Quantcast
[ 3 / biz / cgl / ck / diy / fa / g / ic / jp / lit / sci / tg / vr ] [ index / top / reports / report a bug ] [ 4plebs / archived.moe / rbt ]

Support us on Patreon!

/sci/ - Science & Math


View post   

[ Toggle deleted replies ]
[ERROR] No.3751105 [Reply] [Original] [archived.moe]

Original problem is in the pic.

You have an n episode tv series. You want to watch the episodes in every order possible. What is the least number of episodes that you would have to watch?

Over lapping is allowed. For example, in the case of n=2, watching episode 1, then 2, then 1 again, would fit the criteria.

The orders must be continuous. For example, (1,2,1,3) does NOT contain the sequence (1,2,3)

>> No.3751122

Archives of previous threads for reference:
http://4watch.org/superstring/
http://archive.gentoomen.org/cgi-board.pl/sci/thread/3734198

>> No.3751147

103

>> No.3751167

n^13 or n^14?

Non-math, gayfag guess.

>> No.3751172

14! derp

>> No.3751177

>>3751172
this! lol

>troll is too stupid to include "randomly out of all possible episodes"
too easy

>> No.3751180

>>3751172
Nope, we already have the (trivial) lower bound n+n!−1.

>>3751177
>this! lol
You have only once again reconfirmed my suspicion that /sci/ is one of the boards with the largest proportion of underage b&.

>> No.3751188

14!/2

>> No.3751189

What we know at the moment is that it can be done in <span class="math">\sum_{i=1}^n i![/spoiler] episodes (where n=14 for the original problem).

Here's a Python implementation of the currently known algorithm:
http://pastebin.com/aNwANugC

And some explanation of what's going on:
http://math.stackexchange.com/questions/15510/what-is-the-shortest-string-that-contains-all-permutat
ions-of-an-alphabet

Another way of generating the same string:
http://www.notatt.com/permutations.pdf

However, as of yet it seems no one has found a proof that the algorithm is optimal.

More links with discussion of the problem:
http://www.reddit.com/r/math/related/foj1l/the_shortest_string_containing_all_permutations/
http://oeis.org/A180632
http://stackoverflow.com/questions/2253232/generate-sequence-with-all-permutations/2274978
http://forums.xkcd.com/viewtopic.php?f=17&t=68643

>> No.3751197

I think I have a proof of the lower bound n! + (n-1)! + (n-2)! + n-3 (for <span class="math">n \geq 2[/spoiler]). I'll need to do this in multiple posts. Please look it over for any loopholes I might have missed.

As in other posts, let n (lowercase) = the number of symbols; there are n! permutations to iterate through.

The obvious lower bound is n! + n-1. We can obtain this as follows:

Let
L = the running length of the string
<span class="math">N_0[/spoiler] = the number of permutations visited
<span class="math">X_0 = L - N_0[/spoiler]

When you write down the first permutation, <span class="math">X_0[/spoiler] is already n-1. For each new permutation you visit, the length of the string must increase by at least 1. So <span class="math">X_0[/spoiler] can never decrease. At the end, <span class="math">N_0 = n![/spoiler], giving us <span class="math">L \geq n! + n-1[/spoiler].

I'll use similar methods to go further, but first I'll need to explain my terminology...

>> No.3751199

Edges:

I'm picturing the ways to get from one permutation to the next as a directed graph where the nodes correspond to permutations and the edges to ways to get from one to the next. A k-edge is an edge in which you move k symbols from the beginning of the permutation to the end; for example,

1234567 -> 4567321

would be a 3-edge. Note that I don't include edges like

12345 -> 34512

in which you pass through through a permutation in the middle (in this case 23451). This example would be considered two edges:

12345 -> 23451
23451 -> 34512

From every node there is exactly one 1-edge, e.g.:

12345 -> 23451

These take you around in a cycle of length n. A 2-edge moves the first two symbols to the end. A priori, it could either reverse or maintain the order of those two symbols:

12345 -> 34521
12345 -> 34512

But the second, as already stated, is not counted as a 2-edge because it is a composition of two 1-edges. So there is exactly one 2-edge from every node.

>> No.3751204

1-loops:

I call the set of n permutations connected by a cyclic path of 1-edges a 1-loop. There are (n-1)! 1-loops.

The concept of 1-loops is enough to get the next easiest lower bound of n! + (n-1)! + n-2. That's because to pass from one 1-loop to another, it is necessary to take a 2-edge or higher. Let us define:

<span class="math">N_1[/spoiler] = the number of 1-cycles completed or that we are currently in
<span class="math">X_1 = L - N_1 - N_2[/spoiler]

The definition of <span class="math">N_1[/spoiler] is a bit more complicated than we need for this proof, but we'll need it later. You might ask, isn't <span class="math">N_1[/spoiler] just one more than the number of completed 1-cycles? No! When we have just completed a 1-cycle, it is equal to the number of completed 1-cycles.

In order to increment <span class="math">N_1[/spoiler], we have to take a 2-edge, which increases L by 2 instead of 1. Therefore <span class="math">X_1[/spoiler] can never decrease. Since <span class="math">X_1[/spoiler] starts out with the value n-2, and we have to complete all (n-1)! 1-loops, we get the lower bound n! + (n-1)! + n-2.

>> No.3751205

2-loops:

Suppose we enter a 1-loop, iterate through all n nodes (as is done in the greedy palindrome algorithm), and then take a 2-edge out. The edge we exit by is determined by the entry point. The permutation that the 2-edge takes us to is determined by taking the entry point and rotating the first n-1 characters, e.g.:

12345
is taken by n-1 1-edges to
51234
which is taken by a 2-edge to
23415

If we repeat this process, it takes us around in a larger loop passing through n(n-1) permutations. I call this greater loop a 2-loop.

The greedy palindrome algorithm uses ever-larger loops; it connects (n-k+1) k-loops via (k+1)-edges to make (k+1)-loops. But I haven't been able to prove anything about these larger loops yet.

The tricky thing about 2-loops is that which 2-loop you're in depends on the point at which you entered the current 1-loop. Each of the n possible entry points to a 1-loop gives you a different 2-loop, so there are n*(n-2)! 2-loops, which overlap.

>> No.3751207

And now for the proof of the n! + (n-1)! + (n-2)! lower bound...

To review:
n = alphabet length
L = running string length
<span class="math">N_0[/spoiler] = number of permutations visited
<span class="math">X_0 = L - N_0[/spoiler]
<span class="math">N_1[/spoiler] = number of 1-cycles completed or that we are currently in
<span class="math">X_1 = L - N_1 - N_2[/spoiler]

In order to increase <span class="math">N_1[/spoiler], you must jump to a new 1-cycle -- having completed the one you are leaving. That means the next permutation P' in the 1-cycle (following your exit point P) is one you have already visited. Either you have at some point entered the 1-cycle at P', or this is the second or greater time you've visited P. If you have ever entered the 1-cycle at P', leaving at P by a 2-edge will not take you to a new 2-cycle; you will be in the same 2-cycle you were in when you entered at P'.

So these are the available ways to enter a 2-cycle you've never been in before:
* take a 3-edge or higher
* take a 2-edge but don't increase <span class="math">N_1[/spoiler]
* take a 2-edge from a permutation P that you were visiting for the second or greater time

In the first two cases, <span class="math">X_1[/spoiler] increases by 1 in the step under consideration. In the third case, <span class="math">X_1[/spoiler] must have increased by 1 in the previous step. Because of this third case, it is convenient to regard any series of edge traversals that takes you through permutations you've already visited as a single step. Then if we define

<span class="math">N_2[/spoiler] = number of 2-cycles visited
<span class="math">X_2 = L - N_0 - N_1 - N_2[/spoiler]

the quantity <span class="math">X_2[/spoiler] does not decrease in any step. Since 2-cycles are n(n-1) long, you must visit at least (n-2)! 2-cycles. <span class="math">X_2[/spoiler] is initially n-3, giving us the lower bound

<span class="math">L \geq n! + (n-1)! + (n-2)! + n-3[/spoiler].

>> No.3751212

Guise!
Itsa trick question!

>>What is the least number of episodes you would have to watch?

I can watch each episode 1,000 times but I've still only watched 14 episodes.

So the answer is just 14. (no factorial) :p I win!

>> No.3751227

>>3751212

>Ops face when he realizes how idiotic his attempt to answer the question is

>> No.3751240

>>3751212
>>3751227
you knew what I mean. I could say if each ep was 30min, then how many hours would you have to watch, but that would be just semantics

>> No.3751241

Someone in another thread wanted the two n=5 strings, so reposting from last thread:

The "standard" solution given by the algorithm we've seen expressed several ways now which I think are equivalent:
(I'm just listing the cycles, so 01234 means it goes through the permutations 01234,12340,23401,34012,40123.)
01234 12304 23014 30124
12034 20314 03124 31204
20134 01324 13204 32014

10234 02314 23104 31024
02134 21304 13024 30214
21034 10324 03214 32104

The "alternate" solution:
01234 12304 23014 30124
12034 20314 03124 31204
20134 01324 13204 32014

10243 02413 24103 41023
02143 21403 14023 40213
21043 10423 04213 42103

The alternate solution deviates from the standard one in the central step where the next permutation only shares one symbol with the previous permutation. Where the standard solution hits the permutation 10234, the alternate one uses 10243. It continues on in the same manner as the standard one except that the 3 and 4 are reversed.

>> No.3751251

So I've come to the conclusion that http://www.notatt.com/permutations.pdf is complete bullshit. Anyone disagree?

>> No.3751264

>>3751251
It would be nice to hear some reasoning for that conclusion. I don't see any problem with what he wrote.

>> No.3751288

Greetings again, good sir.

Let's get all the 14! and 14*14! derps out of the way now so the big boys can talk math

>> No.3751313

Alright, after that pretentious statement, I'll acknowledge that I'm not a big boy at math at all, I'm quite a novice.

Here's my thoughts, from the ground up:

Initially, intuition sets the upper bound at 14*14! (1.22 * 10^12), for obvious reasons. Extending beyond that is redundancy. That gentleman from the other night showed that a more workable upper bound is the sum of the factorials (9.39 ^ 10.)

That's a huge step forward. What about the lower bounds? Intuitively, 13 + 14! would be the initial lower bound, being the 13 necessary as filler for the first permutation, and the possibility of a sequential permutation for each episode added.

We know that this isn't true-- that you can't add one episode and get one new permutation continuously. That much is intuitive. How would one go about proving that?

I'm trying to look at some sort of pattern in the attainability of new permutations for n different episodes, but I wouldn't even know where to start.

>> No.3751318

>>3751251
how is it bullshit? its very solid

>>3751288
ha. /sci/ has improved a great deal when it comes to that in these threads. The first one was full of 14!*14 /thread comments, people telling them

>> No.3751326

>>3751313
9.39 * 10^10, I meant to say.

>> No.3751343

>>3751313
this is my line of thinking. In the most brute force way of doing the problem is just the episode numbers. A slightly more sophisticated way of doing that is looking at the permutations. Even better than that, We discovered we could use cycle groups, i.e. each group represents its permutations, and only the order of the cycle group matters.

This is an important innovation because the order of cycle groups is much more succinct and generalizable than just looking at permutations.

Two questions must be asked:
In an efficient string, must the permutations of a cycle group be listed consecutively? i.e. for n=6, does each efficient string contain 1,2,3,4,5,6,1,2,3,4,5? If the answer is yes, that means a cycle groups only appear once.

Is there a way to generalize the algorithm based on cycle groups?

