I would like to thank Robert Gerbicz for his solution to the conjecture in the video, and HexagonVideo for explaining it well in video form. Cheers everyone!

@phyphor

Жыл бұрын

Came here to say something similar so will instead just add my voice to support this comment.

@1224chrisng

Жыл бұрын

It's an especially elegant proof, the idea of transforming one sequence into another and preserving its structure, though the bit from 4900 and onwards is a beyond me

@RobotProctor

Жыл бұрын

Ninja pairs ftw

I don't appreciate Matt starting us off with a Parker sequence of numbers. It was almost right when he told us to give it a go.

square in title and parker in thumbnail do not go very well together

@SteamPunkLV

6 жыл бұрын

xD

@K1lostream

6 жыл бұрын

Still want me a Parker square t-shirt! (And a Parker circle one - remember that?!)

@standupmaths

6 жыл бұрын

ಠ_ಠ

@wynautvideos4263

6 жыл бұрын

Treleleleleoellelele

@UltraLuigi2401

6 жыл бұрын

The 'Give it a go' screen has a Parker Square in the background.

Matt's really playing with fire here, he needs to stay away from the square topics

@KyleJMitchell

6 жыл бұрын

What would that help? The comments for videos he's in are asinine no matter what he's discussing.

@joshyoung1440

2 жыл бұрын

@@KyleJMitchell not sure if you caught the whole Parker square thing

@nif4345

2 жыл бұрын

Why?

@sneddypie

2 жыл бұрын

@@joshyoung1440 i think he did

@Noughtgate

Жыл бұрын

Silence, he's in his element

0:59 suspicious Parker square...

@rosebuster

6 жыл бұрын

Parker square is all about giving things a go and not getting upset that you failed. :P

Ahem , *The Parker Square-Sum Problem*

@DrDress

6 жыл бұрын

I hadn't even seen the video, but was gonna write this. An hour too late I guess.

@htmlguy88

6 жыл бұрын

To be fair it can be related to it.

@ethanpfeiffer7403

6 жыл бұрын

We all were thinking that.

@anticorncob6

6 жыл бұрын

I actually thought that the video was going to state that they found a magic square with perfect squares.

@nickcorrado5105

6 жыл бұрын

I believe the aborted beginning (8, 1, 3, 6, 10) he gives you is known as the Parker Square-Sum.

One of my favorite logic puzzles in video games is apparently basically finding hamiltonians. In Oracle of Ages, there's a few rooms where you're expected to walk over every tile (turning it a different color), and in the Minish Cap as well. Something similar in Link's Awakening, where you push some strange tile machine around in turtle rock, filling up all the holes to get keys. Not really numbery in those games unlike this, but for some reason I just really like those puzzles.

@AlphaFX-kv4ud

Ай бұрын

There's one of those in pokemon

I solved it basically in the same way, but by tabulating the different ways each square number could be made. I then counted the number of times each number appeared. 8 and 9 appeared only once each, so they must go on the ends of the line. 1 and 3 appeared 3 times, but they can only touch 2 others if on a line, so we must ignore the pairing {1,3} to make 4. This leaves one unique chain.

@stereobub

6 жыл бұрын

You can also just go through them and look at the "square neighbours" they have - it's really easy to check since the only reachable squares are 4,9,16,25. Then you will see that 8 and 9 only have a single neighbour. For any set of numbers where exactly 2 numbers only have one neighbour, this thing is possible. So you don't even need to draw graphs or guess random ways through them. :)

@AvidAstronomer

6 жыл бұрын

You can't rule out there being a closed cycle at some point in the future though. That wouldn't be solvable and also could still have 2 numbers that are alone.

@stereobub

6 жыл бұрын

True, I didnt think about that! Fortunately it looks like from 14 upwards no closed cycles show up - the only way to introduce that would be if bigger numbers didn't connect in any way to the previous ones but only to themselves, and that seems unlikely... although I can't prove that for now.

@grojan808

6 жыл бұрын

Solved it the same way

@antroflux8969

6 жыл бұрын

I randomly guessed a few times, and got it right so I didn't have to do any of that lol... Though thats what I would have resorted to...

that sneaky parker start

I see Matt Parker, I click the video

@numberphile

6 жыл бұрын

Well now I know how to Rick Roll you!!!

