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newbie
Activity: 42
Merit: 0
October 02, 2014, 05:53:53 AM
The probability of observing 4 blocks in a minute when those come from Poisson distribution (the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event - Wikipedia) is P(X=4) = 0.01532 (calculation here: http://www.wolframalpha.com/input/?i=Poisson+distribution+X%3D4+mean%3D1). This makes it happen about 22 times a day which is once each 65 minutes on average. When the difficulty changes those numbers could slightly vary. We don't have any statistical evidence about something fishy occurring.

Did you miss the entire discussion about permutations of consecutive independent trials (i.e. not separated by 65 minutes each)?
newbie
Activity: 42
Merit: 0
October 02, 2014, 05:51:42 AM
It is the "next month", and Cryptonote is alive. There is no real evidence of attack along those lines, but CN will certainly be attacked in the future using various paths. I would join NewLiberty in saying that our real test is how to make maximum good come out of this attack threat, which demonstrated our commitment to defend Monero, proved that the coin is not so easy to attack, and encouraged the owners to join the MEW in much higher numbers than anticipated. This is a good start.

I just caution you on celebrating too soon. You might end up being correct and BCX may be full of shit, or he might have been thwarted already by the checkpointing.

But I am not yet convinced that anyone has a model that can tell us there is no evidence of an attack. Apparently our models are blind and tell us nothing. Distinguish between null set (empty) and an undefined set (no information). Refer to my prior reply to xulescu and NewLiberty.

Perhaps I can be convinced we have a model that is telling us there is no evidence. I am open minded. Let me read any rebuttals that follow.

Edit: in short, don't confuse lucky hubris with repeatable science though I suppose your argument is speculators operate with imperfect information and form probabilities. Although we may not have technical information, you may have other information that is feeding your calculation, e.g. experience at analyzing personalities, motives, etc.

Edit#2: normally I would agree with "status quo" absent a model with clear information. But in this case, BCX has taken down coins in the past. I've read that he did threaten Litecoin and ended up not following through with the attack and instead profited on buying the dip. But did he actually say the attack had begun? Apparently Litcoin had then a much higher network hashrate than XMR does now.
hero member
Activity: 794
Merit: 1000
Monero (XMR) - secure, private, untraceable
October 02, 2014, 05:50:19 AM
...

At some point I am sure the XMR team will realize they do indeed need my help and we may work something out.

But anyway the image below posted by nutildah is interesting. Check the blocks just prior to the circle.

Later guys.


~BCX~




another 4 blocks in the last minute.

By my math, with 1 block per minute mean rate, one should see 4 blocks in the same minute about once every hour or so.  Is this correct?

I see 12 blocks in 4 minutes.

We apply the Poisson distribution.

The probability that we will get 4 blocks in 4 minutes when the expected rate is 1 block per minute (4 blocks per 4 minutes) is:

p = 44 / 4!e4 ≈ 19.5%, i.e. an occurrence expected roughly every 5 minutes.

The probability that we will get 12 blocks in 4 minutes when the expected rate is 1 block per minute (4 blocks per 4 minutes) is:

p = 412 / 12!e4 ≈ 0.064%, i.e. an occurrence expected roughly every 1559 minutes which is every 26 hours.

And note that the probably we get 10 - 14 blocks in 4 minutes is going to several times higher because we sum the probabilities for each of 10, 11, 12, 13, and 14, thus an occurrence expected several times per day.

I believe the math above is incorrect, because each 1 minute trial is independent (which is one of the requirements for a Poisson distribution). Thus we have four consecutive events, two are 4 blocks in a minute and two are 2 blocks in a minute. Thus the probability is as follows.

p = (14 / 4!e1)2 × (12 / 2!e1)2  ≈ 0.000795%, i.e. an occurrence expected roughly every 125,794 minutes which is every 87 days!

If my correction is correct, we do have evidence of something rarely occurring.
The probability of observing 4 blocks in a minute when those come from Poisson distribution (the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event - Wikipedia) is P(X=4) = 0.01532 (calculation here: http://www.wolframalpha.com/input/?i=Poisson+distribution+X%3D4+mean%3D1). This makes it happen about 22 times a day which is once each 65 minutes on average. When the difficulty changes those numbers could slightly vary. We don't have any statistical evidence about something fishy occurring.
donator
Activity: 1722
Merit: 1036
October 02, 2014, 05:46:32 AM
Risto only said that there was a 4-8% likelihood this coin wouldn't live next month, that's not the same as BCX wouldn't attack. BCX could still attack but the coin may live on after that..

