# Sierpinski Network



## qqwref (Dec 3, 2011)

Here's a puzzle from Meep's site:
http://meep.cubing.net/html5/sierpinski.html
There is also a higher-order version for crazy people:
http://meep.cubing.net/html5/bigsierpinski.html

In this topic we can discuss methods, times, tricks, and so on.

I think I have something vaguely resembling a method now. I got a very lucky 9.43 single on level 3 (the highest level on the main puzzle) and a 199.83 first solve on level 6.

EDIT: 6.73 lololsingle on level 3


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## Ickenicke (Dec 3, 2011)

Funny puzzlez. But it is hard to find a good method!


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## ben1996123 (Dec 3, 2011)

First attempt at level 6: 17:28.70.


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## Ickenicke (Dec 3, 2011)

How do I get a totally white puzzle to black at the easiest puzzle? Fast?


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## y235 (Dec 3, 2011)

click on every point one time


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## aronpm (Dec 3, 2011)

Ickenicke said:


> How do I get a totally white puzzle to black at the easiest puzzle? Fast?


 
Click every node


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## mr. giggums (Dec 3, 2011)

Level 3
Lolsingle: 5.10
NLsingle: 5.60
Could easily be fast if I were more acurate.

EDIT: 2.17 lucky 4 clicks
EDIT2: It was Level 2 not Level 3.


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## Ickenicke (Dec 3, 2011)

y235 said:


> click on every point one time



Thank you, I found out that by myself


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## y235 (Dec 3, 2011)

Interesr Fact: If solving the Sierpinski Network optimally, you don't have any node pressed twice, and the order of the nodes that you press doesn't matter.
Another Fact: A Sierpinski Network of any order can be fully changed from white to black by pressing all the nodes one time.


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## Ezy Ryder (Dec 3, 2011)

Just got three 0.03 singles on the basic level. It's fun.


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## emolover (Dec 3, 2011)

293.73 level six. It is so unresponsive.


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## Stefan (Dec 3, 2011)

I wish the background was grey or yellow or whatever, would make white nodes easier to see.


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## mrpotatoman14 (Dec 3, 2011)

3.2 average on lvl.2 I'm really slow at clicking accurately on the nodes.


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## Meep (Dec 3, 2011)

My best on level 3 was 11.00 without having some really easy solve (10 clicks). I got like 500s on level 6 but I was half paying attention lol. I made a general grid-based light's out network generating thing where you draw the puzzle in a text file but it's an exe (Windows only ): ).

http://meep.cubing.net/html5/lightsoutnetwork.zip

Other puzzles I made that may be of interest:
http://meep.cubing.net/html5/meepuilibrium.html
http://meep.cubing.net/html5/separ4te.html


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## qqwref (Dec 3, 2011)

mr. giggums said:


> Level 3
> Lolsingle: 5.10
> NLsingle: 5.60
> Could easily be fast if I were more acurate.
> ...


4 clicks on level 3 wtf o_0
And your other times are ridiculous too, what's your method?

Also: 174.73 level 6. Oddly enough I can't get anywhere near 1/3 of this time on level 5.
And 5.80 lucky level 3, plus some sub20s (lol) with parity.


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## Carrot (Dec 3, 2011)

EDIT: I'm lol..

Level 2:
1.30 single

Level 3:
21.53


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## emolover (Dec 3, 2011)

qqwref said:


> 4 clicks on level 3 wtf o_0
> And your other times are ridiculous too, what's your method?
> 
> Also: 174.73 level 6. Oddly enough I can't get anywhere near 1/3 of this time on level 5.
> And 5.80 lucky level 3, plus some sub20s (lol) with parity.


 
Can you tell me your parity? Mine is stupidly long.


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## Itchy Cacti (Dec 3, 2011)

:Lololol .43 2-click solve
Edit: 1-click solve-.5:fp
Edit 2: 1-click .03


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## qqwref (Dec 3, 2011)

Here it is:






I've discovered a more 'mathematical' explanation of parity. Look at the vertices that form a corner of one of the smallest (6-node) triangles; we'll call these corners. It's easy to see how to toggle the colors of two corners. But, if you click them all, you get a pattern that looks locally solvable but actually affects an odd number of corner colors. So it'd be hard to actually predict as you go. I'm pretty sure that every parity algorithm must press all of the corners and then use the other pieces to fix the changes that were made. In fact, if you look at the trapezoidy things on mine, the two non-corner presses fix two corners, so it's easy to see how it works.