@PW0610

6 жыл бұрын

How to subtly give ideas for April Fools

@nikitacunskis1853

6 жыл бұрын

a clickbait for math geeks

@phaustho

6 жыл бұрын

Now isn't that the main reason why we're all here? :P

@elmajore4818

6 жыл бұрын

Would that be a slightly not perfect lure ... a parker lure including parker unable to not include and therefor not wrong. This sentence is false. o.O

YES!! Matt's back! I've been making my way through his numberphile playlist for the past week or so

@standupmaths

6 жыл бұрын

Fear not for I am always with you.

This was a really fun problem to get my brain going at 6am! I made a list from 1 - 15 and wrote next to them all of the possible combinations that would equal 4, 9, 16 and/or 25 and saw that 8 and 9 only had one possible combination so I knew they had to go at the end. It was pretty quick to fill in the rest although I got stuck going from the 9 end at the number 3 and had to go from the 8 end (remembering that 1 had to go with 8). I ended up with the correct order but backwards from what was later shown in the video haha. I also like my list of numbers a little more than the graph since that looks like it'll get pretty messy once you start crossing lines and making curved ones and such. It's a really cool visualisation, though! Thanks for the video and the little puzzle ^^

I love how Parker Square is now a thing :)

@steliostoulis1875

6 жыл бұрын

Normie

@ryanmahon1

6 жыл бұрын

A thing 2+ years running

@Jivvi

4 жыл бұрын

4+ years now.

@gouravchouhan1790

3 жыл бұрын

5+ years now

1:01 I see what you did there.

@sibax7776

6 жыл бұрын

PARKER SQUARE!!!!!

@liborkundrat185

6 жыл бұрын

Does anyone know the name of the music - it's so soothing!

I got Matt's book for Christmas. It was my favourite gift :)

Fun puzzle! I always love these videos. Keep up the great work!

Solved today

I started with the fact that 15 has to be between 1 and 10 because it can only sum up to 16 or 25. I continued on a chain from 10 using the only possible choices. Once I had 3 used, I picked 8 next to 1 as the only possible choice and continued on from 3 again (since 8 is a dead end). And it worked out: 9,7,2,14,11,5,4,12,13,3,6,10,15,1,8

love matt in these numberphile vids, such a cheerful maths guy

Parker always gives great exposition, enthusiastic and enlightening

The thumbnail spoiled it!! I wouldn't have immediately thought of finding a Hamiltonian path but the graph in the thumbnail gave it away :P

I almost got it but a couple of numbers were in the wrong place. I called it The Parker Sequence.

I would bave never come up with such a solution. Brilliant.

This whole video is so interesting to me. When the puzzle was first explained at the beginning, I really didn't think it would be that difficult. But once I thought about it and tried doing it out in my head I realized how difficult it really is. I think it's so cool how at first glance it really doesn't seem all that challenging when in reality it actually takes a lot of dedication and it must be perfect. What confused me the most about this is how it works up to any number, not just 15. This video inspired me to try solving this puzzle which I quickly gave up on out of frustration.

The first time I tried this, I started with 8, 1,15 - and so because there was only one path-I got it on the first go, this is really cool!

I managed to figure it out with 10 mins of concerted effort, I figured that he would give a false start, so I just wrote out 1-15 chose 8 as a starting place (it was in the middle) and went on from there. I did attempt it at first with 1 at the start, which was not a great idea, and led to many minutes of just staring angrily at the paper...

Matt gave the same problem when he met our school! Thnx for the amazing day Matt.

Amazing channel! Thanks guys!

I went with the way I intuitively thought it would work, if it worked at all. So I started with 1 and then took the highest possible number to pair up with it, then the lowest possible number to pair up with that one, then the highest again, and so forth. This gave me 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9. Then I slapped the remaining 8 in front and Bob's your uncle. Didn't watch the rest of the video yet and I don't know if this is significant in any way, but I notice that the squares form a pattern: 9, 16, 25, 16, 9, 16, 25, 16, 9, 16, 25, 16, 9, 16.

@iman3508

6 жыл бұрын

Yeah I got the same sequence

@RWBHere

6 жыл бұрын

The pattern of squares should change in interesting ways as the available integer set becomes larger.

@keeperofthegood

6 жыл бұрын

Not only the squares. And not only a pattern. When you make an ordered list of possibles [1,3][2,2][1,3] in rows for squares 4 9 16 25 etc there is oscillations both when just listed 1 to 25 or listed in solution order. Also as you approach a point of it failing the pattern breaks.

@glarynth

6 жыл бұрын

When I paused the video I wrote 1 through 15 in a circle clockwise and then added the edges. The result is approximately a square grid (if you ignore the [1, 3] link, which isn't used anyway). The horizontal edges are the ones that sum to 16, while the verticals are 25 on the left, 9 on the right. As you trace the path, you have to alternate horizontal with vertical, and left-side with right-side. So there's at least some geometric significance to the pattern. Try it!