I am not convinced even he knew what random variable he was computing. You can try to quote him to correct my understanding, but when I read it the first time in private, I got confused. Perhaps I was tired.

And I don't remember it being carefully worded to make it clear he wasn't saying only 4 - 8% chance to be worried about BCX. Seemed to me to be saying, "never mind BCX".

(this soap opera is all about politics?)

What do you personally think are the chances of a coin killer attack? And second, did you sell a percentage of your stash?

I am quite an insider in the situation, since I belong to the remedy team, and have communicated with all the main actors. I cannot evaluate the tech, but I know the turns of the events.

I currently give a 92-96% chance that Cryptonote will live to see the next month Smiley

As a result, I believe that currently the market is too bearish.

Here you go.

Sounds like "ignore BCX" to me. How do you interpret it?

It is the "next month", and Cryptonote is alive. There is no real evidence of attack along those lines, but CN will certainly be attacked in the future using various paths. I would join NewLiberty in saying that our real test is how to make maximum good come out of this attack threat, which demonstrated our commitment to defend Monero, proved that the coin is not so easy to attack, and encouraged the owners to join the MEW in much higher numbers than anticipated. This is a good start.
newbie
Activity: 42
Merit: 0
October 02, 2014, 05:38:18 AM
If my correction is correct, we do have evidence of something rarely occurring.

Thank you for undertaking this.

What we have in that sample is evidence that there are inaccurate clocks in some miners.  (This much is clear from a time stamp preceding a block it has hashed as the previous in the chain.)
Those time stamps come from the computers of the miners, they are not the times that blocks are received.
NTP (network time protocol, used for clock syncing on computers) is a UDP protocol, it is not reliable, and miners may not even use it.  It also has exploitable holes, MITM vulnerabilities and other issues.  So yes, it could be malice (to generate unjustified fear), it could also be laziness, carelessness or even miner caution or tuning (avoiding an unprofitable process).  What it isn't is evidence of an attack vector.  There is no significant damage resulting from this sort of activity.

I looked at this earlier and wrote a bit more about it up-thread, here: https://bitcointalksearch.org/topic/m.9039996

If your curiosity compels you, it may be interesting to analyze this sample against the data set from the rest of the chain to more accurately assess how much of an anomaly it is (though it may not be worth the bother considering the negligible consequences), and so your calculations here, while accurate, start with this mistaken premise.

What I wrote in red clearly indicates I was not alleging an abnormality nor an attack.

So you can view my point in red above as the beginning of an investigation into modeling.

If the timestamps are basically meaningless then we won't know if an attack is underway or not, i.e. there is no possible model thus claiming "nothing is going on" is a lie (if there is no model to inform us). And I that is the most relevant point.

And if the timestamps are very unreliable, then perhaps the loose rules about timestamps are exploitable.

And maybe not. Any proof one way or the other?

I suppose you assume that with checkpoints the block chain can't be rewound, but are you sure that eliminates all possible damage that can be done by manipulating timestamps?

What about amplifying selfish mining attacks by causing oscillation in the difficulty adjustment via timestamp planting, e.g. to take advantage of the fact that 20% of the timestamps are discarded when the difficulty is calculated. Have ideas like this been analyzed?
newbie
Activity: 42
Merit: 0
October 02, 2014, 05:27:39 AM
TheUsualStuff, I don't think manual snooping is going to be productive. Someone would need to write a script to find all and quantify. You are finding different permutations, and each of them can occur roughly once every 3 months or so and not be an abnormality in the model I proposed to quantify with.

So as I wrote previously, what came out of this is that although more rare than every hour (at least in the model I propose), just a few of these over the months is not evidence for nor against an attack being underway.
newbie
Activity: 42
Merit: 0
October 02, 2014, 05:15:46 AM
Risto only said that there was a 4-8% likelihood this coin wouldn't live next month, that's not the same as BCX wouldn't attack. BCX could still attack but the coin may live on after that..

I am not convinced even he knew what random variable he was computing. You can try to quote him to correct my understanding, but when I read it the first time in private, I got confused. Perhaps I was tired.

