# Mental Challenge (SFW)

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## Main Question or Discussion Point

http://home.cwru.edu/~jnt5/Planarity/ [Broken]

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When does this thing end?

*Kia* said:
http://home.cwru.edu/~jnt5/Planarity/ [Broken]
It gets complicated quick....

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Yep, just beat level 5, but I gotta stop there, for now

Cool game, though.

Gold Member
I wimped out on level 3 but I am really tired so maybe tomorrow eh?

jma2001
Gold Member
Interesting, would anyone like to take a shot at explaining the mathematical concepts behind this game? It reminds me of the Bridges of Konigsberg problem. From my limited experience with the game, it seems that the secret is to place the nodes having the most edges in the center, while the nodes having only two or three edges can be arranged around the perimeter.

jma, that is what I was doing.

AKG
Homework Helper
The Bridges of Konigsberg is a graph theory problem, and this game certainly has to do with graphs (a graph is just a thing with "nodes" as you call them, and edges connecting nodes in some manner). If I recall correctly, a planar graph is any graph that can be drawn in the plane such that no two edges cross each other. If you have 4 nodes forming a square, and edges connecting every pair of points, then you'll get a square with an X in the middle. But you can take one of the diagonals and have that edge go from one corner outside and around the square to the opposite corner, so it's a planar graph.

So in this game, you show that each of the graphs are planar. I think in the Bridges problem, you are trying to find a special kind of circuit (Euler Circuit?). Whether a graph is planar and whether it contains a Euler Circuit may or may not be directly related (i.e. I don't know if there's a theorem that says whether a planar graph has a circuit, or something like that) but both are indirectly related as they both have to do with graph theory. Most of the above is based on sketchy knowledge from over a year ago, so I would recommend looking up some of these things:

Graph and Graph theory
Euler Circuit
Planar Graph
Bridges of Konigsberg

on a site like Mathworld.com.

jma2001
Gold Member
Thanks AKG, that is just the sort of info I was looking for.

In case anyone is curious, here's what level 8 looks like. I'm out.

http://www.jma2001.com/lev8.jpg [Broken]

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Gold Member
nice work.
I believe a eular circuit is where each "node"/vertices is crossed only once.
I could well be wrong but unless that "mass" of lines has only 2 vertices with an odd number of arcs then there are not eular on the other hand if they do only have the two then they could very well be eular.

http://www1.coe.neu.edu/~lrussell/planatary.jpg [Broken]

NO I did not get that far, some other clever person.

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James R
Homework Helper
Gold Member
I stopped after completing level 5. To get to that stage took me about 10 minutes.

If I knew it ended at some stage, I might be motivated to continue...

Nice game, though.

Pff, I was about to post a screenshot of level 8 completed, not anymore Nice work Kia!!!

i finished level 5 in 5min...now i'm sick to my stomach can you save the game?!? i missed all the gui buttons cuz i quit X. My only tactic is to take all the degrees of 2 and move them as close the edge that they adjacent to...wsih you could move groups...

ok i decided to play again level 6 took me not to long maybe 5-7 min but level 7 i'm well past 15 minARG .,..ok is that timer accurate cuz it says it only took me12min. 9 min on level 9

NOOOOO...i finished level 10 and it tells me that a flashscript is running really slow and to abot...then it stalled the game!!!!!.

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jma2001
Gold Member
neurocomp2003 said:
ok i decided to play again level 6 took me not to long maybe 5-7 min but level 7 i'm well past 15 minARG .,..ok is that timer accurate cuz it says it only took me12min. 9 min on level 9

NOOOOO...i finished level 10 and it tells me that a flashscript is running really slow and to abot...then it stalled the game!!!!!.
That happened to me, too. Click 'No' (as in, no, don't abort the script) and wait. You might have to click 'No' a few times, but it will finish eventually.

jma2001
Gold Member
It's true, I have no life ...

http://www.jma2001.com/lev13.jpg [Broken]

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Hell no, that is crazy...

are you using trial and error to figure out what works or did you work out an easier way?

jma2001
Gold Member
Townsend said:
Hell no, that is crazy...

are you using trial and error to figure out what works or did you work out an easier way?
When I was a kid, I spent a lot of time drawing mazes on big sheets of paper, so I guess I developed an ingrained sense of how pathways fit together.

There is a method, it's hard to explain exactly, but in general:

When you click on each node, you will notice that the other nodes it is connected to are highlighted in red. I begin by going around the circle, clicking on each node one by one, and moving it to a point that is roughly equidistant between the other highlighted nodes. That way, all the nodes that are connected to each other are grouped together in the same general area.

Then, I choose one small area on the perimeter and untangle it. Nodes with two or three edges always go to the outside, four-edge nodes go to the center. Move the untangled piece into a corner, as far away from the other nodes as possible.

From there, as cliched as it sounds, it is simply a matter of taking one node at a time, and moving it from the tangled area to the untangled area. There is only one place that each new node can go, so that it is not crossing any of the edges in the untangled grouping.

Every now and then, if you get stuck, go back to the trick of dragging each tangled node to a position that is roughly equidistant between the other connected nodes. That will get you back on the right track.

In the screenshot that I posted, the original untangled area was in the upper right corner. You can see that, as I worked from the upper right outward, the lines connecting the nodes got longer and longer, as I dragged them into place from the lower left to the untangled area.

JamesU
Gold Member
I'm currently on six, and scared, you should see it! :surprised

James R
Homework Helper
Gold Member
I'm worried that the notes say the algorithm doesn't always generate a solvable puzzle.

Now THAT would be very frustrating!

Integral
Staff Emeritus
Gold Member
neurocomp2003 said:
ok i decided to play again level 6 took me not to long maybe 5-7 min but level 7 i'm well past 15 minARG .,..ok is that timer accurate cuz it says it only took me12min. 9 min on level 9

NOOOOO...i finished level 10 and it tells me that a flashscript is running really slow and to abot...then it stalled the game!!!!!.
Mine hung up with that message on level 9... I am at work ...my work computer sux.

Gold Member
mattmns said:
Pff, I was about to post a screenshot of level 8 completed, not anymore Nice work Kia!!!

hahaha not I, some other clever person
VVVVV - posted this under the screen shot - VVVVV
*Kia* said:
NO I did not get that far, some other clever person.

Edit: Done with level 10, but after each move, the error message appears, But i'm determined to go further

Another Edit: just finished level 13, was the easiest of the last 3 i gotta say..

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Hurkyl
Staff Emeritus
Gold Member
Just completed level 12.

Elapsed time: 17:20
Bonus: 203760
Score: 406097

I got the script error on the final move of this. I dunno if it'll let me do 13.

(7:05 on level 11, IIRC!)

jma2001
Gold Member
This has reminded me of a pencil and paper game that I learned from a high school math teacher. Take a blank sheet of paper, and draw on it twenty pairs of circles, numbering each pair from one to twenty. That is, draw two circles in random locations, and label them both '1'. Then draw two more random circles and label them '2', and so on, up to '20'. So you end up with forty numbered circles on the page.

Then, without lifting the pencil from the page, and without crossing any lines, connect each pair of circles with a continuous line. Obviously the first half dozen pairs are easy, but by the time you get to number twenty, the paper looks like a piece of modern art and it takes ten minutes of snaking the pencil around to find a path to the other circle. It also helps to have a sharp pencil for squeezing through narrow passages! A very simple game, but fun for anyone who is interested by abstract patterns.