@TheReligiousAtheists

6 жыл бұрын

DaTux91 I did it by getting rid of all the square numbers first. So I crammed them in as soon as I could. My sequence was 9,7,2,14,11,5,4,12,13,3,6,10,15,1,8. I got it right the first time itself using this method. I left out 1 for later, though, because it's pretty easy to link various numbers using 1. My pattern was 16 9 16 25 16 9 16 25...

I can tell what will happen in the comments just by looking at the thumbnail and the title of this video.

Two Matt Parker videos in one day? Awesome.

This is actually a very similar topic to what I did my dissertation on. I was looking for patterns amongst numbers such that a + b^2 = c^2 a - b^2 = d^2 where a,b,c,d are all natural numbers and b^2 is the next square number below a such that no number (we'll call e) exists where b^2 < e^2 < a

That sneaky Parker square

This problem has now been solved!🥳

@TTnarg1

Жыл бұрын

yes, see video by HexagonVideos

I wrote a script to generate square sums graphs in OmniGraffle when I read about this in your book, and I started work on a script to try to find a Hamiltonian path through any given OmniGraffle graph, but I got distracted by another project. I did solve some big square sums graphs but it didn’t work on all the ones where it’s possible because I didn’t get around to adding proper backtracking.

I've literally done this yesterday after reading in Matts book.

Cycles are clearly more fun than path. Give us a value with an hamilonian cycle!

i just came for the Parker Square jokes..

The new Parker Square update is looking great!

@Numberphile I have a question on the execution of the code of finding hamming path. It is known that the problem is NP-Complete and as you shown your program can compute the Ham-path quite quickly. I used standard SAT solvers, for the same problem, but could not reach any closer to the speed you are showing. Can you provide the tools you used?

Something really cool happens if you use Fibonacci numbers instead of Square numbers. You can string together all of the numbers from 1 to Fn -1 and the pair sums will just F(n-1), Fn and F(n+1). For example, up to 20 is 17,4,9,12,1,20,14,7,6,15,19,2,11,10,3,18,16,5,8,13 and the pair sums will be 21,13,21,13,21,34, etc.

@franzscheerer

9 ай бұрын

Lets list the first Fibonacci numbers 1,1,2,3,5,8,13,21,34 so that we can check it.

@franzscheerer

9 ай бұрын

Can you prove that?

@franzscheerer

9 ай бұрын

Yes, the last two numbers are Fibonacci numbers. I can add them to find the next Fibonacci number. So I can extend this list by the following Fibonacci numbers.

"I deliberately and meanly gave you a -- umm -- a starting point that does not work." "Why would you do that?!" "Because I am angry at the world about my hairline."

@to2podemosaprender630

4 жыл бұрын

Hahaha

I solved this in about 5 minutes. Before I watch the rest of the video, I'd just like to say how I did it. So I first added 14 and 15, the two largest numbers and got 29. Therefore the largest square number that can possibly appear is 25. I then took a random number from the list, e.g. 11, then went, well, 11 can form 25 or 16 (both greater than itself, of course) with two other numbers, which will be 5 and 14. This means 5 and 14 will be on either side of 11. Then I did the same thing for 5 and 14, finding the two numbers that they will be in between, one of which will be 11. Repeating this process is quite easy and the chain quickly formed. There are two particular numbers that I came across when doing this, which are 3 and 9 (1 also, but by the time I got to 1 there was only 8 left); 9 only worked with 7 for 16, and since there's no 0 or 16, it must be on one end of the chain, or string. Eventually things pieced together and gave me the answer (I think that's right, I'm gonna hope he doesn't say that it's actually impossible and I did or understood something wrong). So now I'll go finish the video and see if they did it the same way :) Edit: I meant 8, 3 was already used so it wouldn't be the other end. Idiot.

such a badass problem and awesome solution

@Numberphile Where is the video on the new biggest known prime number?

@TaiFerret

6 жыл бұрын

There is no biggest prime number.

@janeerland6449

6 жыл бұрын

TaiFerret 'known'

@shadowshedinja6124

5 жыл бұрын

@@janeerland6449 there is no biggest known prime. There are mathematical formulas that give a prime number for any positive integer input (though none yet that list every prime).

