The Square-Sum Problem - Numberphile

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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!

mayabartolabac

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

ShantanuAryan

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.

mattcelder

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

robmckennie

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.

tovarischkrasnyjeshi

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.

AvidAstronomer

Ahem, *The Parker Square-Sum Problem*

munjee

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

ciscoortega

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

Sam_on_YouTube

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 ^^

DomikaClarke

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

Tiptop

I love how Parker Square is now a thing :)

nicosmind

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.

DaTux