Name: The Square-Sum Problem - Numberphile
Uploaded: 2020-04-05T02:53:20.000Z
Duration: 9 min 7 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Future simple

Today we have a puzzle, so I'm gonna give you a ll the numbers from 1 to 15.

Present continuous

I suspect you're gonna shorten this dramatically in the challenges.

And can you rearrange them into a new warder?

Such that any two adjacent numbers add to give you a square number.

We can put one there and then next to it, we could put three.

Because of the three is for that's a square number.

I could chuck six here because a group of six is nine.

Oh, why am I gonna do, uh what can I add to that?

To make it a square number 10 work, right.

And then someone So we'll give you a second if you want to try it.

Any two that are adjacent Have to add to a square number way.

Thank you for trying the puzzle if you got it, could it could be days later.

You saying Brady you didn't think it was possible?

It feels unlikely, you know, But it can be done.

It doesn't work if you have these numbers in this order.

So I deliberately and very meanly gave you a, um starting boy, that does not work.

I want people to work it out for themselves.

Every two of these do add to give you a square number.

But then you just you can't join up the rest of them, right?

So the way I went about solving this when I first did, it was I thought, OK, I'm gonna draw a ll the possible links because you start looking at this and you're like, Okay, what?

And so, actually, I've got other options for how I put them in the same order.

And some of them have more possible links or neighbors.

Think toe one, because I guess before that is a square number now, Ford doesn't work with anything so far, but does work with five foot five over there.

So you can see if I only had the numbers from 1 to 6, it wouldn't be possible to order them.

So every single payer adds to a square number seven into the mix.

Gives you 99 fits in off seven because I get 16.

10 links into 6 16 11 and still, Now, I've got these serious I could use.

In fact, if this looks familiar that there is the original Siri's I gave 8136 10 is one possible ordering, but there's no way so far to link it up with the rest of them.

Will keep filling these in 12 to 4 13 will also linked to 12 because I could get 25 but we got to get 16 so that links to half.

Okay, so now we're trying to join this all together.

That's put in 14 and 14 is the first number where now everything holds together cause 14 25 in 16.

We've now got a connected network or graph whatever you wanna call it, but there's no path.

Right said this would work, But you've missed one in eight.

So at 14 it's all joined together because work 15 is the one you need to hold all together because 15 fills in this gap.

There's 25 16 and now there's our solution.

81 15 10 63 13 12 And then away along that tail.

You've gotta put those numbers so that every single pair between them adds to a square number, and I annoyingly I picked this bit here of this curve, knowing that that is not a valid part off the path that goes all the way through this square sums network.

That makes 15 pretty special number that makes between a prisoner's number.

It's the first number for which you can order the numbers.

And it's because I picked 15 because up until then doesn't work.

I couldn't pick 16 actually, because 16 you can add on to nine to get 25.

And so now you think that you guys put in this apart 16 all the way through to 17.

There's 18 0 now, now we've got a problem, because if you put 18 over there, there's no longer a way to go through the whole network going through every single number once and once.

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The Square-Sum Problem - Numberphile

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