@I1am2me3DuhP

5 жыл бұрын

He means the biggest prime that's currently been found. We know that they keep going, but mathematicians (and this very channel) frequently like to discuss when the new largest "known" prime is determined.

@shadowshedinja6124

5 жыл бұрын

@Keks 257 any prime above 3 can be described by either 6x+1 or 6x-1

When will you make a video on the Parker Square-sum problem?! :D

@brokenwave6125

6 жыл бұрын

Andrew S Please stop. Youre not clever or funny.

@elfro1237

3 жыл бұрын

Broken Wave look in a mirror

If you put the numbers in a circle, it’s easier to visualize the path as it bounces around and around... very neat problem! Thx for sharing! :D (I love it when I can actually solve these... so often I get stumped or run out of patience, but this was a fun little puzzler!)

I solved it by writing a program to iterate permutations of (1,2,...,14,15) with early pruning. Associating numbers with lists of numbers that can be added to them to make squares occurred to me only as an optimized alternative to checking each remaining element; I didn't realize you could just make a graph out of it and find solutions as paths

@franzscheerer

9 ай бұрын

It is much faster than to go through all permutations.

Something something Parker Square something something.

@felicitas206

6 жыл бұрын

MattTheCatThatShatInTheHat I had a good laugh at that

@brokenwave6125

6 жыл бұрын

Please stop

Hamiltonian? I'm not throwing away my, plot! I'm not throwing away my, plot!

@bwayagnes2452

6 жыл бұрын

kujmous 😂😂😂 omg HAHAHAHA

Love the SET game on the shelf in the background! :-)

I see Matt Parker, I tune in for a good mornings working out

Well guess what Matt merry Christmas the problem's been solved

What if instead of squared number it's a cubed number

@baguettely

6 жыл бұрын

Callum Williams I've gone up to 100 and it's not worked thus far, apart from a list 1 number long. Cuz, you know- 1. It looks as though it's either going to be a pretty massive number or impossible. I have no proofs or anything though. :/

@andrewxc1335

6 жыл бұрын

It's pretty boring; there aren't a lot of connections for any of the lower cubes, and eventually, they may get added in, but like I said... boring. I'm actually adding them by pairs: 27 is 1+26 or 2+25 or 3+24 or ... , so it may make the whole thing harder.

@carabarnes1254

6 жыл бұрын

8 27 64 125 I would try with 124 numbers does that work?

@baguettely

6 жыл бұрын

Ooh, I want to do the prime one now...

@baguettely

6 жыл бұрын

cara cara orange it doesn't unfortunately. They just hang together in little clumps of 4s or so.

Excellent problem, clear explanation. What more could you ask for on a foggy Friday morning, right?! Cheers!

For once I solved one before watching through! my order is 9-7-2-14-11-5-4-12-13-3-6-10-15-1-8. I found it by making a grid, with 1-15 on one side, and 1, 4, 9, 16, and 25 on the other (as 36 is greater than 29, or 14+15) and writing in the number required to sum to the top square with the left number. crossing out all cases where the number was outside of 1-15, or the number was the same as the side number (2+2=4), i was left with one case where the number could only sum with one number : 9, with 7. I then made a tree diagram, using the numbers as a choose-your-own-adventure book guide. where there were two possible choices, i followed them both until one terminated (by not having an option that was not already used.)

0:08 Best editing I've ever seen

@albertb8999

6 жыл бұрын

And the most useful one!

I'm going to ignore the fact that it is believed to work ad infintum past 25 and focus exclusively on the fact that it works for 42.

Absolutely nailed it on my first go; figured out Matt was trying to pull me a Parker Square :P

I went about a different way actually! Looking at which numbers fit with just one other number (with the original 15). I realized that 8 only pairs with 1 and 9 works solely with 7. Knowing that, I went off starting with 8 and came up with the same order as in the video. Neat puzzle! I’m going to have to challenge my pals with this one to see if they can solve it.

Where's the next calculator unboxing video at

The thumbnail gave it a bit away how you can solve it (even though it had different numbers): 9,7,2,14,11,5,4,12,13,3,6,10,15,1,8

@cilingirc

6 жыл бұрын

Der Mathze omg , is there only one way to solve ? I find it same

@theboss112358

6 жыл бұрын

Technically 2 but you can reverse it.

Amazing. I'm a university maths youtube vlogger and I can't tell you how much numberphile has helped and inspired me over the years! :)

Hi Brady, I think it would be awesome for guys like Matt or James etc. to mention (the link in the description to) their KZread channels in the actual video to support them.

Parker Square Number!