>> No.3751366

>>3751313
The moves where you add a string of length 1 to get the next permutation take the symbol from the start of the last permutation and appends it to the end. This rotates the symbols in the permutation, and after n such moves you're back where you started:

12345
23451
34512
45123
51234
12345

You can only go in between the n-cycles with a move that adds a string of at least 2. Since there are (n-1)! - 1 such n-cycles, that gives the n! + (n-1)! + n-2 lower bound.

I think I've proven n! + (n-1)! + (n-2)! + n-3 as a lower bound also, but my reasoning needs to be checked by other eyes:
>>3751197
>>3751199
>>3751204
>>3751205
>>3751207

>> No.3751370

>>3751197
Ok, I'm going to read through your posts carefully. I like that you're looking at the places where you change cycle groups, but one thing I'm thinking is, how do we know that NOT completing a cycle graph would lead to a better solution. i.e. maybe we could start with 1,2,3,4,5,6,7 then put 2,3,4,5,6,7,1 somewhere later down the road

>> No.3751373

OK, I'm almost...
not quite, but almost...
ready to conjecture that the number of different ways of achieving this (likely optimal) sequence length is:
the product from 1 to n-3 of k!

>> No.3751384

>>3751343
After seeing these cycle groups mentioned many times, I think I'm starting to get it..

The 123451234 makes sense as starting with the natural pattern and obtaining 4 additional permutations promptly, and from there you'd take the 234 at the end and start 15, then repeat the first four for 234152341?

123451234
-----------234152341
And so on, until you get back to 123451234? That makes sense, but what does this accomplish? Does it just give us a pattern to run with?

>> No.3751403

>>3751370
>how do we know that NOT completing a cycle graph would lead to a better solution
I assume you mean wouldn't. At the moment, we don't know that. But leaving a cycle early and coming back to finish it later has an associated cost. And what I'm doing is trying to carefully quantify that cost. Doing so only gives you a lower bound. It might be that when n is large you can avoid the really long moves of the standard algorithm by making a few strategic early departures from the smaller loops.

>> No.3751404

>>3751373
Oh damn. This is one question I asked last time. I don't think the world is ready for that madness. in those cases where only one element overlaps, ALL (n-1)!/2 cycle groups are up for grabs. luckily, for n=4 and n=5 this only happens once in the middle, but how do we know this doesn't happen again.

Also I think I have figured something out. We only need to prove that the first half is efficient, because these are all palindromes. i.e. the proof you make with the first (n-1)!/2 cycle groups is guarentteed to work withe the second half

>> No.3751407

>>3751370
This was my initial thought, too.

So with the cycle groups, it's 1 addition per permutation until switching between cycle groups, at which point it's 2? Are there larger gaps in between there, like moving from one set of cycle groups to the next?

And would I be asking too much if you explained
Since there are (n-1)! - 1 such n-cycles" why this is true?

Thanks a bunch mr. mathematicians

>> No.3751421

>>3751407
>>3751366
Sorry, that should be
>Since there are (n-1)! such n-cycles
(n-1)! - 1 is the number of times you have to move between n-cycles. And the reason there are (n-1)! n-cycles is simple: n! permutations, n in each n-cycle, so (n-1)! n-cycles.

>> No.3751441

>>3751384
Yes. But I'm still not sure how to choose the groups. Because sometimes you have more than one option. Check the google doc for an explanation of that. Please comment on it if you want changes or additions

>>3751403
Oops, you're right. I mean it wouldn't. Yeah it's all a cost benefit thing. Staying in a cycle means we'd be giving up the chance to have a 1-edge as the other poster calls it. And the total amount of these should be low as possible. But what if sacrificing a 1-edge for a 2-edge, meant we could avoid higher edges along the way?

Like one thing that keeps appearing is the n-1 edge, i.e. when only one digit overlaps between cycle groups. Those points are very high cost, and occur in the middle of n=4 and n=5. how do we know those can't be avoided with incomplete cycle groups

>> No.3751474

>>3751407
when you switch between cycle groups, there is variable cost. For example in n=4, sometimes there needs to be an addition of 2, sometimes 3. check the google doc listed at the top for an explanation.

In our algorithm that produces a palindrome sequence, we'd always been prioritizing low edge numbers. i.e. cycle groups are ALWAYS completed (you'd never have 12345124, because that interrupts the group.) then you always try and get a 2-edge. The way I see it, its all about making the sum of edges numbers low as possible. The derp 14!*14 way of doing it would involve n-edges, i.e. no overlap

>> No.3751476

>>3751441
>Those points are very high cost, and occur in the middle of n=4 and n=5. how do we know those can't be avoided with incomplete cycle groups
For large n (meaning n>4), we don't know that yet. For n=4, according to the n!+(n-1)!+(n-2)!+n-3 argument, it may be possible to avoid taking the 3-edge, but not without doing something else of equal cost, specifically either repeating a permutation you've already been over, or taking a 2-edge that doesn't gain you anything.

>> No.3751492

>>3751441
>>3751474
I think you either forgot to post the Google doc, or your post didn't go through, because I don't see it.

>> No.3751503

>>3751476
do we know any alternative sequences for n=4? Hopefully we can show that repeating a permutation is never going to be const efficient
>>3751492
oops, https://docs.google.com/document/d/1AXXx1516LLq3wpiIZT_FayLnp6Q7xw8JlmFqsyyoy8Y/edit?hl=en_US&pl
i=1

>> No.3751507

Guys, I think this was way easier than we thought.
The proof of
>>3751373
(or finding a different answer for it) seems much harder.

>> No.3751522

>>3751507
Easier than we thought? Most people, including me thought this was gonna be a snap at first. But 5 minutes into it, I realized there are so many paths and options to account for. Even worse, is that there are multiple efficient sequences.

But finding out how many relies on that initial question. I think if we truly understood why the sum of factorials works, we'd know how many options there are. My body isn't ready for that second question though.

>> No.3751541

>>3751204
That's a great way to think about it, only looking at the gaps. With your permission, I'd like to add this to my google doc under the tag Anonymous or with any tripcode you might use

>> No.3751556

>>3751441
>Yes. But I'm still not sure how to choose the groups. Because sometimes you have more than one option. Check the google doc for an explanation of that. Please comment on it if you want changes or additions

The simple rule is that whenever you have to add n symbols to the string to get the next permutation, they should be the n symbols from the beginning of the previous permutation, in reverse order.

This gives you a series of nested loops, each of which rotates the first certain number of characters of the string.

For n=4:
http://pastebin.com/TgPzZeZu

Given any permutation, you can figure out where it will be found in this cycle by rotating the 4 until it's at the end, then rotating the first 3 characters until the 3 is at the end, and so on. This guarantees you'll hit all permutations.

>> No.3751570

>>3751541
Feel free to do so.

Actually, what we might want is a small wiki for this sort of stuff. By which I mean collaborative work on this and future math problems.

>> No.3751588

>>3751556
Er, but sometimes there are 2 or more cycle-groups to choose from.
see >>3751241

>> No.3751621

Answer comin up.
Damn it took a long time to type.

>> No.3751625

Thanks for showing me the google doc and bringing me up to speed. I'll ponder my feeble mind on it throughout the week.

I doubt I'll be able to provide any insightful answers, but as someone who's intensely interested in understanding what's going on, I might stumble upon the right questions to ask.

>> No.3751626

>>3751570
doesn't /sci/ have a wiki? If not it should have one for explorations in math
>>3751621
answer to?

>> No.3751627

>>3751621
cant wait

>> No.3751630

>>3751588
It's a rule, not the only rule. I don't pretend to know all possible strings of sum-of-factorial length.

But as far as generalizations go:

I think the standard algorithm can be generalized by replacing the step that moves the first k symbols to the end of the permutation in the reverse order, e.g. (with k=4, n=5)

43201 -> 10234

with any step that moves the kth symbol to the end, followed by the (k-1)th symbol, followed by the first (k-2) symbols in arbitrary order, e.g.

43201 -> 10243.

This is the sort of generalization that gives you the second n=5 string.

Another observation:

In both the standard algorithm and the generalized one, the moves in each k-loop preserve the cyclic ordering of n-k+1 of the symbols, specifically the n-k+1 symbols at the beginning of the permutation at the entry point of the loop, and also at the entry point of each (k-1)- subloop. This is important to verifying that the generalized algorithm hits all permutations. Don't have an explanation of this ready-typed, though, and I'm a bit tired.

>> No.3751636

Yes, easier than we thought. Hopefully I didn't make a mistake and embarrass myself

Let a k-iteration be the process of adding k numbers in a row without making a new permutation, such that the next number will make a new permutation (the other guy called it a k-edge)
so 1234 -> 2341 would require a 0 iteration
1234 -> 3421 would require a 1 iteration and some 0 iterations


Assume x is the highest number of permutations you can get with j0 0-iterations, j1 1-iterations, j2 2-iterations, up to jk k-iterations. Now, we need to move up to a*x permutations, where a is an integer. Clearly, we must use at least one permutation of order higher than k, and if there is a solution using (a*j1) 1-iterations, (a*j2) 2-iterations, up to (a*jk) k-iterations, along with (a-1) k+1 iterations, it is the most efficient way to get 2x permutations.
Applying this to the problem, we know that the most efficient way to get n permutations (starting from a permutation) is to use n-1 0-iterations. Therefore, the most efficient way to get n*(n-1) permutations is to use n-2 1-iterations and (n-1)*(n-1) 0-iterations, as we have seen.

>> No.3751642

>>3751636
Now I just have to show that those iterations actually add up to sum(k!)

>> No.3751646

>>3751636
>Clearly, we must use at least one permutation of order higher than k
Why is this?

>> No.3751652

>>3751636
Or when you say
>Assume x is the highest number of permutations you can get with j0 0-iterations, j1 1-iterations, j2 2-iterations, up to jk k-iterations.
do you mean for the <span class="math">j_i[/spoiler]s to be arbitrary, and x is the highest you can get with any values of the <span class="math">j_i[/spoiler]s? Because you can get to any permutation using only 1- and 2- iterations.

>> No.3751663

>>3751646
Hmm, I was trying to do it a bit differently but it became a pain so i wrote that up. Perhaps I should go back to try the other way.

>> No.3751685

>>3751636
what do you mean by move up to a*x permutations.
I'm not actually sure how this lower bounds the problem

>> No.3751691 [DELETED] 

>>3751652
>Because you can get to any permutation using only 1- and 2- iterations.
Are you sure? Its a pretty strict restraint to have to resume making more permutations after every couple digits

>> No.3751718

>>3751691
1-iterations allow you to rotate the string.
Using a 2-iteration followed by (n-2) 1-iterations, we can exchange the first two elements:

12345
34521
45213
52134
21345

And by conjugating that with a rotation, we can exchange arbitrary adjacent elements. And from there you can generate any permutation by moving the element you want first up to first place, the element you want second into second place, and so on.

>> No.3751754

>>3751630
An implementation of the generalized algorithm:
http://pastebin.com/D16PrjvR

>> No.3751769

well shit
I'll blame the fact that its 3am

>> No.3751773

>>3751626
Found it:
http://sciref.wikispaces.com/message/list/home

>> No.3751795

>>3751769
it's ok, we'll continue this. I'm still blown away by the follow up problem. My mind is broken, it's time for me to watch anime.

