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Tallest Lego building with 4 pieces? (medium.com)
405 points by lorenzosnap on May 29, 2017 | hide | past | web | favorite | 98 comments

One commentator here questioned why is this on HN (and was DVd somewhat) There is the fact that dad teaches stuff to daughter. The lesson is fun and interactive. The concepts dealt with are pretty profound and can be quite deep: constraints, maxima and minima.

Well done dad - you've covered some complex stuff in a fun and accessible way. Good skills.

If anyone else doubts why this is valid Hacker News, they may want to simply hand in their nerd card and do something else.

Slamming my nerd card down so hard the whole table spins around

It's hacker news, not motivational team building shared insight news. I'd expect a GA solver which selected the four pieces which could be constructed into the tallest possible structure (with all the dirty tricks e.g. a boat hull attached to a wobbly assemblage of Giant Base/wing plates with a 12x24 brick balanced on the top), with a Speculation section positing possible future pieces which would allow an even taller structure (with plausible details of the sets & why they would need even longer pieces than those currently available).

... and where do you think new hackers come from?

Personally speaking, I have no idea what a GA solver is but my initial solution would involve putting all the pieces on top of each other with their longest edges aligned - that's the maximum. Then we look at the constraints: gravity is a bit of a bugger. etc etc

Keep your card and open your mind. You might be a bright lad but you can still learn to look at problems from a fresh angle. The OP's daughter is in safe hands as far as I can see - she'll learn critical thinking and that is a real gift.

BTW: what is a GA solver?

> with their longest edges aligned

Longest axes aligned. Longest edges is not the maximum. The article's final solution uses a long axis rather than an edge.

Whoops, it is surprisingly easy to think one word and type another.

> what is a GA solver

Genetic Algorithm solver, I assume.

Ok, got it (thanks) - something that would simply follow the rules to find a solution yet be unable to think outside the box. It would, for example, not even "think" of dabbing a small amount of Super-Glue on the edges to achieve the theoretical maximum.

I don't recall the initial problem as stated precluding outside assistance.

My point stands: dad is pushing daughter to use the rather large brain that she has to solve a problem. Whether or not she becomes a Hacker as we know it does not matter - she is learning critical and analytical thought processes through this game.

That is one of the many gifts that any parent can bestow on their progeny and I'm impressed at his approach in this case. Society as a whole becomes a little richer as a whole through these little steps.

Couldn't agree more. It's a lesson in perceiving the largest range of possibilities.

Coming from a family with a less money than average North Americans, this is an especially good lesson. For countries with enormous possibility, but few open paths to achievement, the value of this kind of ability in thinking can not be overstated.

No, the whole elegance here is in the simplicity of the puzzle, and no child would get excited about anything like what you are suggesting. Unless you're missing a /s tag somewhere.

I think the sarcasm is too strong for it not to be a parody of the lightest-gray comments in this thread.

My opinion is 100% genuine and stupid. i don't read the comments.

Genetic algorithms? What is this, 1995? Show me the TensorFlow dataset or this post is as good as [dead].

More seriously, though -- I think problems like this can actually be more interesting than solutions. They get you thinking about what the solution might be. Lots of interesting work starts with a problem rather than a particular solution technique. That said, I'd be interested to see your GA solver solution, or any other solution someone can find!

Bugger GA (whatever) thingies. I've got some super glue - stick all Lego bits together on their longest axis: problem solved as posed but probably not as intended.

The large thing between my ears beats the crap out of a GA thingie any day, provided that the problem is loosely defined 8)

Does superglue work on Lego? I found that gluing pieces of plastic together (especially nice plastic like Lego) is the most challenging of all. Wood, paper, rubber, even metal with welding. The best experience I have with plastics is with PVC and the nasty chemical cements that temporarily dissolve the material.

That said it would probably work well enough for this problem.

You need to use the Kraggle.

Yes it works like magic. PVC glue works as well.

>I think problems like this can actually be more interesting than solutions

Reminds me of an animated shortfilm I saw not too long ago but not that recently either.

There's this person that has a box full of questions and s/he encounters an elderly person that has "all the answers", and I'm not going to spoil the rest.

I just can't for the life of me remember what it was called and I can't find it with any web search I can think of either. Anyone know which one I'm thinking of?

I don't, but I bet you can find it if you ask to "stack overflow movies".

link: https://movies.stackexchange.com/

Such over-engineering does not smack of interesting material for a site called "hacker news". This is great material in itself, especially considering the context of education here.

> context of education

Oh, advancement through self-education? There's practically zero pedagogic content on HN. Or in this submission! How did the father guide his daughter? Through examples & showing a restricted subset of the problem? By following the technique in How to Solve It & steadfast avoiding showing the student anything but patiently & gently reminding them of what they know & which skill to apply in each circumstance?

And HNers wonder "Why do so few people major in computer science?"

Enabling potential CS Majors to encounter technically-unencumbered problems is a great first step!

If novel solutions to trivial technical problems aren't of interest to hackers, I dunno what is.

> novel

The problem & solution seemed trivial, not novel: tallest structure with _these four_ pieces (get them on their sides) vs. _any four_ pieces (hmm what is the longest piece, will it be stable on its side, can they be stacked, what will help them stack, etc.)

