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# 518

Graph Puzzle - July 27, 2012
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OMG, how does it work?!

The short answer is because of the theorem "Every finite strongly connected aperiodic directed graph of uniform out-degree has a synchronizing coloring." The above is one such coloring along with synchronizing words for the relevant nodes.

It doesn't work - you should switch the 'T' and the 'K'.

Umm... works for me.

Oh, it turns out I cannot read directions.
Oh well.

did u use 'Blue-red-red' only once?

So that's where the name XKCD came from

The letters and their positions are arbitrary.

^ clearly doesn't read SM very often.

^ Clearly doesn't get that he's saying that while the pattern produces xkcd, the pattern and the labelling of the nodes is arbitrary, so it is not the source of inspiration for the name xkcd.

^clearly doesn't get that Rainman said Andrew don't read SM often because Andrew didn't realize that Aaron was just making a joke

^clearly doesn't understand that RainmanDen.XXX does not know that

^ Clearly enjoys nested replies.

^I'm just being ridiculous here

^Clearly loves breaking the pattern.

^Clearly is an idiot.

^^All clearly trying to keep the pattern going.

I don't see any patterns here. Please tell me where they are.

blue red blue leads to the following pattern:
To A: From A,D
To D: From Z,X
To Z: From K,C,E
To C: From T

Therefore, any chain will eventually lead to A, but the longest chain is T->C->Z->D->A and it does not work with just 3 iterations.

red blue red:
To T: A,X,T
To X: Z
To A: D,E
To E: K
To K: C
Longest chain is C->K->E->A->T, and everything leads to T.

blue blue blue and red red red do not work as they just use one color and the graph has cycles of 3.

Doesn't everyone?
(Okay, I don't so much anymore -- but I'll click on links to good ones when I see them posted.)

So I worked out that the first letter was X, then noticed XKCD was in the tags...

XKCD...

ok, I think this is a cool graph and all, but is this really a comic? I mean, we haven't seen any actual comic strips recently. This graph IS amazing, but not funny.

Stop being a stupid commentor! This is a great comic.

you misunderstood, i think. I love spiked math. It is great. It has been funny. Yesterday's comic was great. All I said was that today's comic wasn't funny. But this graph puzzle was pretty impressive.

It was interesting and mathy, though. I actually prefer a mix of interesting ones and funny ones.

well, yes.

I think it's funny if you imagine the blank expression on a non-mathematician's face as you enthusiastically deliver the punchline "because every finite strongly connected aperiodic directed graph of uniform out-degree has a synchronizing colouring!!".

That punchline makes me think of graphs at a fashion show, only some of which can colour-coordinate or find clothes to suit them. Or the motivational catchphrase/slogan of an image consultant who gives fashion advice to finite strongly-connected aperiodic directed graphs of uniform out-degree. The image consultant's company would probably be called something like 'Graph-ic Design' or 'Graphic Imagery'.

well, I'm sorry.

Doesn't work. :-/

Never mind, it turns out that I didn't read the direction. LOL...

I'm seeing what happens, when I use mike's email commenting.

hmmm... Why aren't the comments working?(I mean for me)

You got that idea from me.

I know, I just wanted to test it

really cause i got: TEXD.... lol i dont get it....

Almost failing the "at least one update each month" written at the top.

... What's XKCD?

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