>> No.3751809

>>3751626
If /sci/ has a wiki I couldn't find it. In either case, I propped one up real quick, it should be easy enough to maintain for this sort of stuff. If a better one exists then dropping this one's easy enough.

http://mathsci.wikia.com/wiki//sci/_-_Math_%26_Science_Wiki

>> No.3751825

using the iteration notation, if each new element yielded a new permutation, then the string would have n elements from the first permutation + (n-1)!-1 element for the remaining permutation. so S=n+(n-1)!-1

but since you can't use only 0-iterations, this isn't the case. each i-iteration has an added cost of i. you use <span class="math">j_i[/spoiler] i-iterations. the maximum of i is n-2, because that is the number of elements you'd add if the overlap was only 1 element. So the goal would be to minimize
<span class="math">\sum_{i=1}^{n-1} i*j_i[/spoiler]

>> No.3751849

>>3751809
ah cool joining. Next week I'll post another, easier but quite peculiar exploration. It involves polynomials, series, and pascals triangle.

>> No.3751860

/sci/ - Math & Science

Yep.

>> No.3751869

>>3751860
just like it was meant to be.
can you add the google doc?

>> No.3751897

>>3751869
Aye, I just plopped it all on there. I'll organize it into something intelligible tomorrow, Kaiji just ruined my brain.

http://www.youtube.com/watch?v=OeLxUVACQF0

>> No.3751914

So something that could be important:
a 0-iteration switches the order of no elements (it just rotates the cycle without moving the cycle around). A 1-iteration can switch 2 elements around. A 2-iteration can switch 3 elements around. Basically, a k iteration can switch k+1 elements around in the cycle.
Example: A 1-iteration can take (1 2 3 4 5) to (1 2 4 3 5), and a 3 iteration can take (1 2 3 4 5) to (4 3 2 1 5) (this is allowing any number of 0 iterations). The important thing is that a k-2 iteration, combined with some number of 0 iterations, can do things that (k-3) 1-iterations + an arbitrary number of 0 iterations CANNOT do (for example, to rotate k-1 elements).
For example, a 3 iteration could take (1 2 3 4 5) to (4 1 2 3 5), but 2 1-iterations could not.
This seems like it could be generalized without too much difficulty to state that iterations with a total weight <= k-3 are weaker than a single k-2 iteration.

>> No.3751932 [DELETED] 

>>3751914
oops, i think k should be n for most of that, I don't think its true for k < n-2

>> No.3751949

>>3751914
k should be n for most of this

>> No.3751950

>>3751914
So I guess you're defining adjacency for the cycles. If a new permutation requires a 1-iteration, the cycle group it belongs to is adjacent to the previous. Adjacency is neither reflexive or transitive.

i.e. (1 2 3 4) is adjacent to (1 4 2 3) which is adjacent to (1 2 4 3). But (1 4 2 3) is not adjacent to (1 2 3 4) which is not adjacent to ( 1 2 4 3)

>> No.3751953

>>3751949
would you mind reposting? Also does /sci/ have an archive? because when I tried searching for thread I, I only found the opening post

>> No.3751965

>>3751914
>For example, a 3 iteration could take (1 2 3 4 5) to (4 1 2 3 5), but 2 1-iterations could not.
You only need a single 1-iteration (combined with 0-iterations) to do that:
1 2 3 4 5
2 3 4 5 1
3 4 5 1 2
4 5 1 2 3
1 2 3 5 4 (the 1-iteration)
2 3 5 4 1
3 5 4 1 2
5 4 1 2 3
4 1 2 3 5

>> No.3751979 [DELETED] 

>>3751953
The gentooman archive does archive things, but um. I can only ever retrieve individual posts, not the entire threads.

>> No.3751980

>>3751953
I'll just leave it at this - this is what happens when you start typing before you're done thinking about stuff:

So something that could be important:
a 0-iteration switches the order of no elements (it just rotates the cycle without moving the cycle around). A 1-iteration can switch 2 elements around. A 2-iteration can switch 3 elements around. Basically, a k iteration can switch k+1 elements around in the cycle.
Example: A 1-iteration can take (1 2 3 4 5) to (1 2 4 3 5), and a 3 iteration can take (1 2 3 4 5) to (4 3 2 1 5) (this is allowing any number of 0 iterations). The important thing is that a k iteration, combined with some number of 0 iterations, can do things that (k-1) 1-iterations + an arbitrary number of 0 iterations CANNOT do (for example, to rotate k+1 elements).
For example, a 3 iteration could take (1 2 3 4 5) to (4 1 2 3 5), but 2 1-iterations could not.
This seems like it could be generalized without too much difficulty to state that iterations with a total weight < k are weaker than a single k iteration.


Anyway, the goal would be more to show the triangle inequality with distance than to define adjacency. It doesn't seem like it would be that hard, but I'm too tired atm.

>> No.3751984

>>3751953
Thread 1 happened at the same time as changes in 4chan's HTML code that broke the archiver for a while, but see
>>3751122
for a copy.
But Thread II and this one are showing up on archive.gentoomen.org just fine.

>> No.3751995

>>3751965
Hmm
Make it: (1234567) -> (4123567)

>> No.3751996

>>3751718
should be 0-iteration and 1-iteration.
Was confused since the k-iteration is the (k+1)-edge from before.

>> No.3751997

>>3751953
I think I understand your point, that sometimes the amount of overlap will be 1,2..n. The only case I've looked at extensively is n=4. In that case, you'd have 0-iterations (obviously) as well as 1-iterations and 2-iterations (maximum). I wonder if for case n, if you must have a non-zero number of 0,1,2...n-2 iterations in the efficient process.

>> No.3752034

I wonder if there are any situations where a k iteration could be strictly stronger than every sum k set of iterations.

>> No.3752047

>>3752034
nevermind thats dumb. My intelligence has fallen enough that I'll force myself to sleep.

>> No.3752047,1 [INTERNAL] 

cevap 1 :D

>> No.3752047,2 [INTERNAL] 

>>3751197
nice

>> No.3752047,3 [INTERNAL] 

im gay #wow #whoa

>> No.3752047,4 [INTERNAL] 

niggers

>> No.3752047,5 [INTERNAL] 

put me in the screencap

>> No.3752047,6 [INTERNAL] 

Put THIS in your research paper:
BRAAAAAAAAAAP

>> No.3752047,7 [INTERNAL] 

*tink* *tink* *tink*
Attention everyone! Honestly, I have just one thing to say: Fuck mods and fuck jannies. Long live frogposters and funposting. Cheers.

>> No.3752047,8 [INTERNAL] 

Cite my anus

>> No.3752047,9 [INTERNAL] 

░░░░░░░░░▄▀▀▀░░░░░░░▀▄░░░░░░░
░░░░░░░▄▀░░░░░░░░░░░░▀▄░░░░░░
░░░░░░▄▀░░░░░░░░░░▄▀▀▄▀▄░░░░░
░░░░▄▀░░░░░░░░░░▄▀░░██▄▀▄░░░░
░░░▄▀░░▄▀▀▀▄░░░░█░░░▀▀░█▀▄░░░
░░░█░░█▄░░░░█░░░▀▄░░░░░▐░█░░░
░░▐▌░░█▀░░░▄▀░░░░░▀▄▄▄▄▀░░█░░
░░▐▌░░█░░░▄▀░░░░░░░░░░░░░░█░░
░░▐▌░░░▀▀▀░░░░░░░░░░░░░░░░▐▌░
░░▐▌░░░░░░░░░░░░░░░▄░░░░░░▐▌░
░░▐▌░░░░░░░░░▄░░░░░█░░░░░░▐▌░
░░░█░░░░░░░░░▀█▄░░▄█░░░░░░▐▌░
░░░▐▌░░░░░░░░░░▀▀▀▀░░░░░░░▐▌░
░░░░█░░░░░░░░░░░░░░░░░░░░░█░░
░░░░▐▌▀▄░░░░░░░░░░░░░░░░░▐▌░░
░░░░░█░░▀░░░░░░░░░░░░░░░░▀░░░

>> No.3752047,10 [INTERNAL] 

I miss moot

>> No.3752047,11 [INTERNAL] 

daily reminder to stay hydrated

>> No.3752047,12 [INTERNAL] 

Gas the kikes fuck off normalfags

>> No.3752047,13 [INTERNAL] 

put me in the research paper

>> No.3752047,14 [INTERNAL] 

Sup niggas this is some sick math shit yo

>> No.3752047,15 [INTERNAL] 

Ebin suomi :D

>> No.3752047,16 [INTERNAL] 

based

>> No.3752047,17 [INTERNAL] 

I think I solved it.

First calculate the max string which is the number of permutations multiplied by n.
Then divide the max string by n - 1
Then add to the answer the fibonacci number located at 2(n-3)

int max_string = n! * n;
int answer = max_string / (n - 1);
answer += fib(2(n-3));

Example for n = 5;

max_string = 5! * 5 = 600
answer = 600 / 4 = 150
answer += fib(2(5-3)) = fib(4) = 3
answer = 153

Here is the first 14 using this method:

2 -> 3
3 -> 9
4 -> 33
5 -> 153
6 -> 872
7 -> 5901
8 -> 46135
9 -> 408384
10 -> 4032377
11 -> 43909467
12 -> 522549784
13 -> 6745945965
14 -> 93884331311

>> No.3752047,18 [INTERNAL] 

Coma back when you found a solution to the nigger problem in the US

>> No.3752047,19 [INTERNAL] 

Congratulations, you newfags have discovered that new comments on archived threads are not locked down.

>> No.3752047,20 [INTERNAL] 

Very nice problem solving a true display of autism I could not be prouder of you autistic niggers

>> No.3752047,21 [INTERNAL] 

sage goes in every field goes in every field

>> No.3752047,22 [INTERNAL] 

WE DID IT REDDIT

ps bring back ghostposting on /jp/

>> No.3752047,23 [INTERNAL] 

im kinda confused with some of the terminology seeing as im only taking geometry rn so can someone explain edges/iterations/loops

>> No.3752047,24 [INTERNAL] 

Can someone implement this in a C-like lang so I can understand what the fuck is going on?

>> No.3752047,25 [INTERNAL] 

>>3751197
okay but what about the part where Jews make up 2% of the American population but 50% of Harvard graduates?

>> No.3752047,26 [INTERNAL] 

gewr

>> No.3752047,27 [INTERNAL] 

Ohohohaha ohohohehee ha.
Hello me old chum.
I'm gnot a gnelf.
I'm gnot a gnoblin.
I'm a gnome.
And you've been gnomed.