Hah, my first thought was actually a boat hull a diamond building platform sail!

here is mine. collectible somewhere across the atlantic ocean. dont get me wrong i loved lego. but my playing days are about 20 years behind me.

Have you tried recently? It's still fun, just unfairly stigmatized as a kids only thing.

As an adult no one bats an eye if you play something like Cities: Skylines, minecraft or dwarf fortress. There's an army of adults playing FarmVille. So why not lego?

Ah, jacquesm bait, ok here is my solution (left), right one is an alternative to yours.


just the tops:


I feel like they should be attached and not stacked?


Fwiw: 10.3cm


Measured 10.7cm: https://i.imgur.com/I637r2v.jpg

What have you done to me!? Can't stop.

I never considered that the backplane is the same height as the inter dot distance. I thing I can think of as a possible improvement would be to put the single dot side ways, and put a grain of salt on each side. Or find a very slight indentation to put it in.

I really like the thinking of moving the smallest piece to the very bottom!

This would make a great quiz night team challenge or corporate team-building activity.

One of the conditions was that it should be able to stand on its own ('freestanding'), that one can't balance on the lower piece.

LOL. Can't wait to show those pictures to my daughter. thanks

You're welcome :) That's a nasty trick though but it is actually designed to be used that way, Lego has all kinds of interesting tricks.

Come to think of it this is an interesting game in the making, much better than most (or even all) games that lego makes:

Given x pieces from some set you get to take turns trying to make the highest combination, or, alternatively, all kids at a party are handed the same lego pieces and the winner gets some prize.

As a former Lego building champion I couldn't resist ;-)


Show with real parts that it remains standing. I tried building that one and could not get it to balance. Maybe you can find some position where the COG is over the little piece.

Reminds of a genetic algorithm that was made to optimize lego structures[0]. One of the most notable results of this was optimizing for a structure as long as possible with a single support. What they got was a 2 meter long organic looking cantilever that experienced significant brick deformation[1]

[0]http://www.demo.cs.brandeis.edu/pr/buildable/evocad/aid00/ [1]http://www.demo.cs.brandeis.edu/pr/buildable/long_bridge/

I think you can do ever so slightly better by moving the pink dot to the highest pip on the 2x2 green cylinder - it extends a little beyond the pip, so you'd gain about a millimeter that way.

If it's not cheating to have parts not completely attached, you could maybe even balance the pink dot on top of the green cylinder for an extra 3-4mm.

if you dont have to be attached then place it under the blue brick

easier to balance on top, but I think it's not a "building" any more than.

Maybe not a building, but still a structure ;)

I had exactly those two ideas, even before looking at the solution proposed in the article :)

Ok, an even better one:


You could make the one on the left even taller by tilting the yellow rectangle so it also utilizes the hypotenuse

now do one with the top piece upside down (or put that piece on the bottom)

I tried, it will not balance (nor at the bottom, because COG is off-center too far from the center of the round 1x1 plate for it to be able to stand on its own).

I'd love for someone to beat this one.

>The only rule is “The structure needs to stand on its own.”

Melt it down and recast it, duh. :)

Well, taking away the implicit rules, the limit becomes simply "the tallest structure we can build with current technology".

For example, put the four Lego pieces on top of the Eiffel Tower, and you've now created a structure that is height "Eiffel Tower + Lego" - and it's made with those four pieces ('with', not 'only with' :) )

I think that is cheating, because after the recasting is done you are left with a single piece. The instructions clearly say 4 pieces ;)

Recast the individual pieces, then.

I'm sure I can do better with a good knife.

Or recast as one long one and cut it up.

People like you ruin rubix cubes. :p

Nah, they break one piece out, flip it and then put it back in, then mess up the pattern and gift it to someone for their birthday.

I got my girlfriend a 5x5x5 for her birthday and she accused me of swapping tiles when she got stuck on the last two. Almost ended the relationship.

The lesson here: If you gift a puzzle, you better be able to solve the puzzle ^.^

Or cut all the pieces into as much long pieces as possible, then stack them.

Very fun! It reminds me of teaching my son to play tic-tac-toe. He started in the top-left, I went center, he went top-center, I blocked top-right, he went in between top-left and top-center and quickly claimed victory. I gave him that one and said he had to go in an unused square. Next game he started top-left, I went center, he went top-center and then before I could go he hurried and went top-right and again claimed victory. I don't remember what we did after that but I do remember thinking it was more fun pushing the rules than the actual game.

Childrens logic: if it isn't said outright before the game then it isn't a rule. You lost fair & square.

To entertain myself, I gave this some thought before I clicked. I assumed exactly what the title says: which 4 lego pieces create the tallest structure that stands on it's own.

Well, we need the biggest bricks we can find, my mind went to the ship hulls: https://www.ebay.com/p/?iid=282223262072&&&dispItem=1&chn=ps

So how can we connect 2 of these together, and make it stand vertical? Or can we?

It might be that we need the 3 pieces to make the brick stand... I'm not sure.

And then I clicked on the article...