PS:
7.60, (21.67[p]), 8.57, (6.53), 7.70 => 7.96
8.93, 20.37[p], 9.50, 7.90, 11.23, 9.90, (21.83[p]), 7.60, 21.67[p], 8.57, (6.53), 7.70 => 11.34


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## Meep (Dec 3, 2011)

qqwref said:


> Also: 174.73 level 6. Oddly enough I can't get anywhere near 1/3 of this time on level 5.
> And 5.80 lucky level 3, plus some sub20s (lol) with parity.


 
I think it's the way I made the timer. If your computer's performance slows down unfortunately the timer would too (Which is why I capped it at n=6, cause my work computer starts to slow down at n=7 though my home computer does at n=6). It might be best stackmatting the higher order ones.

Also yeah, what's your parity fix? I always just restart if I get parity 'cause my fix is stupidly long. Also, is there a way to determine parity at the start? I was looking for patterns as to whether I should start at a certain corner etc.

Edit: Ninja'd on parity


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## qqwref (Dec 3, 2011)

For the curious, my current method is to use only corner presses to make all the groups of three non-corners in the smallest triangles either all black or all white. Then the second step is to solve everything without corner presses, and apply parity if necessary. I usually start from the top and work my way down.

You could try to predict the parity by counting the number of white corners plus the number of corner presses your plan would involve to solve the first step. If you typically start from the top, and typically avoid pressing the topmost corner, your parity fix would be to press the top corner at the very start. It'd be tough, though, since you'd have to essentially lookahead the entire first step.

EDIT: Hey, I managed to predict parity a couple times in a row (on level 3 which is almost certainly the maximum this is possible for). It wasn't always within 15 seconds, though, and I mispredicted it a few times after that. Just saying, it is definitely doable.


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## Stefan (Dec 3, 2011)

474.83 for level 6 (and now I'll probably never want to do this again, I'm just glad I didn't have parity)


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## emolover (Dec 3, 2011)

Stefan said:


> 474.83 for level 6 (and now I'll probably never want to do this again, I'm just glad I didn't have parity)


 
You can only get parity on 3, 5 and I guess 1.


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## ben1996123 (Dec 4, 2011)

1:31.90 on n=4.

Edit: 1:17.27


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## mr. giggums (Dec 4, 2011)

qqwref said:


> 4 clicks on level 3 wtf o_0
> And your other times are ridiculous too, what's your method?
> 
> Also: 174.73 level 6. Oddly enough I can't get anywhere near 1/3 of this time on level 5.
> And 5.80 lucky level 3, plus some sub20s (lol) with parity.


 
I just realized that it was level two not three.

EDIT: 32.50 on the real level three.


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## emolover (Dec 4, 2011)

15.90 on n=4

With average with solves without parity I average like 23.


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## qqwref (Dec 4, 2011)

I did 100 level 3 solves with parity prediction  Made some mistakes, but fortunately not too many.
(Yeah, this is WITHOUT choosing only parity-free solves - I solved 100 scrambles in a row.)

avg5: 7.48 (σ = 0.71)
6.50, 8.17, 7.77, (20.40), (6.47)

avg12: 8.48 (σ = 0.84)
(6.93), 8.80, (21.83), 9.40, 8.53, 8.37, 9.60, 9.50, 6.97, 7.77, 8.33, 7.50

avg100: 10.85 (σ = 3.55)