>> No.3752047,28 [INTERNAL] 

toasting in an epic (archived) bread

>> No.3752047,29 [INTERNAL] 

NIGGERS (this goes in the paper)

>> No.3752047,30 [INTERNAL] 

>>3752047,24
>the absolute state of cs ni/g/gers

>> No.3752047,31 [INTERNAL] 

Daddy’s 🧔 cummies, 💦 nice 😊 and yummy 😋
Thick 😫👌and gooey, feel like honey 🍯
That sweet 🍭 milk, 🥛 oh-so-tasty 🤤
Daddy, 🧔 Daddy, 🧔 please be hasty!💨
My tongue 👅 swirls 😛 round 🔁 and round 🔁
While Daddy 🧔 gives my ass 🍑 a great big pound 🤜💥
Over 😑 in the corner, wrapped 🎁 in chains ⛓
Mommy 👩 huddled over, screaming 😱 in pain 😪
“Shut up, bitch! 👩 Stay on the floor!”
Mommy 👩 sobbing 😭 louder, I 👧 call 🗣 her a whore
She reaches behind her 👩 for her gun 💀
While Daddy gropes 👋 and tickles 🤗 my sweet 🍬 buns 🍑
Puts the barrel 😛 between 👉👈 her teeth 👄
And Daddy’s 🧔 semen 💦 begins to seep ☔️
Gunpowder, blood, 💉 brains 🧠 and gore 😎
Mommy’s 👩 lifeless 👻 corpse slumps ⬇️ to the floor 😂
Cummies, 💦 cummies 💦 filling my throat
My pussy 🐱 is completely 😍 soaked 💦
But Daddy’s cock 🍆 just gets bigger 😳😲
Over near 😯 the drawers, he grabs the scissors ✂️
Cuts 🔪 a hole 🕳 in Mommy’s 👩 stomach
In her hand, 🤲 a gin and tonic 🍺
He 🧔 begins to unravel her strings of intestines 😝
“Look 👀 closely, you’ll learn 👨‍🏫 a lesson”
Ties a noose, 😔 rigs it tight 😫
“Sweetie, 👧 sweetie, 👧 no need to fight” 👊💥
Puts her 👩 guts 🤤 around 🔄 my neck
“Looks like everything’s good 👍 and set” 👌
Lets me fall down ⬇️ about 🤔💭 a yard
Face 👧 turning blue, choking 🤭 hard 💪
All the while, 🕑 Daddy’s 🧔 stroking his cock 🍆
And for a moment, 😳 our eyes 👁 lock 🔒
Tears 😭 of joy 😊 stream down my face 👧
I’m going to 😵 a better ✨ place~

>> No.3752047,32 [INTERNAL] 

Bill Clinton is a rapist! INFOWARS.COM

>> No.3752047,33 [INTERNAL] 

>░░▄░░░░░░░░░░▄▄██████▄▄░░░░░░░░░░░░▄▄▄▄ GNFOS.COM
>▄▄███▀░░░░░░▄██████████░░░░░░░░░░░░▀███ GNFOS.COM
>░▀███▄░░░░░░▀█████████░░░░░░░░░░░░░░████ GNFOS.COM
>░▄███▀░░░░░░░█████████░░░░░░░░░░░░░▄█▀▀▀ GNFOS.COM
>░░░░██░░░░░░░░░▀██████▄▄▄░░░░░░░░░██ GNFOS.COM
>░░░░░▐█▄░░░░░░▄███████████░░░░░░▄██▀ GNFOS.COM
>░░░░░░▀██▄░░▄█████████████▄░░░░██▀ GNFOS.COM
>░░░░░░░░▀▀█████████████████▄▄██▀ GNFOS.COM
>░░░░░░░░░░▐███████████████▌ GNFOS.COM
>░░░░░░░░░░▐██████████████▀█▀ GNFOS.COM
>░░░░░░░░░░█▌░░▀████████▀░░█▄ GNFOS.COM
>░░░░░░░░░░█▀░░░░██████░░░░██▄ GNFOS.COM
>░░░░░░░░░░█▄░░░░░█████░░░░▐█ GNFOS.COM
>░░░░░░░░░░██▄░░░░▀███▌░░░░▐█ GNFOS.COM
>░░░░░░░░░░▀█▄░░░░░███▀░░░░▐█ GNFOS.COM
>░░░░░░░░░░░▀█▄░░░░███▄░░░░██ GNFOS.COM
>░░░░░░░░░░░░██░░░░▀▀▀░░░░░█▌ GNFOS.COM
>░░░░░░░░▀▀▀▀▀▀░░░░░░░░░░░░██▄▄▄ GNFOS.COM

>> No.3752047,34 [INTERNAL] 

me bone me jo

>> No.3752047,35 [INTERNAL] 

toasting in epic bread

>> No.3752047,36 [INTERNAL] 

lo

>> No.3752047,37 [INTERNAL] 

okay so basically im monky (paper reference)

>> No.3752047,38 [INTERNAL] 

isn't it strange that 13% of the population commits over 50% of crimes?

>> No.3752047,39 [INTERNAL] 

>>3752047,38
It's not strange, it's genetics. Blacks are considerably more violent than most races.

>> No.3752047,40 [INTERNAL] 

cum

>> No.3752047,41 [INTERNAL] 

Animes are fucking gay and they can suck my proverbial dick
……………………………………….¸„„„„
…………………….…………...„--~*'¯…….'\
………….…………………… („-~~--„¸_….,/ì'Ì
…….…………………….¸„-^"¯ : : : : :¸-¯"¯/'
……………………¸„„-^"¯ : : : : : : : '\¸„„,-"
**¯¯¯'^^~-„„„---~^*'"¯ : : : : : : : : : :¸"
.:.:.:.:.„-^" : : : : : : : : : : : : : : : : :„-"
:.:.:.:.:.:.:.:.:.:.: : : : : : : : : : ¸„-^¯
.::.:.:.:.:.:.:.:. : : : : : : : ¸„„-^¯
:.' : : '\ : : : : : : : ;¸„„-~"
:.:.:: :"-„""***/*'ì¸'¯
:.': : : : :"-„ : : :"\
.:.:.: : : : :" : : : : \,
:.: : : : : : : : : : : : 'Ì
: : : : : : :, : : : : : :/
"-„_::::_„-*__„„~"

>> No.3752047,42 [INTERNAL] 

>>3752047,38
Nah man, it's poverty and racism.

Let's say a black dude is born in a poor area with bad public infrastructure, underfunded public education, and very few job opportunities. And even if he applies for good jobs in other areas, he will be discriminated against because of his race, which can make upward mobility or leaving a bad area a very difficult thing to do. So there's a cycle of poverty that is almost impossible to escape.

Then, let's say this guy is impoverished and is having difficulty in finding employment, so in an act of desperation, he steals some food from a gas station. Then the media will jump on him and make it sound like he's lazy and evil and therefore deserves to be poor. But that's not true at all.

Of course, that's not to say that all people are in poverty, or that all black people steal. What I am saying is that crime stats are skewed because vulnerable populations, such as those who are poor or discriminated against, might be more likely to commit crime because of their bad life circumstances, and if you were in a similar situation, you would do something similar too. Even poor white people are more likely to commit crimes than wealthy white people. Financial stability really helps.

It's easy to dehumanize other people if you don't have to face the same kind of adversity, but have some empathy and try to understand where other people are coming from.

You think crime is an issue of race. I think crime is an issue of poverty. Bring people out of poverty and they will stop committing crimes. You can pretend that success is all about an individual's actions, but a lot of it is actually about circumstances out of your control, such as the environment you grow up in.

>> No.3752047,43 [INTERNAL] 

>>3751197
now this is EPIC

>> No.3752047,44 [INTERNAL] 

math is fucking stupid yall are fucking virgin's

>> No.3752047,45 [INTERNAL] 

I can't stop farting. Farting on combinatorics algorithms!

>> No.3752047,46 [INTERNAL] 

>>3752047,44

Well you are just a nigger who can't do math. kys

>> No.3752047,47 [INTERNAL] 

Here come the desperate journalists, thanks to glorious standupmaths.

>> No.3752047,48 [INTERNAL] 

nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger nigger

>> No.3752047,49 [INTERNAL] 

If you read this you're a redditor

>> No.3752047,50 [INTERNAL] 

Matt Parker is a soy boy cuck

>> No.3752047,51 [INTERNAL] 

He did it for free

>> No.3752047,52 [INTERNAL] 

Yeah but what if I want kill every stinky nigger and jew in the US of A and use the least amount of money and gas, how would I do it??????

>> No.3752047,53 [INTERNAL] 

NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER

>> No.3752047,54 [INTERNAL] 

>>3752047,38
This really makes u think

>> No.3752047,55 [INTERNAL] 

NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGENIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER NIGGER

>> No.3752047,56 [INTERNAL] 

PARKER SQUARE
A
R
K
E
R

S
Q
U
A
R
E

>> No.3752047,57 [INTERNAL] 

29² 1² 47²
41² 37² 1²
23² 41² 29²

>> No.3752047,58 [INTERNAL] 

>people have invaded the archive since the video...

straal is gay

>> No.3752047,59 [INTERNAL] 

PS: Frank rocks btw

>> No.3752047,60 [INTERNAL] 

Dear intellectual elite, I appeal to you, the elite of society. Tell the fool where you ordered the essay?

>> No.3752047,61 [INTERNAL] 

Well, actually, I can advise you a pretty good service for writing an essay. I think this can completely solve your problem. The service works quickly and efficiently. I already had to contact this service before, so I can guarantee you the quality with my personal experience. Here is this service https://peachyessay.com/ . Try it, sure it will help you.

>> No.3752047,62 [INTERNAL] 

Oh no the spammers are here.

>> No.3752047,63 [INTERNAL] 

REDDIT REDDIT REDDIT r/woosh r/tech r/4chan

>> No.3752047,64 [INTERNAL] 

>>3751197
FUCK NIGGERS

>> No.3752047,65 [INTERNAL] 

Thanks for bringing up the topic. For essay writing services you can contact us or simply visit our website: https://peachyessay.com/

>> No.3752047,66 [INTERNAL] 

cmkasms

>> No.3752047,67 [INTERNAL] 

I love anime women, guns, and India.

>> No.3752047,68 [INTERNAL] 

BASED

>> No.3752047,69 [INTERNAL] 

>>3751197
Hi mom I'm on a mathematic theorem!
Also Kurisu is best girl and jews belong in the oven

>> No.3752047,70 [INTERNAL] 

>>3752047,64
log off kid

>> No.3752047,71 [INTERNAL] 

WE DID IT REDDIT

>> No.3752047,72 [INTERNAL] 

I hate anime women, guns, and India.

>> No.3752047,73 [INTERNAL] 

nigger

>> No.3752047,74 [INTERNAL] 

>>3751197
despite being 13% of the population

>> No.3752047,75 [INTERNAL] 

If you are an exhausted student of numerous academic assignments, I recommend you to use trusted custom essay writing service https://bestwritingservice.com/ which will ease your life a lot.

>> No.3752047,76 [INTERNAL] 

>>3752047,75
eat my penor you fuckin spic

>> No.3752047,77 [INTERNAL] 

asd

>> No.3752047,78 [INTERNAL] 

>>3751197
There are 26 bicycles and you want to find out how many different ways you can steal them all.

>> No.3752047,79 [INTERNAL] 

yes

>> No.3752047,80 [INTERNAL] 

Put me in the screenshot senpai

>> No.3752047,81 [INTERNAL] 

This is truly an unorthodox way of working. The results are always surprising using this method. https://www.vatnumberuk.com

>> No.3752047,82 [INTERNAL] 

>░░▄░░░░░░░░░░▄▄██████▄▄░░░░░░░░░░░░▄▄▄▄ GNFOS.COM
>▄▄███▀░░░░░░▄██████████░░░░░░░░░░░░▀███ GNFOS.COM
>░▀███▄░░░░░░▀█████████░░░░░░░░░░░░░░████ GNFOS.COM
>░▄███▀░░░░░░░█████████░░░░░░░░░░░░░▄█▀▀▀ GNFOS.COM
>░░░░██░░░░░░░░░▀██████▄▄▄░░░░░░░░░██ GNFOS.COM
>░░░░░▐█▄░░░░░░▄███████████░░░░░░▄██▀ GNFOS.COM
>░░░░░░▀██▄░░▄█████████████▄░░░░██▀ GNFOS.COM
>░░░░░░░░▀▀█████████████████▄▄██▀ GNFOS.COM
>░░░░░░░░░░▐███████████████▌ GNFOS.COM
>░░░░░░░░░░▐██████████████▀█▀ GNFOS.COM
>░░░░░░░░░░█▌░░▀████████▀░░█▄ GNFOS.COM
>░░░░░░░░░░█▀░░░░██████░░░░██▄ GNFOS.COM
>░░░░░░░░░░█▄░░░░░█████░░░░▐█ GNFOS.COM
>░░░░░░░░░░██▄░░░░▀███▌░░░░▐█ GNFOS.COM
>░░░░░░░░░░▀█▄░░░░░███▀░░░░▐█ GNFOS.COM
>░░░░░░░░░░░▀█▄░░░░███▄░░░░██ GNFOS.COM
>░░░░░░░░░░░░██░░░░▀▀▀░░░░░█▌ GNFOS.COM
>░░░░░░░░▀▀▀▀▀▀░░░░░░░░░░░░██▄▄▄ GNFOS.COM

>> No.3752047,83 [INTERNAL] 

A reliable writing service should be in the mind of every student, even the smartest. For example, I use the site from time to time https://www.customwritings.ws/ and order hard papers online for little money. This saves me from bad grades and saves me a lot of time.