(I'm not sure if I've even found the largest brick, or if I've found a 3 brick component; how do we define "brick"? Why do I care? Please comment and subscribe, it really helps ;)

I need to add, I clicked on the article, and totally enjoyed the content. (With a small caveat, noted above.)

Envy, I think that's the word for the weird vitriol in this thread.

You could do a tall 1x1 block on the Stern and then attach something as a base, and then an arch attached to the bow (https://www.toysperiod.com/img/cache/67/800x600/d4e4o5g414l4...)

Or three arches, two at the Stern for a base.

10.9cm free standing, no glue or tricks but top two bricks are just resting, not attached.


2mm below the tallest, but how earth do you get the pink piece to balance on the gray piece?

I bow to the master.

There is a taller one? Do tell! Link?

Edit: and as to how to get the pink one to stay, it was just some delicate balancing. And the pink one is tilted slightly toward the viewer/left, in other words aside from being (obviously) oriented diagonally, it's also not oriented straight up and down in the other axis. Managed to do it a few times for different attempts, as the first time the pip wasn't riding as high as it could be. The pip just stays on (barely) by friction, btw.


That one is 11.1 by my tape measure.

You could put them side-by-side.

Still amazed you got that to balance. I tried it (after seeing your picture) but gave up :)

It might be interesting to compare the height achieved by a given configuration, to the upper bound on heights (sum over largest dimension of all 4 pieces).

You can do a bit better if you put the round piece at the base, and make the blue piece diagonal just like the big flat piece.

You'd need to balance everything on the round piece, but the little pink dot should assist in that.

Kind of like those balanced rocks thing :)

yep, that was along the same line of thought I had

Gain an extra 2mm or so by just resting the pink piece on top?

you are right. I will do it and then take another photo

Asking questions, challenging assumptions, bending the rules, and just trying things are all core to the hacker mentality. Well done sir!

It's funny, but I feel like this is exactly the kind of skill required in engineering or business generally -- "How can we creatively maximize 'x' given what we've got?"

In fact, it wouldn't strike me as an unreasonable interview question, using the physical pieces. Of course some people are better with spatial reasoning than others (and experience with Legos is another leg up) -- but using several simple, general-purpose questions along these lines almost feels like a FizzBuzz for any job where problem-solving is an important part.

There's this joke about an Ikea job interview: interviewer tosses a bunch of parts on the floor in the interview room and says: take a chair.

Sorry but isn't two or three cheating? These are not valid ways to connect Lego are they?

Yeah, that's what I thought too.


I think this is an example of a very early set using this technique. But yes, this is possible and holds rigidly

Very cool post, in regards to the people clicking on the link and then bashing the author, it would be nice if you could bring some arguments to your disliking/bashing.

Thank you. I've now had a similar discussion with my two girls (Aged 11 and 4). Was a far better way to spend the evening than a typical night of Netflix.

"My daughter asked me"

kudos to Lego marketing department for great viral

LEGO Group marketing is on another level.

I have no idea why this post is so popular. I'm equally confused at why I find it so interesting.


What does this have to do with the post.

Absolutely nothing.

It takes a really hardened individual to completely ignore the beauty of a father spending time with his daughter and building things with her in order to talk shit about Evan Williams and Medium.

If this story was on an ugly Wordpress site, no one would upvote it.

Does this content really belong to hackernews?

Your comment got treated rather harshly, so let me try to explain. The post is on topic for HN because, although the question is a whimsical one, it gratifies intellectual curiosity (please see https://news.ycombinator.com/newsguidelines.html). Whimsical submissions like it have always been welcome here, as long as they're uncorrelated with anything that's appeared recently. (Sometimes people start doing the copycat thing of posting stories on almost the same topic. Those get old quickly unless they're really interesting, so the bar gets higher superlinearly.)

It isn't just a question of the community upvoting it. Plenty of stories get plenty of upvotes yet still don't belong on HN—e.g. most sensational controversies.

Many HN users value the diversity of the stories that appear here and don't take well to comments that appear to want to narrow the site down. That might be why your question got flamed.

Thanks for contructive answer. Got it. I was just curious. I am lurking here for long time and it seems to me, that the ratio of technical posts is really declining over last few months so I was wondering about the guidelines.

also Lego have the hacker nature.


While my view is that if someone posted it on HN and it was upvoted high enough—it belongs there; there is little in this post that "gratifies intellectual curiosity". Unless we are talking about the child involved, but I doubt she reads HN. There is often a complaint about negativity on HN, but I don't think swinging the pendulum too far in the opposite direction adds quality. If anything it devalues really interesting content.

Intellectual curiosity doesn't only mean studying great work or deep problems. It's closely allied with a playful spirit that likes to do things just because. That playful spirit is vulnerable to being dismissed as unserious, so it needs protecting. We protect it here.

Of course opinions will always differ about any given submission, but that's the general approach.

Every post starts out at 0. The community decides who to upvote and downvote. So does it deserve to be on hackernews? Hackernews users decided it does.

It does, but anonymous accounts questioning what belongs on HN and what does not do not.

The users who make up hackernews have voted. It do.

moderators sometimes manually take down up-voted stories...

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