Spoiler



11.53, 20.90, 14.60, 12.20, 7.67, 9.57, 14.30, 12.00, 12.50, 13.47, 12.03, 9.90, 23.00, 8.40, 10.30, 10.13, 10.73, 8.20, 11.20, 10.67, 7.83, 9.97, 9.33, 7.83, 18.17, 13.17, 14.63, 9.37, 10.03, 7.60, 9.80, 8.43, 12.30, 9.60, 7.93, 18.73, 11.30, 11.13, 8.00, 9.93, 11.63, 10.67, 8.57, 10.30, 6.87, 9.27, 7.93, 11.00, 11.00, 8.53, 10.47, 11.53, 9.73, 6.93, 8.80, 21.83, 9.40, 8.53, 8.37, 9.60, 9.50, 6.97, 7.77, 8.33, 7.50, 14.23, 13.97, 9.83, 8.10, 9.23, 9.13, 17.03, 7.33, 9.57, 6.50, 8.17, 7.77, 20.40, (6.47), 8.40, 8.63, 15.43, 8.50, (24.90), 9.73, 7.07, 10.93, 10.07, 11.03, 11.00, 8.83, 17.40, 10.70, 8.23, 11.53, 12.03, 8.13, 11.10, 10.90, 22.97




EDIT:


emolover said:


> 15.90 on n=4
> 
> With average with solves without parity I average like 23.


Crazy. What's your technique? I'm getting like 40ish (probably because of the teeny tiny dots).


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## emolover (Dec 4, 2011)

qqwref said:


> EDIT:
> 
> Crazy. What's your technique? I'm getting like 40ish (probably because of the teeny tiny dots).


 
Your right that is crazy. I truly don't even know that got there because I was doing 3x3 at the time/eating dinner. I don't even know...

Maybe I meant n=3? But I dont know because my best is 11.XX...

But I will make a video showing my technique.


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## aronpm (Dec 4, 2011)

243.83 for n=6



Spoiler











my timer was running super slow it was actually like 15 minutes


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## RNewms27 (Dec 4, 2011)

aronpm said:


> 243.83 for n=6


 
243.93/243 ~ 1 sec/puzzle



aronpm said:


> my timer was running super slow it was actually like 15 minutes



~900/243 ~ 3.7 sec/puzzle


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## qqwref (Dec 4, 2011)

I'm not sure what you mean by "per puzzle". I think n=6 has 1098 dots (each is 3 times the previous one, minus 3), so maybe that's more useful.

Also: wow, this timer is spectacularly bad. I solved the n=6 and got a time of 153.67, but it was timed on qqtimer as well, and there it was a 6:49 (this is probably much more realistic). The js is heavily obfuscated, so I have no idea what was done for the timer, but I'd really suggest using something like the current system clock (which qqtimer uses).


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## Meep (Dec 4, 2011)

qqwref said:


> I'm not sure what you mean by "per puzzle". I think n=6 has 1098 dots (each is 3 times the previous one, minus 3), so maybe that's more useful.
> 
> Also: wow, this timer is spectacularly bad. I solved the n=6 and got a time of 153.67, but it was timed on qqtimer as well, and there it was a 6:49 (this is probably much more realistic). The js is heavily obfuscated, so I have no idea what was done for the timer, but I'd really suggest using something like the current system clock (which qqtimer uses).


 
Yeah that was with an issue of me not knowing how, but Justin just showed me and I'll probably fix it when I get home later.


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## qqwref (Dec 4, 2011)

Awesome, glad to hear you're updating it. While you're at it, would it be possible to increase the size of the dots on the bigsierpinski one (at least for n<6)? They're pretty hard to hit and I'd like to be able to get times comparable to the smaller app.


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## Meep (Dec 4, 2011)

Yeah I can experiment and try to scale them with n.


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## Meep (Dec 4, 2011)

I fixed the timer to use the system clock, and it now uses the big nodes for everything but n = 6.

I also removed the 'bigsierpinski.html' page and just made the regular one go up to 6. I made the big one just to watch my script generate higher iterations of the fractal, not expecting people to want to play them. =P

Link: http://meep.cubing.net/html5/sierpinski.html


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## aaronb (Dec 4, 2011)

How do you fix it when you just have one corner still white on n=3?


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## Stefan (Dec 4, 2011)

n = 4
43.26, (38.63), (48.61), 42.88, 47.11 => *44.42*

Definitely my favorite size.


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## Meep (Dec 4, 2011)

aaronb said:


> How do you fix it when you just have one corner still white on n=3?


 
See the previous posts for qq's parity fix/explanation. It happens on the odd-iterations (1,3,5).


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## qqwref (Dec 4, 2011)

Yeah, n=4 is pretty fun. Not too ridiculously large, not too small, and no parity.

