Be Excellent To Each Other

How many shapes can be made with 10 standard 3x2 Lego bricks?

It's Maths.

Define shape.

At the same time?

Between 1 and 10, obviously

Yes. Those

Not really - you can make at least 10 shapes using just two bricks.

Needs more detail - do the bricks have to be properly attached, or can they be, eg, side-by side? Are we ignoring shapes that are mirror images of each other? eg: -=_ and _=- (sorry, that's a terribly example)?

Do the blocks have to be affixed to each other?

At the same time?

Oh shush.

Or it's Legos.

do you mean a lego with 6 nobbles, or 2 nobbles, 3 flat legos high?

Malc

You could probably do a phd on this.

If you take a 2x3 lego brick, then you can place a 2nd 2x3 lego brick on top of it in (I think) 27 different ways. Obviously, you can place the remaining 8 pieces on top of the previous piece, each time in 27 different ways, but that doesn't make allowances for putting the 3rd piece on top of the 1st piece again, or even underneath the second piece.

I'm just killing time in the hope that something has happened in the scum game...

Edit - Nope.

assuming you mean 6 nobbles, and they have to be connected, then 2 blocks = 62 possibilities... 2*(4*4 +5*3) (with lots of symetry that coud eliminate some options)

So, then you need to do that to power of 9, and then minus the combinations where the legos would be in the same physical space and thus couldn't be there...

So, that's a lot.

Malc

So... how many?

lots..
If you want someone to guess, then 6768543273131776

Malc

Also when you place a full brick on one of the corner nobbles, you can twist them on an angle a bit, do you have to count them by every degree?

Or what if some of them are a different colour !

Or, this.

Right angles only. How many positions are possible

I believe the answer is "Fuckloads"

Do they have to be attached properly, and are you counting mirror-images?

All bricks have to be used. All must be connected to the structure by at least one nipple.

Colour is irrelevant

oh, in that case, 65.

I always thought a standard lego brick was 2x4. The question fails. And my guess is 2. A square and a rectangle are the only shapes possible at right angles. I dont think "L shape" is an actual shape. Anyway, you should charge £1 a guess and have a weekend at Grims (or something of similar value) for whoever gets it right.

I reckon it's 13 at 2 bricks (including 1 brick on its own). 3 bricks would be 12 for each position at 2 bricks, so 144, plus 12 for two bricks, plus 1 for 1 brick. Added to that would then be loads more for two bricks attached to the one brick, rather than in a stack of 3. Fuck knows. Tons, and I've no idea how to work it out without actually trying to do it.

No, wait - 9 at 2 bricks.

DP hasnt confirmed if you can have mirror images or not yet,so 2 bricks could be way more than 9.

Seen it. Sequel's even worse.

I've assumed not, because it would be silly otherwise.

Whereas ignoring similar shapes is perfectly sensible?

What I need to solve this is a shit load of lego. But first, I need a beer.

If you imagine the first brick is set like this:



Then you place the 2nd brick in the same orientation, and start with the top right bobble linking to the bottom left nobble, that's 1, then you move the 2nd brick down 1, so 2 bobbles are linked, then again, so all three are matched, then you have 2 more on that side. That's 5.

Then you move the 2nd brick to the left one, and repeat, so you have 5 more, and finally, move it to left, so you have 5 more, that's 15.

Then repeat the job, but you have the 2nd brick in this orientation:



And you can do the same thing, but there are 4 lots of 4, instead of 5 lots of 3, so that's 16, for a total of 31.

Then you can fix the 2nd brick underneath the first, instead of the top, for 62.

Like, I say, then you can link 3 together, in 62^2 combinations, but some of the 3rd blocks will be connected in the same place as the 2nd one, which is impossible, I cba to work out those combos, especially when you add in another 7 levels...

Malc

This is a combinatorial optimisation problem. I did do a PhD in this

Brilliant.

Except that this:



and this:



Are the same 'shape'.

Great. What's the answer?

Bollocks are they, otherwise artificial wouldn't work, plus Tetris would be really easy...

Malc

Did someone mention (@)(@) ?

So I have no idea what the answer is, still I feel it only appropriate to mention a recent edition of Megafactories, about the Lego factory, as it was quite brilliant.

http://natgeotv.com.au/videos/Highlight ... 583C7.aspx

I might consider those to be the same shape, I did have the caveat of symetry in my first post in this thread, but DP didn't respond, so...

MAlc

No mirror images.

Is it a google/googol?

Try putting your left hand into your right glove then (without turning the glove inside out)

Malc

After a beer and a bit of scribbly diagrams, I get 16 shapes for 2 bricks by arranging 8 ll ll that way and 8 ll= this way.

Doc please save my brain and just tell us what the answer is as Im starting to doubt Dav actually knows the answer.

Piece of piss, flip either the glove or your hand.

You have opposable pinkies as apposed to opposable thumbs?

You might be able to get your hand in, but it doesn't "fit"

Also, I'll go back to artifical sweetners, they are "left handed", and normal sugar is "right handed", apart from that they are identical. The body only has "right handed gloves" so can't absorb left handed molecules, so you can drink diet coke withought putting on weight...

Malc

That's not right - it is true that the molecules are the same shape (not sure about mirror-ness), as that's how your tongue defines how things taste. But you don't put on weight because the sweeteners don't have any calories in, mainly because they're made out of something that isn't 'food'.

Yeah, sweeteners aren't isomers of sugars. Not even slightly. Aspartame is, for example, aspartyl-phenylalanine methyl ester (C14H18N2O5). Nothing like any of the sugars.

The fact that the way sweeteners, particularly aspartame, are made does mean that they are generally made up of a much higher proportion of one of the isomer-types, and I think that's linked to why they're not particularly good for you - but it's got nothing to do with why they are less calorific than sugars.

Maybe topic title needs to be changed to Science.

Scienceses, surely.

It... was obviously a boring forum day today, then.