle, the star, the pyramid, tetrahedron, or the famous terrier (dog). If you've never seen the snake [wizardschest.com], it's

  • Once you've learned how to solve the cube (using some simple methods I can get it done in around 2 minutes, nothing impressive), the next fun thing to do is trying to obtain other geometric patterns starting from the solved one. For example, you can rotate the left side 90 degreees upwards and the right side 90 degrees downwards, then face the left side of the cube, apply the same transformation and so on... If I remember correctly, at some point you end up with "Z" shapes on the 4 lateral sides. And if you

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