And I don't remember it being carefully worded to make it clear he wasn't saying only 4 - 8% chance to be worried about BCX. Seemed to me to be saying, "never mind BCX".

(this soap opera is all about politics?)

What do you personally think are the chances of a coin killer attack? And second, did you sell a percentage of your stash?

I am quite an insider in the situation, since I belong to the remedy team, and have communicated with all the main actors. I cannot evaluate the tech, but I know the turns of the events.

I currently give a 92-96% chance that Cryptonote will live to see the next month Smiley

As a result, I believe that currently the market is too bearish.

Here you go.

Sounds like "ignore BCX" to me. How do you interpret it?
newbie
Activity: 42
Merit: 0
October 02, 2014, 05:10:46 AM
For the fourth time, the burden of proof rests on you to prove material change. You cannot prove lack of material change in a stochastic environment because you need infinite data. That is not the case with proving change.

Why do you keep attacking me with strawmen?

I never claimed an attack! I wanted to analyze the rareness of the cited event. I didn't even claim it was abnormal.

You conflate investigation with intent. You desire to make an argument where there was none, because you assume any investigation is pro-attack. Why this immense emotional resistance to probing and the scientific method of peer review? Could it be you have some vested interest? (Rhetorical question)

Of course the probabilities are not 0.5. But they also don't matter much. Since both my semantic simile and your argument assume independence, order does not matter. Thus all permutations are in the same class of rarety.

Each trial in a coin toss has a 0.5 probability shared between two outcomes. Chaining independent trials does give rarer probabilities for certain permutations. Each trial in the Poisson distribution is an infinite range of probabilities shared between infinite possible outcomes. Thus there is a much higher stratification possible within just one trial or a few trials than is possible with a coin toss. Thus we are able to see very, very unlikely events with only a few trials, unlike for a coin toss. Thus we find that the majority of the events are clustered in certain patterns over just a few trials that aren't so rare, and if we see an outlier from that occurring much more frequently then we can posit an abnormality (assuming the Poisson distribution is a predictive model of normality). Thus I asserted your analogy is inapplicable.

You are attempting to claim that distribution functions don't matter and thus the distribution of permutations between different distributions are the same. FAIL.

Furthermore, if only counts of "short" vs "long" gaps matter, then instead of x seconds times 8 + y seconds times 4 you also need to include small deviations. Such as, for example, x-1, x+1, x times 6 + y times 4, and all the permutations of each of these. So you are integrating over all partitions on 12 elements, which is a gigantic set when you generalize enough to learn the blockchain in any meaningful way. The blockchain has too little data to believe your statement with even 60% confidencence. We're talking 0.1 sigma deviations here and a combinatorially monstrous set, with only a quarter of a million of data points. Not gonna happen.

On the contrary, my position is that given the amount of entropy there is in the blockchain so far, and adding time dependence to the combinatorial mess (because independence is false), we cannot say that there is something wrong with meaningful certainty.

You are attempting to model block occurrences via regression assuming you have no known distribution. Thus of course you need a lot more data to find a model. You assume the Poisson distribution is incorrect, but have you proven it? Even so, my argument wasn't initially about whether the Poisson distribution is a useless model. I was only arguing what it would say if it is the chosen model.

Finally, over all this academic modelling exercise that we went through, the reality is, as I mentioned in my first post and smoothie detailed, that even if you were right on the modelling, what we know about how timestamps work and how they are somewhat adversarially arbitrary for you as the modeller, your conclusion holds no epistemic water.

And timestamps are how we compute difficulty, which is intimately related to TW-like attacks. So if the timestamps are unreliable, that gives me a lot of confidence that we are immune to a TW attack. I actually have some ideas about how to make timestamps reliable and no that doesn't mean relying on an NTP without network hiccups.

You are right on the Maths. You are wrong on many levels on your modelling. Even if you were right on the modelling, you are still wrong on what conclusions you can draw from the results.

I never asserted I had the correct model. I was analyzing what the Poisson model would say.

Your argument is "something could be wrong".

No it wasn't. My argument was it might be more rare than once per hour. My argument was neatly compartmentalized, but you tried to build a strawman to attack me with.

My counterargument above is "even if that was the case, you don't have enough entropy to draw that conclusion".

In your regression yes, but in the assumed Poisson distribution incorrect.