27.45, (24.76), 26.77, (30.63), 27.79, 26.02, 25.51, 27.97, 24.82, 27.18, 29.31, 25.92 => 26.87

EDIT: 84.72 on n=5.

*n=6 is broken now...*


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## benskoning (Dec 4, 2011)

my PB 3.14


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## Deluchie (Dec 4, 2011)

How do you change the "n" value? Its probably so simple but I don't know how :/


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## cubernya (Dec 4, 2011)

Look at the bottom of the page


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## aaronb (Dec 4, 2011)

Meep said:


> See the previous posts for qq's parity fix/explanation. It happens on the odd-iterations (1,3,5).


 
Thank you; don't know how I missed that. 

n=4

150.79

Edit: 118.44

Edit2: 106.49

Edit3: 76.00


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## Deluchie (Dec 4, 2011)

Wow, that would've been a good thing to do..... :fp


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## Meep (Dec 4, 2011)

qqwref said:


> *n=6 is broken now...*



As in, it doesn't stop the timer when it's solved?


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## qqwref (Dec 4, 2011)

Meep said:


> As in, it doesn't stop the timer when it's solved?


As in, there's something wrong with the graphics:


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## Meep (Dec 4, 2011)

qqwref said:


> As in, there's something wrong with the graphics:


 
That's really strange, it's not happening to me. Did you try clearing your cache? It might be trying to load the images from the old version, 'Cause I did away with hidden big pink circles in the newer one.

Edit: Other people I sent it to seem to see it properly too


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## qqwref (Dec 4, 2011)

Ah, alright. It works now, thanks.

Solved n=6 in 322.92  I have an easier time hitting the dots than I did in the last version.


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## Meep (Dec 4, 2011)

qqwref said:


> Ah, alright. It works now, thanks.
> 
> Solved n=6 in 322.92  I have an easier time hitting the dots than I did in the last version.



I also made it only check for the solved state on each click instead of each loop, so that probably made it much more responsive (it was negligible on the lower iterations).


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## Stefan (Dec 5, 2011)

Stefan said:


> 474.83 for level 6 (and now I'll probably never want to do this again, I'm just glad I didn't have parity)


 
Just once more to see how much all the level 4 practice helped...



Spoiler



575.94, dammit.

Though I'm guessing the first time was actually longer, because of the timer issue


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## Julian (Dec 5, 2011)

Uh, just solved level 6, the timer says 86978.86 :/


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## qqwref (Dec 5, 2011)

This might be useful to someone  I plan to memorize it soon. In case it's not obvious, the solutions are to click on the red-dotted nodes.


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## RCTACameron (Dec 5, 2011)

On n=1:

0.90, (0.01), (2.09), 0.01, 0.45 = 0.45
1.55, 1.59, 0.90, (0.01), (2.09), 0.01, 0.45, 1.79, 0.38, 1.11, 1.65, 1.15 = 1.06
Btw, 0.01 is actually meant to be 0.

This is fun.


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## Stefan (Dec 5, 2011)

Challenge: Find the smallest non-empty click-pattern that does nothing.


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## whauk (Dec 5, 2011)

made from qq's pictures, a graph showing every possible move on n=1

(sry for my paint skills)

@stefan: click two times at the same spot? (too easy but i dont see a problem)


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## Stefan (Dec 5, 2011)

No, with click-pattern I meant something like qq's patterns, i.e., a subset of the nodes (not clicking a node twice).

Edit: And with "smallest", I originally meant smallest number of nodes, though I'd also be interested in smallest "diameter".


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## qqwref (Dec 5, 2011)

n=1, lots of misclicks  (By the way, you can enter in a 0 as 0.001; that shouldn't affect the times too much.)

0.39, (1.76), (0.00), 0.20, 0.00 => 0.20
(0.00), 0.20, 0.00, (0.83), 0.69, 0.36, 0.00, 0.69, 0.64, 0.46, 0.38, 0.37 => 0.38
0.62 avg100


Stefan: I'm pretty sure this is it:


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## Stefan (Dec 5, 2011)

Ah yes, that looks very small. I just tried it myself and re-invented the top third of your parity fix (three arcs). Should've thought of yours, so obvious now...