>> No.3752047,84 [INTERNAL] 

https://www.google.com
<a href="https://www.google.com">ajay</a>
[url=www.google.com]kumar[/url]
keyword

>> No.3752047,85 [INTERNAL] 

Call +18333340433 & get instant resolution for all printers relates queries.
Get 24x7 supports by dialing Printer, Scanners customer care toll free USA phone number +18333340433. To fix any Printer, Scanners related issues contact our Printer Technical team

https://printersupportnumber.com/
https://printersupportnumber.com/epson-printer-support/
https://printersupportnumber.com/brother-printer-support/
https://printersupportnumber.com/canon-printer-support/
https://printersupportnumber.com/hp-printer-support/
https://printersupportnumber.com/dell-printer-support/
https://printersupportnumber.com/lexmark-support/
https://printersupportnumber.com/toshiba-support/
https://printersupportnumber.com/hewlett-packard-support/

>> No.3752047,86 [INTERNAL] 

https://www.call-support-number.com/
https://www.call-support-number.com/aol-support/aol-customer-service/
https://www.call-support-number.com/aol-support/aol-tech-support/
https://www.call-support-number.com/aol-support/aol-help/
https://www.call-support-number.com/aol-support/
https://www.call-support-number.com/aol-support/aol-phone-number/
https://www.call-support-number.com/aol-support/aol-email-support/
https://www.call-support-number.com/aol-support/aol-com-support/

>> No.3752047,87 [INTERNAL] 

https://www.call-support-number.com/hp-support/
https://www.call-support-number.com/hp-support/hp-printer-support/
https://www.call-support-number.com/hp-support/hp-computer-support/
https://www.call-support-number.com/hp-support/hp-laptop-support/
https://www.call-support-number.com/hp-support/hp-help/
https://www.call-support-number.com/hp-support/hp-contact/
https://www.call-support-number.com/hp-support/hp-tech-support/
https://www.call-support-number.com/hp-support/hp-customer-service/
https://www.call-support-number.com/hp-support/hp-phone-number/

>> No.3752047,88 [INTERNAL] 

https://www.call-support-number.com/canon-support/
https://www.call-support-number.com/canon-support/canon-customer-service/
https://www.call-support-number.com/canon-support/canon-tech-support/
https://www.call-support-number.com/canon-support/canon-phone-number/
https://www.call-support-number.com/canon-support/canon-help/

>> No.3752047,89 [INTERNAL] 

shieeeeet nigga

>> No.3752047,90 [INTERNAL] 

Wow, that's what I was searching for, what a material!present here at this website, thanks admin of this web site.
https://bubble-shooter.co

>> No.3752047,91 [INTERNAL] 

fuark

>> No.3752047,92 [INTERNAL] 

I am a Telecommunications engineer.Telecom Engineering is probably one of those fields that witnessed rapid advancement in recent years. It comes as no surprise that it is among the most pursued careers today. Whether you are a fulltime employee, looking to earn a few extra bucks by the side, or you are a self-employed engineer, simply trying to get your business up and running, there is much scope in freelance telecom engineer.
https://www.fieldengineer.com/sd-wan

>> No.3752047,93 [INTERNAL] 

Thank you for helping loved ones transition, for burying them with blessings and honor.
https://office-product-2019.com

>> No.3752047,94 [INTERNAL] 

For essay writing services you can contact us or simply visit our website: https://westwriters.com/

>> No.3752047,95 [INTERNAL] 

Microsoft Office often releases its latest updated version of its applications and productivity suite, and every latest update comes with various amazing and advanced features for the benefits of the users. Also, Microsoft provides a complete cloud-based productivity suite to fulfill the requirements of office and home users. To download, install, and activate office.com/setup, connect with the Microsoft expert team and avail optimum benefits. Learn how to easily enter 25 digit alphanumeric product activation key code and easily activate it. Get assistance for Office 2007, Office 2010, Office 2013, Office 2016, Office 365, etc.
http://get-office-2019.com/

>> No.3752047,96 [INTERNAL] 

Thanks for sharing information.We provide high quality service for Refrigerator repair in Sharjah. We repair all types of refrigerator at very affordable price.
https://repairairconditionuae.com/refrigerator-repair-in-sharjah/

>> No.3752047,97 [INTERNAL] 

Thanks for posting this info. I just want to let you know that I just check out your site and I find it very interesting and informative.
http://www-mcafeeactivate.support/
http://advisornorton.com/
http://www-office.uk/

>> No.3752047,98 [INTERNAL] 

You took common courtesy to an uncommon level. We’re so grateful for your help.


http://manage-notron.com/
http://offiice-products.com/
http://gofornorton.com/
http://goforoffice.com/
http://1mcafee.com/

>> No.3752047,99 [INTERNAL] 

I am thankful for the article post.Looking forward to visit more.
||http://officesetup-officecomsetup.com||
||http://officecomsetup.com||

>> No.3752047,100 [INTERNAL] 

It's phenomenally a surprising and key bit of information. I'm in remarkable spirits that you in a general sense offered this baffling information to us

>> No.3752047,101 [INTERNAL] 

Got stuck while writing your paper? Welcome to <a href="https://assignmentpress.com/" rel="dofollow">Assignment Press</a> the most complete knowledge base of <a href="https://assignmentpress.com/" rel="dofollow">samples and guides</a> to inspire your creativity.

>> No.3752047,102 [INTERNAL] 

To get started with your Microsoft Office Installation we can help you with our entire process to setup office product online.
||http://officesetup-officecomsetup.com/how-to-find-microsoft-office-product-key||

>> No.3752047,103 [INTERNAL] 

Mcafee provides protection to your data by encrypting the information over the internet.http://mcafee-activation.com

>> No.3752047,104 [INTERNAL] 

There are specific dissertation web-sites by using the online world to build safeguarded web saved with your website online.
Regards - https://ww-woffice.com/setup - http://https-www-office.com/setup - http://www.ms-officesetup.com

>> No.3752047,105 [INTERNAL] 

Thank for sharing us.Keep it up
<b><a href="https://www.bitul.org " title="Download materials">Download materials</a></b>

<b><a href=" https://www.bitul.in/coaching-institute/wbcs-coaching-center-in-kolkata/" title="WBCS Coaching Materials ">Daily Current Affairs</a></b>

<b><a href="https://www.banglatoday.in / " title="Bengali News ">Bangla News </a></b>

>> No.3752047,106 [INTERNAL] 

Great information you have shared through this post. Keep sharing good information with us. Thanks for sharing.

>> No.3752047,107 [INTERNAL] 

Great information you have shared through this post. Keep sharing good information with us. Thanks for sharing.
http://setup-officems.com/

>> No.3752047,108 [INTERNAL] 

Hey Thanks for sharing this valuable information with us. I will come back to your site and keep sharing this information with us.

>> No.3752047,109 [INTERNAL] 

I value all that you have added as far as anyone is concerned base.Admiring the time and exertion you put into your blog and definite data you offer.Thanks.

>> No.3752047,110 [INTERNAL] 

issues call mcafee support number 1-888-722-1666 and get free consultation. If you are facing a downloading issues then click on mcafee.com/activate and resolve your issues.

>> No.3752047,111 [INTERNAL] 

Love all the tips Thank you for sharing them! I hope you will continue to have similar posts to share with everyone.
https://sharepublic.trincoll.edu/SiteDirectory/gmtestblog/Lists/Training%20Request%20Form/DispForm.aspx?ID=405
http://saasurveys.flysaa.com/Lists/Business%20Class%20Concepts/DispForm.aspx?ID=287
https://espace.cern.ch/test-franck-collaboration/Lists/test%20survey/DispForm.aspx?ID=18
https://bighorn.doe.nv.gov/Bighorn/Lists/Count%20Day%20Survey%200809/DispForm.aspx?ID=206
http://www.rree.gob.pe/promocioneconomica/dpe/Lists/Persona%20Juridica%20MRE/DispForm.aspx?ID=366
http://survey.cisv.org/Lists/Evaluation%20of%20the%20Global%20Conference%202015/DispForm.aspx?ID=1023
http://ml007.k12.sd.us/PI/Lists/Post%20Tech%20Integration%20Survey/DispForm.aspx?ID=126
https://servicedesksurvey.cancercare.on.ca/Lists/TicketClosureSurvey/DispForm.aspx?ID=1364
http://ww2.pcypsitna.navarra.es/Participa/Lists/Encuesta%20VISOR%20SITNA%20Internet/DispForm.aspx?ID=101
http://portal.nurse.cmu.ac.th/computer/Lists/Survey/DispForm.aspx?ID=48
https://oag.treasury.gov.za/RMF/Lists/Framework%20Feedback/DispForm.aspx?ID=1664
https://sharepoint.protiviti.com/training/Lists/Student%20Surveys/DispForm.aspx?ID=615
http://www.durban.gov.za/Lists/Feedback/DispForm.aspx?ID=3813
http://ctp.rajasthan.gov.in/Lists/HitCounter/DispForm.aspx?ID=135
http://co60q.esa.int/Lists/ESTEC%20Co60%20Customer%20Satisfaction/DispForm.aspx?ID=776
https://know.obgyn.wisc.edu/sites/sst/Lists/Feedback/DispForm.aspx?ID=58

>> No.3752047,112 [INTERNAL] 

Norton setup - Get started with Norton by downloading the setup and installing it on the device. Enter the unique 25-character alphanumeric product key for activation. Check your subscription at
http://retailcard-activation.com
http://sitemcafee.com
http://offiiceoffice.com
http://2norton.com
http://au-norton.com
http://hbnorton.com

>> No.3752047,113 [INTERNAL] 

Norton.com/nu16 - Norton Utilities 16 is a reasonable program which comes will all the pertinent apparatuses in a simple to explore UI. Vault defragmenter fixes all the broken Windows library records and other related bugs. This clears up a great deal of information and along these lines helps the speed of the PC. http://norton-nu16.com/

>> No.3752047,114 [INTERNAL] 

Norton offers numerous adaptations which has diverse highlights with various value go. Picking the best form according to your necessity is the most astute activity. Here, we have clarified the detail data about the <a href="http://norton-com-nu16.com/">norton.com/nu16</a>. Norton.com/nu16 has the best of highlights which gives you a chance to utilize the PC without agonizing over any spyware or risk.