Smoothie's corrolary is "even if you are right, it doesn't make much of a difference".

We don't know that yet. You guys are quick to jump to conclusions.

Thank you for responding calmly earlier and compelling me to articulate my position.

I am trying but when you keep rebuilding the same strawman and you embed your rebuttals as bold text in my quoted text making it difficult for me to quote you, its FUBAR.
newbie
Activity: 28
Merit: 0
October 02, 2014, 04:51:22 AM
My eyes are starting to bleed Cheesy

159675   2014-08-05 06:09:48 (2 months ago)   294   1   736720673c841a48d5e1ffd25d8e4f287f9ec3e8d51c058b0b78dc2223f722e2
159674   2014-08-05 06:09:20 (2 months ago)   294   1   f036b46869d37f49634f202a90f036251ae704665f28f454cedfbe784d90079c
159673   2014-08-05 06:09:00 (2 months ago)   294   1   a878f796aaa005982594120a5ecbfde7a66d0107d7e5c062d3296496a84886fc
159672   2014-08-05 06:08:52 (2 months ago)   294   1   bf4f3210e71078987cd570ea47a9209d9db5a84f009458013779d0acdeda64a6

159671   2014-08-05 06:08:45 (2 months ago)   660   2   41d98a35d17dc834e0670a0d903c8ff209d49c900ec544340683887c06b166c0

159670   2014-08-05 06:07:47 (2 months ago)   294   1   451dee59a35a7d971d52af26bb55ee85162bde0b252d2a7871744d61bcfd9de2
159669   2014-08-05 06:07:19 (2 months ago)   294   1   9ca0d0d1af34d63084f38a5e74aa40380c1f4f621833178677159c00a90f5cb7
159668   2014-08-05 06:07:39 (2 months ago)   294   1   f6a03ee31dcb8ffdc287b9bb0a0e60a255db469a1a229dd0c196d46808ef34d2
159667   2014-08-05 06:06:47 (2 months ago)   294   1   5309aea53fe5df4027bd7766a0a24f6730dfb63218c0a1f85e7b09cb32a7ccc9

159666   2014-08-05 06:07:52 (2 months ago)   294   1   8547bac87f4ac048ff6baeabca8efb0bed549de79fe27d7ae6908b5138fdfa3c
159665   2014-08-05 06:05:55 (2 months ago)   1301   2   2ec898af58a7893339eed5a9138b63e7aceb62862f540300addb058ed3dda8cc
159664   2014-08-05 06:07:27 (2 months ago)   7081   2   d99963b32f67cb0f81d688136ddf906b094fc60a5992bae0efa99cd476303a16
159663   2014-08-05 06:06:15 (2 months ago)   150343   1068520fc74673acf57895868e4777cb800d715939b2d8d82b6cea09cf8bcc57

I'm putting this one up because it looks like someone had some local timestamps that were weird (prob not synced) but maybe it still fits?

3 minutes, 53 seconds. 13 blocks. in timestamp (NOT block) order:

159675   2014-08-05 06:09:48 (2 months ago)   294   1   736720673c841a48d5e1ffd25d8e4f287f9ec3e8d51c058b0b78dc2223f722e2
159674    2014-08-05 06:09:20 (2 months ago)   294   1   f036b46869d37f49634f202a90f036251ae704665f28f454cedfbe784d90079c
159673    2014-08-05 06:09:00 (2 months ago)   294   1   a878f796aaa005982594120a5ecbfde7a66d0107d7e5c062d3296496a84886fc
159672    2014-08-05 06:08:52 (2 months ago)   294   1   bf4f3210e71078987cd570ea47a9209d9db5a84f009458013779d0acdeda64a6

159671    2014-08-05 06:08:45 (2 months ago)   660   2   41d98a35d17dc834e0670a0d903c8ff209d49c900ec544340683887c06b166c0
159666   2014-08-05 06:07:52 (2 months ago)   294   1   8547bac87f4ac048ff6baeabca8efb0bed549de79fe27d7ae6908b5138fdfa3c