I spy a utilities mug in the background. #shamelessproductplacement #gocheckoutmathsgear

@SimonClarkstone

6 жыл бұрын

That's been around in the videos for ages. It took me a while to request what it was.

That was awesome!

Love the Parker Square background

It's actually pretty easy. I started with 15 because it only makes a square with 1 and 10, and I just went in both directions and branched out from each next number to all possible "partners". Took me about ten minutes. Edit: Just realised that I sould've started with 9 cause it makes a square with only 7.

@sashulkagyl4781

6 жыл бұрын

Ivan Miletic or you could start with 8 and 1

@GoScience123

6 жыл бұрын

I found all the possible sums to make a square for each number and that left me knowing that 8 and 9 only added with one other number to make a square. This allowed me to put those at the ends, then work my way inwards with the other numbers. I finished in the same amount of time. It's cool to see how many diff ways people went about solving this.

Feels similar to the 7 bridges of Konnsburg

@MisterAppleEsq

6 жыл бұрын

Check the bonus video, he mentions that.

@Shadow81989

6 жыл бұрын

It's easier though. Took me under 5 minutes, most of that was just creating a table, to list for each of the numbers, which of the other numbers add to a square. Figuring out the solution took about a minute after that list was done, as there are no choices, no trial and error...

Even with the thumbnail, I didn't consider trying to find a Hamiltonian path on a graph as a solution. Nice video and explanation!

Solved it in 10-12 minutes! Here's how: I wrote down every number from 15 down to 1, and alongside it I wrote any other number(s) which would make it a square sum. (e.g. 15: 1, 10; 14: 2, 11; 13: 3, 12; etc.). Two numbers (8 and 9) had only one pair (1 and 7, respectively), so I decided to use one of those as the starting point of the sequence. Starting with 8, I put its only pair, 1, next to it. I then looked back at my chart to see in which other lines did 1 appear. The only other place it appeared was in the first line (15: 1, 10). And out of those three numbers, the only one that would make a square sum was 15, so I used that to continue the sequence. So then, 15 worked with both 1 and 10, but since 1 had already been used, I chose 10. In turn, 10 worked with both 6 and 15, but since 15 had already been taken, I chose 6. I followed this pattern until I used up all the numbers exactly once. This resulted in the finished sequence.

Goes through all the vertices ALEXANDER HAMILTONian path

@baguettely

6 жыл бұрын

A jacksfilms + numberphile viewer? Is this for real?! 😂

@oldcowbb

6 жыл бұрын

me me big boy

@baguettely

6 жыл бұрын

oldcowbb me me math boy

@yeremiafrans9425

6 жыл бұрын

Me me number boy

@bwayagnes2452

6 жыл бұрын

XD

I've apparently forgotten some important bits of my graph theory course during my computer science degree, because I'm now wondering if it's possible to efficiently calculate (a) whether a Hamiltonian path exists for any given graph and (b) what one example of such a path is for that graph. I know the TSP is NP-complete, but that's specifically looking for the *shortest* Hamiltonian; I don't remember if there was a verdict on calculating *any* Hamiltonian...

@joshuatilley1887

6 жыл бұрын

all hamiltonian paths are the same length

@littlebigphil

6 жыл бұрын

"In general, the problem of finding a Hamiltonian path is NP-complete (Garey and Johnson 1983, pp. 199-200), so the only known way to determine whether a given general graph has a Hamiltonian path is to undertake an exhaustive search." - Wolfram MathWorld, "Hamiltonian Path" TSP is looking for a Hamiltonian cycle, not a path. Hamiltonian paths aren't the same length on a weighted graph.

Is there a sequence for this in OEIS? Number of Hamiltonian paths for n nodes?

When I first saw this in Matt's book, I wanted to see if I could do it with the numbers 1-25. I did, and I was surprised to see that with the way I had written the puzzle, it ended with my birthday 7-18 !

Best I did was 15,10,6,3,13,12,4,5,11 :(

@rayp526

6 жыл бұрын

You're on the right track, keep going! :)

#ParkerSolution

@sebastianespejoloyaga7603

6 жыл бұрын

Because you don't have a way to go to every path, you can't go through 3 and 1.

I started by listing the possible squares: 4, 9, 16, 25. These are the only options that could result from adding two numbers between 1-15. Then I looked at possible pairings and I realized that 8 can ONLY pair with 1. The only way to get to another square using 1-15 would be to add 8 to itself, which isn't allowed. Based on that, I knew that the number line had to start 8, 1... After that, there was only one question: Does 1 pair with 3 to make 4 or 15 to make 16. I tried 3 first and ran out when I hit 9 (8 1 3 13 12 4 5 11 14 2 7 9). Since that didn't work, the only other option was to pair 1 with 15.