>> No.3752047,115 [INTERNAL] 

Collaborate for free with online versions of Microsoft Word, PowerPoint, Excel, and OneNote. Save documents, spreadsheets, and presentations online, in OneDrive.
http://nnortonn.com/
https://setup-product-key.com/
http://www.httpnortoncomsetup.com/
http://how-to-activate.me/

>> No.3752047,116 [INTERNAL] 

Hulu provides the simplest way to stream entertainment to your TV. On your terms. With thousands of available channels. We provide information regarding Hulu Activation Code. Go to hulu.com/activate, and enter the Activation Code

>> No.3752047,117 [INTERNAL] 

Hulu provides the simplest way to stream entertainment to your TV. On your terms. With thousands of available channels. We provide information regarding Hulu Activation Code. Go to hulu.com/activate, and enter the Activation Code

https://activatehulu.com/

https://hulucomactivatecode.com/

>> No.3752047,118 [INTERNAL] 

McAfee has comprehensive cyber security solutions. Secure your computers, endpoints, network and cloud from viruses, malware and other security threats. We provide information regarding McAfee Activation Code. Go to McAfee.com/activate, and create your account and then enter the Activation Code

https://McafeeHelp-Mcafee.com

http://comactivatedownload.com/

>> No.3752047,119 [INTERNAL] 

Webroot delivers next-generation endpoint security and threat intelligence services to protect businesses and individuals in a connected world. And We provide information regarding Webroot Installation with Code. Go to webroot.com/safe and enter Security Code.\

https://secureanywheresetup.com/

>> No.3752047,120 [INTERNAL] 

Stay protected from the latest threats – ransomware, viruses, malware, spyware,unwanted programs, and more.

>> No.3752047,121 [INTERNAL] 

Microsoft Office is a complete and fully updated Office application for all your needs for home and business uses.

http://www-officecomsetup.com

>> No.3752047,122 [INTERNAL] 

sneed feed and seed

>> No.3752047,123 [INTERNAL] 

Hello, I'm Smith Warner. If you are facing issues with mcafee, norton and office product. then you can visit my website.
https://pro-norton.com/
https://go-mcafeecomactivate.com/
https://pro-norton.com/setup/
http://www-offiice.com/
http://www-offiice.com/setup/

>> No.3752047,124 [INTERNAL] 

Microsoft Office is a complete and fully updated Office application for all your needs for home and business uses.http://oofficecomsetupp.com

>> No.3752047,125 [INTERNAL] 

This info very good its really very very informative great stuff post i appreciate your work..


http://manage-notron.com/
http://offiice-products.com/
http://goforoffice.com/
http://gofornorton.com/
http://1mcafee.com/
http://goforoffice.com/setup/
http://gofornorton.com/setup/
http://1mcafee.com/activate/

>> No.3752047,126 [INTERNAL] 

i like the content of your post. thanks

>> No.3752047,127 [INTERNAL] 

Wonderful blog! I found it while browsing on Yahoo News

http://www.officecomsetup-officesetup.com

>> No.3752047,128 [INTERNAL] 

Our leading https://assignmentpress.com provides custom written papers(https://assignmentpress.com/write-my-paper/) in 80+ disciplines. Order either short essays(https://www.westwriters.com/write-my-essay/) or extensive dissertations(https://assignmentpress.com/dissertation-help/) & our expert ENL writers will easily prepare a paper according to your requirements.

>> No.3752047,129 [INTERNAL] 

Talking of good antivirus, we recommend the best antivirus in the market that is Norton Antivirus.

>> No.3752047,130 [INTERNAL] 

I'm extremely pleased to uncover this website. I need to thank you one time, just for this wonderful read
https://www.offiice-settup.com
https://www.office-setupp.com
https://www.offiice-ssetup.com

>> No.3752047,131 [INTERNAL] 

This is a wonderful site on internet exploring knowledge about gifts cards, online survey, and wonderful gifts visit it https://cashogame.com/

>> No.3752047,132 [INTERNAL] 

Pass any drug test with fake urine easily, this the wonderful to know about powdered urine and synthetic urine for info visit http://realpowderedurine.com

>> No.3752047,133 [INTERNAL] 

Get your free car instantly. get participated n govt free cars for needy and people in need visit this https://carsforyourhelp.com

>> No.3752047,134 [INTERNAL] 

Get your free hacked Credit card, virtual credit card, real active credit card visit this https://Govtjobstyari.com

>> No.3752047,135 [INTERNAL] 

Thanks A Lot For The Post. It Has Helped Me Get Some Nice Ideas
https://www.officecomsetup-officesetup.com

>> No.3752047,136 [INTERNAL] 

very good informations
https://www.med-esthetique.net
https://www.med-esthetique.net/sleeve-gastrectomie-tunisie/
https://www.med-esthetique.net/bypass-gastrique-tunisie/
https://www.med-esthetique.net/penoplastie-tunisie/
https://www.med-esthetique.net/facettes-dentaires-tunisie/
https://www.med-esthetique.net/implant-dentaire-tunisie/
https://www.med-esthetique.net/augmentation-mammaire-tunisie/
https://www.med-esthetique.net/augmentation-fesses-tunisie/
https://www.med-esthetique.net/liposuccion-tunisie/
https://www.med-esthetique.net/abdominoplastie-tunisie/

>> No.3752047,137 [INTERNAL] 

Thanks for posting this valuable information, really like the way you used to describe. Hope I'll get such posts in future too.

http://onmcafee.com/activate/
http://aprnorton.com/setup/
http://productmsoffice.com/
http://gomsoffice.com/

>> No.3752047,138 [INTERNAL]  [DELETED] 

For their designated purposes, yes. Let me point out, as viewed here on Quora, those designated purposes are rarely being appraised.
<a href="https://www.worldwide-iq-test.com/iq-tests"> Best online IQ tests</a> are important diagnostic tools for the treatment of those suffering from physical impairments to the brain (conditions, injury or disease) by tracking deterioration or treatment.
They are also excellent for broad parsing of subject groups separating those of average intelligence from those who require special education (the 1 in 6 below average) and those who need greater stimulation/challenge (the 1 in 6 above average). Importantly, this category must be viewed to hold against cultural bias.

Information also in other languages:
<a href="https://www.worldwide-iq-test.com"> Free online IQ test</a>

<a href="https://www.worldwide-iq-test.com/ko">온라인 지능 테스트</a>


<a href="https://www.worldwide-iq-test.com/ja"> オンラインの知能テスト</a>

<a href="https://www.worldwide-iq-test.com/ru"> Тестирование умственных способностей в режиме онлайн</a>

<a href="https://www.worldwide-iq-test.com/es"> Test de inteligencia en línea</a>

>> No.3752047,139 [INTERNAL] 

I think this is an informative post and it is very useful and knowledgeable. therefore, I would like to thank you for the efforts you have made in writing this article. If you are looking for antivirus security for your PC and any other digital devices than. [email protected]: my sites :- http://office-office.org/
http://officecomsetupms.com/
http://comsoffice.com
http://comsnorton.com/

>> No.3752047,140 [INTERNAL] 

http://bitdefender-login.com/
http://www.mcafeeactivates.uk/

>> No.3752047,141 [INTERNAL] 

Do you face problems with your Printers while installing a new wifi printer or fixing the old one .NOT A PROBLEM !
We got here all the answers to questions so that you can fix these problems yourself
All the links related to these problems will be provided here with questions .
For more Info Visit : https://www.brotherprintersupport.co.uk

https://www.brotherprintersupport.co.uk

https://www.brotherprintersupport.co.uk/brother-printer-support/

<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">Brother Printer Support</a> or Call : +44-121-286-4615

How To fix Brother Printer Error TS-02 Call +44-121-286-4615

https://www.brotherprintersupport.co.uk/2019/06/24/how-to-fix-brother-printer-error-ts-02-call-44-121-286-4615/

<a href="https://www.brotherprintersupport.co.uk/2019/06/24/how-to-fix-brother-printer-error-ts-02-call-44-121-286-4615">Brother Printer Support</a> or Call : +44-121-286-4615

How to Solve Brother Printer Error 9923 - Call : +44-121-286-4615

https://www.brotherprintersupport.co.uk/2019/06/24/how-to-solve-brother-printer-error-9923-call-44-121-286-4615/


<a href="https://www.brotherprintersupport.co.uk/2019/06/24/how-to-solve-brother-printer-error-9923-call-44-121-286-4615/">Brother Printer Support</a> or Call : +44-121-286-4615


<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer not printing</a>
<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer error</a>
<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer support number</a>

>> No.3752047,142 [INTERNAL] 

Norton Antivirus Basic provides industry leading protection for your PC - Instantly download and receive your activation code to be protected in minutes!
http://gonortonlogin.com

>> No.3752047,143 [INTERNAL] 

Your PC needs protection against malware, and free antivirus software may be enough.Even if you use your PC for nothing but posting political screeds on social media, you need to protect it with an antivirus.
http://activationkaspersky.services/
http://my-avast.com/
http://Avastlogin.com
http://Avast-login.com

>> No.3752047,144 [INTERNAL] 

McAfee.com/activate - Learn Easy Steps to do McAfee Activate Product Key and Get Started with McAfee Activation using Product Key mentioned on Retail card.

>> No.3752047,145 [INTERNAL] 

McAfee Activate indeed offers its free McAfee antivirus download with the basic set of virus removal features.
<a href="http://mcafeekeyactivates.com/">McAfee.com/Activate</a> <a
href="http://mcafeedellactivate.com/">McAfee.com/Activate</a>

>> No.3752047,146 [INTERNAL] 

For their designated purposes, yes. Let me point out, as viewed here on Quora, those designated purposes are rarely being appraised https://www.worldwide-iq-test.com/iq-tests Best online IQ tests are important diagnostic tools for the treatment of those suffering from physical impairments to the brain (conditions, injury or disease) by tracking deterioration or treatment.
They are also excellent for broad parsing of subject groups separating those of average intelligence from those who require special education (the 1 in 6 below average) and those who need greater stimulation/challenge (the 1 in 6 above average). Importantly, this category must be viewed to hold against cultural bias.

Information also in other languages:

https://www.worldwide-iq-test.com
Free online IQ test

https://www.worldwide-iq-test.com/ko
지능 테스트</a>

https://www.worldwide-iq-test.com/ja
オンラインの知能テスト</a>

https://www.worldwide-iq-test.com/ru
Тестирование умственных способностей в режиме онлайн

https://www.worldwide-iq-test.com/es
Test de inteligencia en línea

>> No.3752047,147 [INTERNAL] 

Avast Support Number For Avast Antivirus download, installation and un-installation error, renew your Avast antivirus subscription.
http://www.customersupportus.com/avast/

>> No.3752047,148 [INTERNAL] 

Are you facing issues in your TomTom GPS device which you aren’t able to solve? Contact the experts to get help via TomTom Customer Support Number USA.
http://www.800tollfreeno.com/tomtom-gps-customer-service-phone-number/

>> No.3752047,149 [INTERNAL] 

Contact HP Printer Support Number to get support for the issues which you face in your printers via HP Printer Support Number to converse with the experts.
http://www.hphelpnumber.net/hp-printer-support/

>> No.3752047,150 [INTERNAL] 

Call HP Printer Support Number for help to resolve issues of printers. Glitches faced on printers - paper load & jams, driver, install, won’t print.
http://www.hpcustomercares.com/hp-printer-support.php

>> No.3752047,151 [INTERNAL] 

Thanks for posting this valuable information, really like the way you used to describe
http://freegiftcardgenrator.com
http://onlinefreegiftcodesgenerator.com
http://onlinefreegiftcardgenerator.com
http://realgiftcardgenerator.com
http://topvideodownloader.com

>> No.3752047,152 [INTERNAL] 

Thank you for sharing this useful information, I will regularly follow your blog
http://norton-setup-usa.com

>> No.3752047,153 [INTERNAL] 

I am a Young fellow who loves to write. I'll quote myself by saying that I am a human by nature, writer by profession and a mighty traveler by passion. I'll always want to write about the things that people are using in their day to day life.

