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Stack identical flat objects so they project over an edge as far as possible (quantamagazine.org)
179 points by dtnewman on Dec 20, 2016 | hide | past | favorite | 38 comments

I've long enjoyed making impossible looking things out of Jenga blocks. For example https://i.stack.imgur.com/xvEpe.jpg?s=328&g=1 has no glue, no nails, and is entirely balanced on a single Jenga block!

It looks impossible, doesn't it? But it is really quite easy.

Step 1: Find 5 blocks with 4 short and one long. You can test by putting several upright on a table with one laid across with pressure. The ones that slide are short, the ones that don't are long.

Step 2: Put the tall upright in the middle, the 4 short around it in a base. Place 2 blocks whose middle crosses the tall one, standing on the others as a base.

Step 3: Pile up your structure. Try to keep it from being off balance as you go, but you have a surprising amount of leeway.

Step 4: Test the base, find which are loose and which are tight. Manipulate the pile until all 4 at the base are loose.

Step 5: (Expect a 50% success rate.) Slide the base out. Everything is now balanced on one!

Step 6: (For fun.) Put the remaining 4 on the very top.

Step 7: Take pictures, show people, etc. Your structure is unstable and can collapse very easily. Which gives you opportunity to build another. :-)

A fun variation is to have 2 starting points, and build piles that extend both ways. You can make a surprisingly long bridge!

Balancing symmetric objects isn't that hard, try something like this: https://www.youtube.com/watch?v=4Eo4gbLhYP8

That's amazing!

And yeah, what I do is just a trick. The end result looks impossible but not much skill is involved.

Are you the one who did this in the AWS booth at re:Invent? It was so perfect that my colleagues did not want to disturb it.

Pretty sure not.

I have done it at other conferences and explained the technique, so it could have been someone who learned it from me.

I "discovered" this same type of structure myself recently while thinking about the overhang problem actually.


That's the easy part.

The hard part is balancing the structure on a single block, which is standing on end.

If you have kids below 10, I heavily recommend the Kapla bricks[0]. You find them in nearly all Kindergarten in Germany and kids love them. Our 6 year old son built a 1000 piece bridge with only 4 bricks at the base.

[0]: http://www.kaplaus.com/

It seems like there's a very serious risk of being bludgeoned to death by your significant other if you're a big Star Trek nerd, however.


Perhaps today is a good day to stack.

My son got Kapla for Sinterklaas, and I admit one of the first things I tried was to get them to hang as far over the table edge as possible. This article is very well timed.

I also allowed blocks to stand on their end, but in retrospect, that might not be a very effective strategy.

+1 on the Kapla blocks! These were one of my favorite toys growing up and they last a long time.

For those who aren't familiar, they are wood blocks sort of like Jenga blocks but with a length:width:height ratio of 5:3:1 which is very useful for building structures. They are made with quality wood and are cut precisely.

The fun part is using them to build bridges and domes. I always have fun seeing how far I can build make a bridge span, which is why I came across this article in the first place.

We have a set of larger EVA blocks in faux woodgrain that are a great buy for young kids too. They look exactly like wooden blocks, but are quiet and you avoid incidents when they're flung around.

My 4yo and I have previously played the "cantilever game" too. Adults get involved when we play "improbable structures" - that quickly gets competitive!

Also, in the US, we have: http://www.kevaplanks.com

Vielen Dank, that looks brilliant. Just spent AU$188 on a Kapla 280 Box + Art book, as well as architect book for my 6 year old. Kind of pricey, but it's the right time of the year for it and quality looks great.

Yes, they are expensive, but they are very precisely cut and they do not deform with the time. You will not be disappointed and your kid will have a lot of fun.

I agree. The precision with which they are made is great. Also those blocks will still be around for your grandchildren.

Exciting, thanks again for the info. With a bit of luck I'll have it just in time for Christmas as well. :)

Interestingly, I just discovered a similar plank building system from Australia called "Green Hat" blocks:


I'm in the UK and didn't realise it was a European thing.

The genie lamp configuration shown seems to have the top two bricks in a position that would have them trivially topple. It leaves me wondering which results in the article and mentioned paper are actually correct.

The article fails to mention that the genie lamp configuration relies on additional "point weights," which are blocks of zero height and width and non-zero weight. In the figure, those are represented by arrows.


I'd really like to buy some of those zero-height, zero-width, nonzero-mass blocks!

You'll have to wait for the Singularity when they go on sale.

Given that the blocks are connected only by gravity, how could that bottom block possibly help?

It's only used to for the logical induction. It doesn't help the blocks above balance any better.

The bottom block hanging over the table with a heavy weight on the top right edge means the whole system is prone to tipping, and moving the bottom block back so we're just worried about the next edge higher up means that the system is, on average, less prone to tip over. It turns out to be easy to calculate the difference in tippyness/torque between these two cases, so we can use this to calculate how far the block can hang over.

One block obviously balances at 1/2, and has a center of mass at the edge. Two blocks obviously still have a center of mass at the edge - else they would tip, or could go closer to the edge without tipping. But how far out is this second block hanging?

If we put the second block flush with the edge of the table, it has a center of mass at -1/2 and a mass of 1, and the top block has a center of mass at 0 and a mass of 1. So the center of mass of the system is at -1/4 and we can shift it this far to the right. With 3 blocks, we have a mass of 2 blocks with the center at position 0, and another block below with a center of mass at -1/2 and a mass of 1, for a system centered at -1/6th (and so on for more blocks). We always shift it over in the end, but it makes the math of how far to shift it easier to compute if we start with it backed up a bit.

If you're talking about the one in the first diagram, it indeed doesn't help. One could argue that the diagram is just before the tower is shifted, as described in the iterative algorithm.

My thought too.

How to run an early 21st century science magazine like Quanta: Raid article subjects from the back of late 20th century Scientific American articles.


This example is found as a problem in pretty much every introduction to series in calculus and discrete math books.

I didn't realize popular science magazines get to call dibs on such problems.

Evidently, they don't.

Are you suggesting they should?

That's ambiguous, isn't it? Maybe I'm just miffed I didn't think of it first.

The title alone brought immediately to mind a scene from childhood of insanely stacked Nat Geo magazines, and the phrase "The Crazy Cantilever". Turns out it the phrase (and I have no doubt the stacked Nat Geo magazines) came out of this book:


What is the author referring to when he says it looks like a 'kingfisher'?

Thanks, yeah I am familiar with the bird but I guess I didn't see it.

There's a photo of one made of glass blocks in the comments that made it click for me.

I've been doing exactly this with my 2yo nephew lately. I build it out, he yells 'CRASH!!' and send the Jenga block flying. Keeps us both amused & out of the way.

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