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1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:07:18 | you did something like N or less | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:07:22 | or maybe N or more | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:07:28 | i read exactly N | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:07:59 | are you saying i'm thinking about a cumulative probability? | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:08:11 | not really | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:08:16 | i don't know | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:09:33 | 1-(5/6)^N is not(die lives for N rolls) | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:09:37 | so N or less | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:09:38 | For one die, P(rolling a six in N rolls) = 1-(5/6)^N, correct? | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:09:58 | yes | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:09:58 | it's a branching process except no branching | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:10:01 | that's N or less | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:10:08 | gimme a sec, this is semi-advanced probability theory | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:10:14 | yeah | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:10:37 | it is a difficult problem but i believe it can probably be solved with simple probability math | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:10:41 | nope | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:10:54 | hopes=crushed | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:10:57 | it's a branching process, you want to bring in the heavyweight stuff, gimme a sec | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:10:59 | you;re answering a different question | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:11:23 | it asks not more and not less than N | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:11:36 | and you're only doing not more | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:11:46 | well | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:11:50 | hmm | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:12:35 | you're right, i'm doing it cumulatively when it should probably be considered individually | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:12:48 | wait i'm a fool | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:12:56 | yeah it's simple enough that you can do it with basic prob | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:12:58 | ok so | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:13:01 | oh? | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:14:29 | probability that it lives through 24 rolls is (5/6)^24
probability that it dies on the 25th roll is 1/6
so probability that it survives 24 rolls but dies on the 25th is just gonna be (1/6) * (5/6)^24 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:14:45 | ok | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:14:49 | that's 1 die | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:14:50 | we know that at least one is like this | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:14:57 | tru | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:15:02 | the rest can be anything, they can live to 25 or less | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:15:20 | ok so really we want the probability that none live to 26 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:15:34 | minus the probability that none live to 25 | 0 | 1 | 766,866,943,566,938,100 | demaw | 0427 | demaw | false | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:15:42 | damn | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:15:54 | 💯 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:16:00 | no i'm erratic | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:16:02 | i'm changing it up | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:16:07 | this is not what i was originally saying | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:16:11 | i'm starting over | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:16:57 | probability that none live to 26 is (1 - P)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:17:13 | where n is the number of dice, P is the probability that any single one makes it to 26 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:17:20 | P is (5/6)^26 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:17:57 | so it's (1 - (5/6)^26)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:18:04 | then the probability that none live to 25 is just | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:18:10 | (1 - (5/6)^25)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:18:32 | so the probability that at least one lives to 25 is 1 - (1 - (5/6)^25)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:18:52 | wait, bugger | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:18:56 | conditionals | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:19:07 | end me | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:19:56 | this is killing me | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:21:11 | so the probability that it ends after N trials is equal to (1-(5/6)^N)-(1-(5/6)^(N-1)) or is that not true | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:21:47 | ok it's fine | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:22:06 | have you solved the problem o great statistical problabilical genius | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:22:13 | the probability that none make it to 26 is (1 - (5/6)^26)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:22:27 | the probability that at least one lives to 25 is 1 - (1 - (5/6)^25)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:22:48 | and you can do it for every number | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:22:50 | so the probability that at least one makes it to 25 but none make it to 26 is the second minus the first | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:22:52 | substitute 26 for N and 25 for N-1 so that we can get a true representation of the variables initially presented in the problem | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:22:53 | and kill them off at the last moment | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:22:59 | 1 - (1 - (5/6)^25)^n - (1 - (5/6)^26)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:23:12 | final answer | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:23:39 | maybe | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:24:02 | it rings tru | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:24:06 | no | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:24:07 | maybe | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:24:07 | it's gibberish | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:24:09 | yea | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:24:11 | there's no way it rings true | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:24:12 | it's madness | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:24:13 | i put it in desmos | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:24:16 | it's too complicated | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:24:17 | it fucking sucks | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:24:30 | how is this problem so difficult | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:28:27 | (1 - (5/6)^26)^n − (1 - (5/6)^25)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:28:38 | just an extra 1 - | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:28:55 | all die minus all die too early | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:29:34 | P(A) = P(a single one reaches 25) = (5/6)^25
P(B) = P(a single one reaches 26) = (5/6)^26
P(C) = P(none of the n dice reach 25) = (1 - P(A))^n
P(D) = P(none of the n dice reach 26) = (1 - P(B))^n
||P(C' and D) = P(at least one die reaches 25 but none reach 26) = P(D) - P(C and D) = P(D) - P(C) = (1 - P(B))^n - (1 - P... | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:29:39 | ok done | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:29:45 | that looks more reasonable now | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:30:20 | but 26 should be before | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:30:37 | why | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:30:45 | oh no yeah | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:30:45 | oh | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:30:48 | i goofed it | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:31:09 | other than that, though, would it be correct | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:31:37 | ok fixed | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:31:59 | wait | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:32:03 | ok so 26 > 25 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:32:16 | so (5/6)^26 < (5/6)^25 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:32:31 | so 1 - (5/6)^26 > 1 - (5/6)^25 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 141,791,176,540,946,430 | frownyfrog | 03/14/2022 22:32:40 | no, that's larger | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:32:43 | fixed already | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:32:56 | so (1 - (5/6)^26)^n > (1 - (5/6)^25)^n | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:33:02 | so (1 - (5/6)^26)^n - (1 - (5/6)^25)^n > 0 | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:33:06 | which is what we want to see | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 209,767,680,100,663,300 | Kaisheng21 | 03/14/2022 22:33:08 | done | 0 | 1 | null | null | null | null | null | |||||
1,253 | help-10 | ee448639576c4143891f4790ad67b2df | 766,866,943,566,938,100 | demaw | 03/14/2022 22:33:19 | yea i believe that would be the correct solution | 0 | 1 | null | null | null | null | null |
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