My Creations : https://rokucomlink11.shutterfly.com
http://rokucomlink.mee.nu/

>> No.3752047,154 [INTERNAL] 

My musical instruments: https://guidessimo.com/guides-type/musical-instrument/
My car alarm: https://guidessimo.com/guides-type/car-alarm/
My clock radio: https://guidessimo.com/guides-type/clock-radio/

>> No.3752047,155 [INTERNAL] 

>thread unironically filled with ad bots
Glad I was here before the second Matt Parker video.

>> No.3752047,156 [INTERNAL] 

mcafee setup is one of the best Security Antivirus product which can completely protect your digital online life. You can securely surf the internet with the mcafee antivirus.
Best regards:- http://mymcafeeactivate.com

>> No.3752047,157 [INTERNAL] 

https://www.brotherprintersupport.co.uk

https://www.brotherprintersupport.co.uk/brother-printer-support/

<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">Brother Printer Support</a> or Call : +44-121-286-4615

How to Solve Installation Problem with my Brother printer using a USB/local connection

https://www.brotherprintersupport.co.uk/2019/06/27/how-to-solve-installation-problem-with-my-brother-printer-using-a-usblocal-connection/

How to Setup Brother Wireless Printer Call +44-121-286-4615
https://www.brotherprintersupport.co.uk/2019/06/28/how-to-setup-brother-wireless-printer-call-44-121-286-4615/
<a href="https://www.brotherprintersupport.co.uk/2019/06/28/how-to-setup-brother-wireless-printer-call-44-121-286-4615/">Brother Wireless Support</a> or Call : +44-121-286-4615

<a href="https://www.brotherprintersupport.co.uk/2019/06/27/how-to-solve-installation-problem-with-my-brother-printer-using-a-usblocal-connection/">Brother Printer Support</a> or Call : +44-121-286-4615

Brother Printer Drivers Call: +44-121-286-4615

https://www.brotherprintersupport.co.uk/2019/06/27/brother-printer-drivers-call-44-121-286-4615/


<a href="https://www.brotherprintersupport.co.uk/2019/06/27/brother-printer-drivers-call-44-121-286-4615/">Brother Printer Support Drivers</a> or Call : +44-121-286-4615


<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer error 1168</a>
<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer error 35</a>
<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer error ys-02</a>

>> No.3752047,158 [INTERNAL] 

Thank you for this interesting post. Please keep updating.

>> No.3752047,159 [INTERNAL] 

Thank you for this interesting post. Please keep updating.
https://www.antorini.com/collections/mens-leather-briefcases

>> No.3752047,160 [INTERNAL] 

AOL specialists caution the AOL clients to check the secret key while composing. AOL User must check the record settings as well. Whenever required, they can talk with AOL specialists. A few AOL users neglected to recall the secret phrase because of unpredictable exercises in a record. All things considered, they have to make a private note of it.
If the AOL Desktop gold users want to know anything about AOL, at that point they are always welcomed to the AOL gold support number. AOL Gold Support team is avail for 24x7 hours.
For More Information, You can visit:
Website: https://supporthelplinenumber.com/
Email address: [email protected]

>> No.3752047,161 [INTERNAL] 

Hulu allows you to stream many movies and shows on your device. For hulu.com/activate, just enter the activation code and link it with your device. Enjoy continuous streaming! To know more, visit https://www.hulu-com-activate.com/

>> No.3752047,162 [INTERNAL] 

drug test is the worst test ever faced for pre employment while givin a kick to marijuana and weed addiction, your pennis wont be useful if urine is not coming out https://bit.ly/2YeFC0S

>> No.3752047,163 [INTERNAL] 

This is damn gud place to get a car from donation, cars from donation and donated cars are waiting for you here http://bit.ly/Salvationarmy

>> No.3752047,164 [INTERNAL] 

here get all your online earning sources which are gonna help you to get freebies and giftcards http://bit.ly/Inboxdollarcash

>> No.3752047,165 [INTERNAL] 

Here you will find all the best and cheap kitchen equipment's to help out housewives and ladies who are seeking for kitchen equipment for cheap price Www.kitchenchimneyexpert.in

>> No.3752047,166 [INTERNAL] 

Download, Install, Re Install or Activate Mcafee Computer & Internet Security to get maximum cyber protection against Online and Offline threats & infections over the internet. https://nortonsetup-key.com | http://msofficesetup.org | http://mymcafeeactivate.com

>> No.3752047,167 [INTERNAL] 

Yahoo mail service in one of the best email service there are lot of users of yahoo mails, if you are one of them and getting issue while accesing your yahoo mail then contact yahoo for support, we will give you best support for your all issue.
https://www.contactyahoohelpdesk.com/contact-yahoo-helpdesk/

>> No.3752047,168 [INTERNAL] 

awesome site..
https://officecommoffice.com

>> No.3752047,169 [INTERNAL] 

https://www.bigvalueshop.com/
https://www.bigvalueshop.com/product-category/sports/
https://www.bigvalueshop.com/shop/

>> No.3752047,170 [INTERNAL] 

Mcafee is one of the best antiviruses in the world of antivirus. If you are getting error in downloading and activation then click on this given link McAfee.com/activate Or we have a second option to resolve the query is that call McAfee support number 1-888-722-1666 and clear your issues.

>> No.3752047,171 [INTERNAL] 

https://www.brotherprintersupport.co.uk

https://www.brotherprintersupport.co.uk/brother-printer-support/

<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">Brother Printer Support</a> or Call : +44-121-286-4615

How to Solve Installation Problem with my Brother printer using a USB/local connection

https://www.brotherprintersupport.co.uk/2019/06/27/how-to-solve-installation-problem-with-my-brother-printer-using-a-usblocal-connection/

How to Setup Brother Wireless Printer Call +44-121-286-4615
https://www.brotherprintersupport.co.uk/2019/06/28/how-to-setup-brother-wireless-printer-call-44-121-286-4615/
<a href="https://www.brotherprintersupport.co.uk/2019/06/28/how-to-setup-brother-wireless-printer-call-44-121-286-4615/">Brother Wireless Support</a> or Call : +44-121-286-4615

<a href="https://www.brotherprintersupport.co.uk/2019/06/27/how-to-solve-installation-problem-with-my-brother-printer-using-a-usblocal-connection/">Brother Printer Support</a> or Call : +44-121-286-4615

Brother Printer Drivers Call: +44-121-286-4615

https://www.brotherprintersupport.co.uk/2019/06/27/brother-printer-drivers-call-44-121-286-4615/


<a href="https://www.brotherprintersupport.co.uk/2019/06/27/brother-printer-drivers-call-44-121-286-4615/">Brother Printer Support Drivers</a> or Call : +44-121-286-4615


<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer helpline</a>
<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer support number</a>
<a href="https://www.brotherprintersupport.co.uk/brother-printer-support/">brother printer technical support</a>

>> No.3752047,172 [INTERNAL] 

One copy of Windows was installed on multiple PCs McAfee Software License Terms specify a certain number of devices (PCs) on which a single copy of McAfee may be installed. Perhaps, your product key is being used on multiple devices (PCs). Under such circumstances, you are likely to face McAfee Activation Errors.

<a href="http://mcafeekeyactivates.com/">McAfee.com/Activate</a>

<a href="http://mcafeedellactivate.com/">McAfee.com/Activate</a>

>> No.3752047,173 [INTERNAL] 

<a title="Cars" href="badcreditcarfinance.eklablog.com/">Cars</a>

>> No.3752047,174 [INTERNAL] 

https://carsforyou.kinja.com

>> No.3752047,175 [INTERNAL] 

Mcafee provides security from all kinds of threats, malware & other security related issues. thanks

>> No.3752047,176 [INTERNAL] 

http://www.123hpsetup123hp.com

>> No.3752047,177 [INTERNAL] 

Microsoft Office is a family of client software, server software, and services developed by Microsoft.
https://www.offiice-office.com

>> No.3752047,178 [INTERNAL] 

I am very happy to discover your post as it will become on top in my collection of favorite blogs to visit.

https://www.godissertationhelp.co.uk/paraphrasing-services/
https://www.godissertationhelp.co.uk/personal-statement-help/
https://www.godissertationhelp.co.uk/book-report-help/

>> No.3752047,179 [INTERNAL] 

office.com/setup, Office Setup with product key Visit www.office.com/setup and follow the on-screen instructions for Office 2019, Office 365, Step by Step.
http://office-officecomoffice.com

>> No.3752047,180 [INTERNAL] 

At present printers are considered as an indispensable gadget. From office use to home purposes, HP printers are used everywhere for printing several documents, pictures, and many more things. But sometimes due to some technical glitches your printers may start to throw some error that disrupts your whole work poorly. One such issue in HP printer is Printer Not Activated Error that users encounter too often. If you are also victim of the same issue, then it is quite important to eliminate the problem before its getting too late. By calling at HP Customer Support Phone Number and taking aid from skilled professionals, you can easily terminate this error from the root. https://www.hpprintersupportpro.com/hp-printer-customer-support

>> No.3752047,181 [INTERNAL] 

Thanks for sharing this information
For AOL mail - Find here step-by-step procedure to setup your AOL mail and create a new AOL mail account. If you forget your AOL mail password or find any other issue in AOL login/sign in or sign up/register, call AOL tech expert toll-free number now.
http://aol-mail.support/
https://www.how-to-uninstall.us/norton-setup/

>> No.3752047,182 [INTERNAL] 

my.avast.com - Manage Avast Account by Avast Login at my.avast.com or id.avast.com and Manage Avast Services like Avast Activation, Billing Information, etc

>> No.3752047,183 [INTERNAL] 

Hulu provides the simplest way to stream entertainment to your TV. On your terms. With thousands of available channels. We provide information regarding Hulu Activation Code. Go to hulu.com/activate, and enter the Activation Code

https://activatehulu.com/

>> No.3752047,184 [INTERNAL] 

Description
Watch your favorite live sports, news, entertainment, and more. Plus, get unlimited access to the entire Hulu streaming library
To activate Hulu code go to url
if you need help to activate Hulu

https://activatehulu.com/

>> No.3752047,185 [INTERNAL] 

Perder peso puede parecer abrumador: debe descubrir cómo comer de manera saludable y alimentar su cuerpo adecuadamente, planificar un régimen de ejercicios que funcione para usted, dormir lo suficiente y, finalmente, tomar cientos de opciones cada día que lo acerquen más. tu objetivo o te tirará completamente fuera de pista.
https://www.saludpulso.com/
https://www.saludpulso.com/200-mejores-consejos-para-perder-peso/

>> No.3752047,186 [INTERNAL] 

Facing issue with Microsoft Office we are here to help ou with step by step instructions.