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## vcuber13 (Dec 5, 2011)

Sierpinski is spelled wrong on the page


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## JonnyWhoopes (Dec 6, 2011)

Wow, these are a huge pain on a trackpad.

Got through n = 3 until I realized I had parity. Haha, screw that.


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## Julian (Dec 6, 2011)

JonnyWhoopes said:


> Wow, these are a huge pain on a trackpad.


Hey, I'm on a trackpad.


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## Meep (Dec 6, 2011)

vcuber13 said:


> Sierpinski is spelled wrong on the page


 
I just fixed it.


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## StachuK1992 (Dec 6, 2011)

Let's organize strategies and such better. I've been into this for a bit now, and it seems really interesting.

-clicking every node will totally invert the network
-for an optimal solution, no node should be clicked twice


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## qqwref (Dec 6, 2011)

Here's a very interesting one, IMO. Recall my method, where I start by using the corners to solve the non-corner pieces into groups of three of the same color. There are always exactly two ways to do this, and they are inverses of each other (that is, every corner is in exactly one of these two solutions). However, for n odd, one of these ways will give you parity when you try to finish the puzzle, and the other will not.

Also, if you don't make mistakes, finding one of these solutions can always be done optimally by a human. It's simply a matter of expanding out from the first node you choose to click or not click, and checking which corners must be clicked and which cannot be clicked to make a consistent solution.


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## y235 (Dec 6, 2011)

StachuK1992 said:


> -clicking every node will totally invert the network
> -for an optimal solution, no node should be clicked twice


I said that on 1st page.


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## qqwref (Dec 7, 2011)

Hey Meep, would you be willing to add some kind of averaging routines to the Sierpinski puzzles? It'd be a lot easier than having to enter all my times into another timer. I basically use the same ones for my sims; you can pretty much copy over the startTimer, pretty, updateTimer, getAvg, and clearTimes functions (and the necessary variables) with slight modifications for where you want to display the averages. You can see how to call these functions from the rest of the code of, say, qCube. I'm thinking the times should be cleared when you change the puzzle size or reset a scrambled puzzle.


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## qqwref (Dec 11, 2011)

Bump with times  Sorry to hurt everyone's chances at being better than me.

n=2:
0.21 single (2 clicks)
0.99 avg5: 2.08, (2.16), 0.47, (0.27), 0.43
1.23 avg12: 0.99, 1.58, 2.26, 0.47, 1.04, 0.77, (2.90), 2.08, 2.16, 0.47, (0.27), 0.43
1.63 avg100:

n=3:
4.00 single
5.48 avg5: 5.70, 4.92, (7.53), (4.41), 5.83
6.41 avg12: 5.85, 6.00, (7.66), 7.37, 6.59, 5.70, 4.92, 7.53, (4.41), 5.83, 7.26, 7.04
7.51 avg100

n=4:
20.62 single
22.79 avg5: 22.96, 24.10, (26.74), 21.32, (20.95)
24.20 avg12: 22.21, 22.96, 24.10, 26.74, 21.32, (20.95), 26.65, 24.66, 25.04, 26.19, (27.09), 22.08

n=5:
1:10.12 single
1:21.23 avg5: 1:23.63, 1:22.18, 1:17.89, (1:10.12), (2:35.95)
1:58.46 avg12: 1:23.63, 1:22.18, 1:17.89, (1:10.12), 2:35.95, 2:38.53, 1:16.49, 1:16.00, 2:37.90, 2:38.64, (2:43.64), 2:37.38

n=6:
4:48.37 single


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## Meep (Dec 11, 2011)

qqwref said:


> Hey Meep, would you be willing to add some kind of averaging routines to the Sierpinski puzzles? It'd be a lot easier than having to enter all my times into another timer. I basically use the same ones for my sims; you can pretty much copy over the startTimer, pretty, updateTimer, getAvg, and clearTimes functions (and the necessary variables) with slight modifications for where you want to display the averages. You can see how to call these functions from the rest of the code of, say, qCube. I'm thinking the times should be cleared when you change the puzzle size or reset a scrambled puzzle.



Ah, I missed this post. I'll think on it and see if I can do it during my breaks at work (That's when I'm most productive/when I made this game in the first place).


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## qqwref (Dec 11, 2011)

Funny, that's basically when I made qqtimer/qCube too


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