159670   2014-08-05 06:07:47 (2 months ago)   294   1   451dee59a35a7d971d52af26bb55ee85162bde0b252d2a7871744d61bcfd9de2
159668   2014-08-05 06:07:39 (2 months ago)   294   1   f6a03ee31dcb8ffdc287b9bb0a0e60a255db469a1a229dd0c196d46808ef34d2
159664   2014-08-05 06:07:27 (2 months ago)   7081   2   d99963b32f67cb0f81d688136ddf906b094fc60a5992bae0efa99cd476303a16
159669   2014-08-05 06:07:19 (2 months ago)   294   1   9ca0d0d1af34d63084f38a5e74aa40380c1f4f621833178677159c00a90f5cb7

159667   2014-08-05 06:06:47 (2 months ago)   294   1   5309aea53fe5df4027bd7766a0a24f6730dfb63218c0a1f85e7b09cb32a7ccc9
159663   2014-08-05 06:06:15 (2 months ago)   150343   1068520fc74673acf57895868e4777cb800d715939b2d8d82b6cea09cf8bcc57
159665   2014-08-05 06:05:55 (2 months ago)   1301   2   2ec898af58a7893339eed5a9138b63e7aceb62862f540300addb058ed3dda8cc

I don't know which one to go by, should I just disregard ones where it looks like the computer that put it in had a non-synced timestamp?
legendary
Activity: 2268
Merit: 1141
October 02, 2014, 04:42:13 AM
Risto only said that there was a 4-8% likelihood this coin wouldn't live next month, that's not the same as BCX wouldn't attack. BCX could still attack but the coin may live on after that..

I am not convinced even he knew what random variable he was computing. You can try to quote him to correct my understanding, but when I read it the first time in private, I got confused. Perhaps I was tired.

And I don't remember it being carefully worded to make it clear he wasn't saying only 4 - 8% chance to be worried about BCX. Seemed to me to be saying, "never mind BCX".

(this soap opera is all about politics?)

What do you personally think are the chances of a coin killer attack? And second, did you sell a percentage of your stash?

I am quite an insider in the situation, since I belong to the remedy team, and have communicated with all the main actors. I cannot evaluate the tech, but I know the turns of the events.

I currently give a 92-96% chance that Cryptonote will live to see the next month Smiley

As a result, I believe that currently the market is too bearish.

Here you go.
newbie
Activity: 42
Merit: 0
October 02, 2014, 04:38:26 AM
I'm looking for about a 4-6 minute window in which this sequence occurrs?

You are looking for basically an average >= 3 blocks per minute for at least 4 consecutive minutes. A minute with very high number of blocks (e.g. 5+) has greater weight than a minute with no or fewer then 3 blocks.

None of this proves an attack is ongoing. It is only a discussion about whether a relatively rare event occurred on the block chain.

You have shown such an event occurred in May and there was no threat of an attack ongoing then, but that was roughly consistent with the alleged model of expected probability of occurrence. If you find those events happen even more frequently than 3 months, then you've blown another hole in that being possible sign of an abnormality. Meaning you've already shown the events are at least occurring at roughly the expected interval, thus even it is rare it is not abnormal.

So about the only thing I accomplished was to refute that it wasn't a rare event. The evidence of an attack is still non-existent.

If you find that such events are occurring much more frequently now as compared to before July and much more frequently than predicted by the probability of my alleged model, then perhaps we can argue about whether it could be evidence of an attack.

At that point, I could start to refute the hashrate variance (geez that's a no brainer!), geographical propagation, etc... But for now, no need for me to go there, unless the Poisson distribution model is actually predicting something useful.
newbie
Activity: 42
Merit: 0
October 02, 2014, 04:27:06 AM
Risto only said that there was a 4-8% likelihood this coin wouldn't live next month, that's not the same as BCX wouldn't attack. BCX could still attack but the coin may live on after that..

I am not convinced even he knew what random variable he was computing. You can try to quote him to correct my understanding, but when I read it the first time in private, I got confused. Perhaps I was tired.

And I don't remember it being carefully worded to make it clear he wasn't saying only 4 - 8% chance to be worried about BCX. Seemed to me to be saying, "never mind BCX".

(this soap opera is all about politics?)
newbie
Activity: 42
Merit: 0
October 02, 2014, 04:24:39 AM
... he said basically until there is an attack there is no attack ...

AnonyMint, this is, trivially, the case.

...

When you reply to a message in the normal way of quoting, then I can reply. I am not going to unravel all your bolded text inserted within a quote of my text. Geez. I am not paid to do this.