>> No.3752047,187 [INTERNAL] 

This post is very simple to read and appreciate without leaving any details out.
https://www.offiice-office.com

>> No.3752047,188 [INTERNAL] 

Setup And Install Your Office Product With Activation Key
<a href="https://www.officeprosetup.co.uk">office.com/setup</a>

>> No.3752047,189 [INTERNAL] 

This post is very <a title="simple" href="https://www.bohemianland.com/">simple</a>
to read and appreciate without leaving any details out

>> No.3752047,190 [INTERNAL] 

Avast Login - Now Login to Avast Account and Access Avast Management Console in order to Manage Services like Subscriptions, Activation etc at my.avast.com"
http://myavastlogin.com/

>> No.3752047,191 [INTERNAL] 

If your purchase of Office came with a product key, you enter your product key subscription.

https://www.offiice-office.com

>> No.3752047,192 [INTERNAL] 

Norton antivirus helps to keep away the viruses from the device, and it also protects them from malware, adware and other things that attempt access and tries to damage the system. If you install Norton antivirus or other Norton products on your device, you can protect your data and save your computer from additional damage.protect and create

>> No.3752047,193 [INTERNAL] 

Norton antivirus helps to keep away the viruses from the device, and it also protects them from malware, adware and other things that attempt access and tries to damage the system. If you install Norton antivirus or other Norton products on your device, you can protect your data and save your computer from additional damage.protect and create
http://norton-setup-account.com/

>> No.3752047,194 [INTERNAL] 

Get the solutions to all the technical issues of your electronic appliances with Geek Squad Online Support. The Geek Squad provides wide no of services over the Internet via remote access and also provides 24/7 telephone and emergency on-site support.
https://geek-customer-care.com/geek-squad-online-support.html

>> No.3752047,195 [INTERNAL] 

Get the best technical help and guidance at Geek Squad Tech Support. Get in touch with extensively trained tech support team for all sort of queries and issues regarding your devices. You can contact Geek Squad round the clock according to your convenience.
https://geekstechs.org/geek-squad-tech-support/

>> No.3752047,196 [INTERNAL] 

Geek Squad Tech Support team assures you solution for every issue that your technical device or gadget may face. Simply reach these Geek Squad experts anytime you require and avail some great help.
https://geekstechs.org/geek-squad/

>> No.3752047,197 [INTERNAL] 

AOL Tech Support Phone Number is a customer care helpline that is offered by one of world's best mail service provider. The experts at this toll-free helpline renders all your forget password, password recovery and other related issues. Reach them anytime of day or night at AOL Tech Support whenever you need their help.

>> No.3752047,198 [INTERNAL] 

Canon Printer Support is a team of experts who takes care of your canon device issue. If face any problem with your device like your device is crashed , device is not working properly or others then contact Canon Support and get instant help.

>> No.3752047,199 [INTERNAL] 

Canon Printer Support is a team of experts who takes care of your canon device issue. If face any problem with your device like your device is crashed , device is not working properly or others then contact Canon Support and get instant help. For more information:- https://hpprinterstroubleshooting.com/canon-printer-support/

>> No.3752047,200 [INTERNAL] 

Dell Printer Support is a team of well experienced experts who takes care of your dell device problems. If face any problem with your device like your device is crashed, device is not working properly, paper jamming or others then contact at Dell Support and get instant help. For more information:- https://hpprinterstroubleshooting.com/dell-printer-support/

>> No.3752047,201 [INTERNAL] 

HP Printer Support is active helpline that is available round the clock to resolve Hp printer problems. If you face any problem with your printer like device is not working properly, paper jamming issue, cable wire problem and others then reach experts of HP Printer Support and get instant help. For more information visit:- https://hpprinterstroubleshooting.com/

>> No.3752047,202 [INTERNAL] 

Dell Support is a team of experts who takes care of your dell device issue. If face any problem with your device like your device is crashed , device is not working properly or others then contact Dell Tech Support and get instant help. For more information:- https://techsupportsnumber.com/dell-support/

>> No.3752047,203 [INTERNAL] 

HP Support is a team of experts who takes care of your hp device issue. If face any problem with your device like your device is crashed , device is not working properly or others then contact HP Tech Support and get instant help. For more information:- https://techsupportsnumber.com/hp-support/

>> No.3752047,204 [INTERNAL] 

To get started with your Microsoft Office Installation we can help you with our entire process to setup office product online.https://officesetup-officecomsetup.com

>> No.3752047,205 [INTERNAL] 

Acer Support is a team of well experienced experts who takes care of your Acer devices. If you are facing any problem with your Acer device like your device is crashed, device is not working properly or any other problem then contact toll free number of Acer Tech Support and get instant help. For more information:- https://techsupportsnumber.com/acer-support/

>> No.3752047,206 [INTERNAL] 

Brother Printer Support is a team of well experienced experts available round the clock to resolve your printer problems. If you face any problem with your device like cable problem, cartage problem, paper jamming and others then reach the experts at Brother Support toll free number and get instant help. For more information:- https://hpprinterstroubleshooting.com/brother-printer-support/

>> No.3752047,207 [INTERNAL] 

Matwave is a leading and trusted electric toothbrush supplier and water flosser supplier serving its customers with the best products for quite some time now.
Visit here: https://matwavecn.com/

>> No.3752047,208 [INTERNAL] 

https://matwavecn.com/product/flo-nasal-irrigation/

>> No.3752047,209 [INTERNAL] 

This artificial stone supplier China is made with the best components. Other than that, you can also request for customized pieces for all your bulk orders.
Website: https://www.jundestoneltd.com/product/artificial-stone/

>> No.3752047,210 [INTERNAL] 

https://fashionaccessoriesantorini.blogspot.com/
https://snakeskinwallets.blogspot.com/
https://mensleatherwallet.blogspot.com/
https://leatherbriefcasesformen.blogspot.com/
https://italiansilkscarves.blogspot.com/
https://leatherfashionaccessories.blogspot.com/

>> No.3752047,211 [INTERNAL] 

Hello guys i am john wick and we provide securty services regarding all types of antivirus . Avast antivirus is one of them So any query related to avast visit our official website .

>> No.3752047,212 [INTERNAL] 

https://www.anpingyadong.com/category/welded-wire-mesh/777912/0
https://www.anpingyadong.com/category/chain-link-fence/777914/0

>> No.3752047,213 [INTERNAL] 

Configuring a home router requires you to log on to it. For that, you need to know the IP address of the router. All routers can be accessed through web and this can be done by using their IP address. Home networks use IP addresses starting with 192.168. Generally, the routers have IP addresses such as 192.168.0.1 or 192.168.1.1
https://192-168-11.me

>> No.3752047,214 [INTERNAL] 

Great post i must say and thanks for the information. Education is definitely a sticky subject. However, is still among the leading topics of our time. I appreciate your post and look forward to more.
Regards: https://office.set-setup.com
https://norton.set-setup.com
https://imcafeecom-activate.me

>> No.3752047,215 [INTERNAL] 

If you getting any issue then contact https://geektechsupport.me/webroot-geek-squad/

>> No.3752047,216 [INTERNAL] 

This is very interesting content! I have thoroughly enjoyed reading your points and have come to the conclusion that you are right about many of them.

>> No.3752047,217 [INTERNAL] 

This is very interesting content! I have thoroughly enjoyed reading your points and have come to the conclusion that you are right about many of them.
best regards: https://www.officecommsetup.com

>> No.3752047,218 [INTERNAL] 

Norton.com/setup - Download Setup, Redeem Product Key and Install Norton on your computer from www.norton.com/setup with Norton Account.
http://nortoncomsetup.xyz

>> No.3752047,219 [INTERNAL] 

Get the support of our best technicians if you have any issue related to Lexmark Printer, you can solve your problems by just following the few steps guided by our technicians over the phone. Even if you do not have any knowledge of computer or printer, our printer specialists will guide you in such a way that it would look like a walk in the park for you.

>> No.3752047,220 [INTERNAL] 

Thanks for the topic. I remember my jitters before the wedding. I just had a session at this time. A resource helped me then ... And I passed the session successfully.

>> No.3752047,221 [INTERNAL] 

Thanks for the topic. I remember my jitters before the wedding. I just had a session at this time. A resource helped me then https://www.essay-company.com/essay-writer. And I passed the session successfully.

>> No.3752047,222 [INTERNAL] 

You are the most joyful individual if you exceed expectations in making your exotic science with your partner a superior one. In any case, you begin getting baffled if you begin seeing issues in your genuine life. If you are discouraged because of the issue of erectile dysfunction, at that point you should begin taking Cenforce 200mg. The best answer for weakness is Cenforce 200 mg. Some of the time, this medication is also used to treat the side effects of favorable prostatic hyperplasia. The oily muscles in the bladder and prostate are loose.
Visit us:
https://www.kamagra24uk.com/product/cenforce-100-sildenafil-citrate-100mg/
https://www.kamagra24uk.com/product/kamagra-sildenafil-citrate/
https://www.kamagra24uk.com/product/cialis-5mg-20mg-40mg/
https://www.kamagra24uk.com/product/fildena-100-mg-purple-pills/
https://www.onlinemenshop.com/buy-online/cenforce-100-mg-sildenafil-citrate/
https://www.onlinemenshop.com/buy-online/cenforce-150-blue-pill/
https://www.onlinemenshop.com/buy-online/cenforce-200-sildenafil-citrate/

>> No.3752047,223 [INTERNAL] 

It was a mesmerizing article, I really owe to you,keep writing such staff which helps readers to evaluate themselves, Thank you
Best Regards- http://https-www-office.com/setup

>> No.3752047,224 [INTERNAL] 

I'm really impressed about the info you provide in your articles. I must say am highly overwhelmed by your whole story. It’s not easy to get such quality information online nowadays. I look forward to staying here for a long time.
Best Regards -http://ww-woffice.com/setup

>> No.3752047,225 [INTERNAL] 

Hello. I am Alex, a professional editor at https://ewriters.pro. I;d love to help you with any task, if needed. Also, I like maing new friends, who share my interests!

>> No.3752047,226 [INTERNAL] 

Avast Login- Login now my avast account at my.avast.com and manage your avast software and services from one area.Get all the support you need for your Avast products.

>> No.3752047,227 [INTERNAL] 

Norton.com/setup - Norton, the world’s largest security software provides high-end protection against all kinds of threats and viruses lurking in the internet marking. These viruses, Trojan horses, scams and other malicious the software can harm important data and steal your confidential information (while accessing your bank account online).You can choose any Norton security software from those mentioned below as per your specific requirements.
http://norton.comsetupkey.co.uk

>> No.3752047,228 [INTERNAL] 

Tomtom Update - TomTom is a popular name when it comes to the navigation and GPS device. Also, other services include action cameras, GPS sports watches, fleet management systems, and location-based products. You can visit the TomTom.com and check various products and services offered by the TomTom.
http://mytomtomupdate.com/

>> No.3752047,229 [INTERNAL] 

Office.com/setup – Microsoft Office is world-renowned suite available for both personal and professional use. If you are one of Microsoft Office users then you would have an idea about the great services provided by them. Furthermore, it one of the oldest and still thriving suites in the market.
http://www.office-com-setup.me/
http://garmincomexpress.com.au/

>> No.3752047,230 [INTERNAL] 

Norton.com/setup – Visit on the official site of Norton and login to your Norton account to download, install and activate Norton Setup.
[url=http://howtoactivate.co/norton-com-setup/]noton.com/setup[/url] | [url=https://anti-mcafee.com/]macfee.com/activate[/url]

>> No.3752047,231 [INTERNAL] 

I'm really impressed about the info you provide in your articles. I must say am highly overwhelmed by your whole story. It’s not easy to get such quality information online nowadays. I look forward to staying here for a long time.
Best Regards -http://www.office-help-setup.com

>> No.3752047,232 [INTERNAL] 

I am amazed by the way you have explained things in this article. This article is quite interesting and I am looking forward to reading more of your posts.
Thanks for sharing this article with us.
http://vwww-norton.com/setup/

>> No.3752047,233 [INTERNAL] 

Really impressive post looking forward to see more posts like that keep it up good going

>>
Name (leave empty)
Comment (leave empty)
Name
E-mail
Subject
Comment
Password [?]Password used for file deletion.
reCAPTCHA
Action