Comments on: Untangle the dots

By: David

David — Fri, 15 Jul 2005 19:18:04 +0000

Just finished Level 16…

http://xs37.xs.to/pics/05285/level16complete.jpg

The lag gets horrible the higher you get. I suspected it might be because it starts to scan itself for intersections at some point in the detangling process (?). I tried something this last time: I took one vertex from a section that I’d completed untangling, and dragged it over said section. And it seemed to work, too—less slowdowns during gameplay, as the scan picked up on the area I’d retangled PDQ and aborted itself.

Unfortunately, though, no solutions for the lag at the end of a level—each time it takes longer, and I have to keep telling the computer not to abort the script (whatever that means)…

Does this game have an end? Please tell me that it doesn’t go on forever, ‘cause I don’t think my OCD brain could handle it.

Oh, well, back to untangling the Xmas lights…

By: Vaughn Cato

Vaughn Cato — Thu, 14 Jul 2005 17:34:34 +0000

I’ve found a provably unsolvable one for Level 3. Assuming the number in the lower left corner is the random number seed, it is 00198901. It has a K3,3 equivalent subgraph.

By: Thon Brocket

Thon Brocket — Thu, 14 Jul 2005 10:13:48 +0000

Absolutely the worst bloody time-thief I’ve ever come across. Curse you, John Tantalo.

By: Shannon Clark

Shannon Clark — Thu, 14 Jul 2005 08:36:02 +0000

Well I’m up to level 15 with a current score score of 1605809… dangerous…

but addictive.

By: Sebastian Holsclaw

Sebastian Holsclaw — Thu, 14 Jul 2005 05:33:58 +0000

Hmm, I didn’t find the game very hard until around level 10. I use what I thought of as an ‘insideness/outsideness’ concept. Nodes with 3 links belong on the outside, nodes with more belong inside 3 link nodes. At the high levels you have interlocking sets of 3 link nodes surrounding more link nodes. There is probably something more sophisticated to the arrangement of the more link nodes but I haven’t consciously interpreted it.

I think this is similar to dylan’s algorithm.

By: dylan

dylan — Thu, 14 Jul 2005 01:51:42 +0000

there’s an “easy/simple” algorithm to use on this game. First find any triangle (3 vertices, each of which is connected to the other 2) and fix it’s position around the border, then repeatedly position each vertex in the center of gravity of it’s neighbors. through some sort of black magic created by laszlo lovasz, you manage to find an embeding. of course this doesn’t work well with too many dots though.

By: g

Wed, 13 Jul 2005 11:16:07 +0000

There are efficient algorithms for embedding planar graphs. It would be entertaining to write a program that interacts with John’s game and moves the vertices according to such an algorithm. Perhaps Kagashin did. :-)

By: Ars Mathematica » Blog Archive » Pure Planar Evil

Ars Mathematica » Blog Archive » Pure Planar Evil — Wed, 13 Jul 2005 06:57:10 +0000

[...] Via Eszter at Crooked Timber. [...]

By: george

george — Wed, 13 Jul 2005 04:44:36 +0000

This game is evil. I spent the better part of my one free day this week achieving the hollow victory of level 9. But I do have a question: how does the scoring work? It seemed like I was roughly doubling each level, but not exactly. If that’s how it works, Kashagin must have gotten into the 30s.

By: Jeremy Osner

Jeremy Osner — Wed, 13 Jul 2005 02:54:04 +0000

Thanks, Walt

By: John Tantalo

John Tantalo — Wed, 13 Jul 2005 02:05:03 +0000

Hi, programmer here.

The method I designed to create the graph insures that every graph is solvable. Basically, the game generates n random lines and finds all the intersections. The segments between these intersections become edges. For n lines, there are n choose 2 vertices. The difficulty scales by incrementing this line number by one each level (initially, n is four).

One guy figured out how to crack the trivial protection I placed on my high score database, this much I’m sure of. Plenty have tried, though. The high score right now, 6378867134884 from Kagashin, may look false, but he has several seemingly-legit scores lower than that, so I’m inclined to believe that he did not use a crack.

By: Walt Pohl

Walt Pohl — Wed, 13 Jul 2005 00:22:59 +0000

Jeremy Osner: Dots with lines, like in the game, are known as “graphs”. There are two “bad” graphs that are the minimal unsolvable examples. If a graph contains one of the minimal unsolvable examples, then it is unsolvable; otherwise it’s solvable. (The graph is then called “planar”.)

The minimal unsolvable graphs are known as K5 and K3,3. K5 is the graph with five dots, all of which are connected to each other. K3,3 is when you have two groups of three dots, and all of the dots in one group are connected to all of the dots in the other group.

This result is known as Kuratowski’s Theorem.

By: Jeremy Osner

Jeremy Osner — Wed, 13 Jul 2005 00:09:21 +0000

Question for the math whizzes—how does one prove that a particular arrangement of dots with lines connecting them is soluble or insoluble? I think there must be some layout of this game that can’t be solved, and the people who wrote the game must have ensured that such a layout would not come up; but I can’t imagine how you would do that.

By: Eszter

Eszter — Tue, 12 Jul 2005 23:37:04 +0000

g - I took that as a challenge. I have now completed level 13. The game gets very slow so the timing is not perfect. I did level 12 in 8:22 and got a time of 17:31 for level 13. However, by the end, there was a 15-20 sec pause between moves. This is what the screen looked like close to the start. This is what the completed screen looked like.

By: Dick Durata

Dick Durata — Tue, 12 Jul 2005 21:56:32 +0000

Tuesday seems right to me. Aren’t these games usually played at work?