Btw, your arguments were very weak. Please do fix it so I can blow up your logic.
legendary
Activity: 2268
Merit: 1141
October 02, 2014, 04:24:03 AM
I know xulescu addressed this as a misperception, but how can something that happened after the announced attack have contributed to the attack.

Afair, fluffypony did that during the 72 hour countdown, before the decision to attack had become final. I am not referring to the copy+paste of the feedback from the mathematicians, rather the prior exchange upthread.

I believe also Risto's proclamation of the likelihood occurred during the 72 hour countdown.

Hey I am not saying any body did anything out of their roles. This is a soap opera ya know. I'm included.  Embarrassed

Risto only said that there was a 4-8% likelihood this coin wouldn't live next month, that's not the same as BCX wouldn't attack. BCX could still attack but the coin may live on after that..
newbie
Activity: 42
Merit: 0
October 02, 2014, 04:11:52 AM
I'm looking for about a 4-6 minute window in which this sequence occurrs?

You are looking for basically an average >= 3 blocks per minute for at least 4 consecutive minutes. A minute with very high number of blocks (e.g. 5+) has greater weight than a minute with no or fewer then 3 blocks.

None of this proves an attack is ongoing. It is only a discussion about whether a relatively rare event occurred on the block chain.

You have shown such an event occurred in May and there was no threat of an attack ongoing then, but that was roughly consistent with the alleged model of expected probability of occurrence. If you find those events happen even more frequently than 3 months, then you've blown another hole in that being possible sign of an abnormality. Meaning you've already shown the events are at least occurring at roughly the expected interval, thus even it is rare it is not abnormal.

So about the only thing I accomplished was to refute that it wasn't a rare event. The evidence of an attack is still non-existent.
newbie
Activity: 28
Merit: 0
October 02, 2014, 04:07:41 AM
newbie
Activity: 42
Merit: 0
October 02, 2014, 04:06:19 AM
Are you suggesting Risto should feel guilty for BCX's continued wrath?

I am just trying to consider what could possibly be BCX's motivation other than buying cheap XMR. It is wild speculation.

I am not trying to place blame. Evolution doesn't care about feelings. I am trying to see if I can figure out what the reality is. Maybe we just have to wait and benefit from hindsight.

I just don't like it when there is one side to a discussion and the other side isn't presented.
newbie
Activity: 42
Merit: 0
October 02, 2014, 03:55:43 AM
newbie
Activity: 42
Merit: 0
October 02, 2014, 03:43:17 AM
Let me redo this more carefully. We were deceived by the screen capture.

235653    14-09-27 05:13:35 -
235652    14-09-27 05:13:15  | 12:40 - 13:40 (1 minute)
235651    14-09-27 05:13:07 -

235650    14-09-27 05:12:17 -
235649    14-09-27 05:12:39  | 11:40 - 12:40 (1 minute)
235648    14-09-27 05:11:53 -

235647    14-09-27 05:11:23 -
235646    14-09-27 05:10:58  | 10:40 - 11:40 (1 minute)
235645    14-09-27 05:10:59 -

235644    14-09-27 05:10:36 -
235643    14-09-27 05:10:05  |
235642    14-09-27 05:09:52  | 9:40 - 10:40 (1 minute)
235641    14-09-27 05:09:40 -

p = (14 / 4!e1)(13 / 3!e1)3 ≈ 0.00035%


Let's compare to the one found 4 months prior.

89966   2014-06-18 00:03:18 -
89965   2014-06-18 00:03:12  | 2:55 - 3:55 (1 minute)

89964   2014-06-18 00:02:52 -
89963   2014-06-18 00:02:37  |
89962   2014-06-18 00:02:35  |
89961   2014-06-18 00:02:26  | 1:55 - 2:55 (1 minute)
89960   2014-06-18 00:02:24 -

(no blocks)                  | 0:55 - 1:55 (1 minute)

89959   2014-06-18 00:00:40 -
89958   2014-06-18 00:00:53  |
89957   2014-06-18 00:00:11  | 59:55 - 0:55 (1 minute)
89956   2014-06-17 23:59:55 -

p = (15 / 5!e1)(14 / 4!e1)(12 / 2!e1)(10 / 0!e1) ≈ 0.00032%
hero member
Activity: 714
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October 02, 2014, 03:41:40 AM
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