I made a chart of the “factors” of each number, then I used those to make a “factor tree” and I got my answer!

It's very easy because 9 must be at one endpoint, then all the other numbers are uniquely determined. So you can even conclude there are only two such sequences.

@FinetalPies

6 жыл бұрын

More than that, 8 must go on the other end.

@alephnull4044

6 жыл бұрын

That's included in what I said - all the other numbers are uniquely determined.

@JamesSpeiser

6 жыл бұрын

nice

@TheBlazeThrower

6 жыл бұрын

Yeah, that's how I solved it in a minute or two

@tgwnn

6 жыл бұрын

Aleph Null It's not really included in what you said. You could have a series in which a number with 2 possible neighbours needs to go to the other end out of necessity.

8,1,15,10,6,3,13,12,4,5,11,14,2,7,9

@moroccangeographer8993

6 жыл бұрын

If you reverse the order it's still a valid solution because addition is commutative

@mahendragupta2896

6 жыл бұрын

Same After 2.43 minutes

@mahendragupta2896

6 жыл бұрын

After 3 it started do find the correct number automatically

Actually figured it out! Fun.

I solved it myself, took me about 10 minutes. Have never been happier!

Parker sum

More like Parker square sum ( someone had to do it )

@KyleJMitchell

6 жыл бұрын

And since literally millions of people already have, you didn't need to.

What about finding one that cycles for higher numbers? So the first and last also look around to add a square number?

the misleading sequenced kinda helped me, cause once i was stuck starting from your sequence, i immediately figured out that 8 and 9 must be on the sides, and it's a downslope from there

...so you could actually do 0-17 !! Just add the zero behind the 16 :-P

so, is this a parker square-sum problem?

@gabinletueur

6 жыл бұрын

This joke is so annoying

@aWildLupi

6 жыл бұрын

I just had to give it a go!

@brokenwave6125

6 жыл бұрын

Kolly.G Yeah...its so used up and far from funny. People see the word "square" now and they think its so clever to make the same joke as everyone else.

Did it! Paused at 0:58 9,7,2,14,11,5,4,12,13,3,6,10,15,1,8. So the pattern of sums goes: 16, 9, 16, 25, 16, 9, 16, 25... and so on

You guys should do a video on the Thompson Problem!

Matt noes da wae

I just tried by myself, the game can actually be extended to 1-17 Fml I didn't finish the video I'm sorry

@standupmaths

6 жыл бұрын

That's ok: you gave it a go and you got excited!

@FrostDirt

6 жыл бұрын

standupmaths Hey!

@KyleJMitchell

6 жыл бұрын

Encouraging experimentation and discovery regardless of what others may have previously found is the best thing you could be doing. You're a hero of mine, Matt Parker.

While talking about hamilton graphes: Does anyone know whether there exists a easy test on whether a grid graph has a hamiltonian path? I know that there does not exist an easy test for hamiltonian paths in graphs in general, but does it exist for grid graphs?

Cool. It was simple yet very interesting :)

8 1 15 10 6 3 13 12 4 5 11 14 2 7 9 This is what I got I hope I'm right

I didn't see the answer yet, but: 9,7,2,14,11,5,4,12,13,3,6,10,15,1,8 I generated a list of pair of numbers that summed give a square number between 4 (the lowest square number you make up) and 25 (the higher square number you make up). The code to do this on Python is: i=1 while i

@joshtheegotist

6 жыл бұрын

Neat I got a different order... 8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9

@Shadow81989

6 жыл бұрын

If you turn it around, you will see it's the same order, just inverted. I put the numbers in Excel (more convenient for me than coding something), and made a list: For every number from 1 to 15, which of the other number(-s) can you use, to add up to any square number. This quickly shows that 8 and 9 only have one "partner", so they can't be anywhere in the middle. Then I worked my way in - for the first step there was only one possibility from either end, but from the end starting 8-1, you have 2 choices. So I left that open, went from the other end, and voila: There was only one choice at any given point, until it was finished, because for the numbers that connect to 3 others, one of these 3 had been used on a previous step, one came immediately before it, so only one was left to follow. Took about 5 minutes, I think, to prove by example that there is one and ONLY one way.

It took me a minute. Really fun.

@_catzee

5 жыл бұрын

I forgot 7 and 9 smh

Great video