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General discussion[Forum game] Forum Mafia - Administration and general discussion(8542 posts)(8542 posts)
(8542 posts)
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This is my favourite topic
Posted March 14, 2019
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JoeSapphire: So everybody who enters has as much chance of fixing Vitek's mess as they have of ruining everything.
Yes, that's the result in plain words. Interesting that one doesn't even need much maths to solve this seemingly difficult problem. :-)
Posted March 14, 2019
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Lifthrasil: Interesting that one doesn't even need much maths to solve this seemingly difficult problem. :-)
that's the type of problem I'm perfect for ;)
Posted March 14, 2019
I neglected one case in my above formula, also it contains a mathematical error. There are actually two special seats one has to consider. The chance that 'Vitek' sits in his own seat was covered. But there is also the chance that he sits in the seat of the last person. In which case the chance to get it correct is 0.

So the correct formula would be: P(n) = (1/n)*1 + (1/n)*0 + ((n-2)/n)*P(n-1). Sure, the (1/n)*0 falls out of the equation since it's 0. But the -2 instead of the -1 makes a big difference. It allows to solve by forward induction instead of working backwards over sums (which I neglected to do formally correct).

We know that P(2)=1/2
Now let's take the above equation while assuming that we know that P(n-1)=1/2

P(n) = 1/n + ((n-2)/n)*(1/2)
= 2/2n + (n-2)/2n = (2+n-2)/2n = n/2n = 1/2

So, if any P(n) is 1/2, then all higher P(n+m) are also 1/2 and we know that for n=2 the assumption P(n)=1/2 is true.
Posted March 14, 2019
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Lifthrasil: I neglected one case in my above formula, also it contains a mathematical error. There are actually two special seats one has to consider. The chance that 'Vitek' sits in his own seat was covered. But there is also the chance that he sits in the seat of the last person. In which case the chance to get it correct is 0.

So the correct formula would be: P(n) = (1/n)*1 + (1/n)*0 + ((n-2)/n)*P(n-1). Sure, the (1/n)*0 falls out of the equation since it's 0. But the -2 instead of the -1 makes a big difference. It allows to solve by forward induction instead of working backwards over sums (which I neglected to do formally correct).

We know that P(2)=1/2
Now let's take the above equation while assuming that we know that P(n-1)=1/2

P(n) = 1/n + ((n-2)/n)*(1/2)
= 2/2n + (n-2)/2n = (2+n-2)/2n = n/2n = 1/2

So, if any P(n) is 1/2, then all higher P(n+m) are also 1/2 and we know that for n=2 the assumption P(n)=1/2 is true.
I checked your working for you, and it's all correct.

glad I could help. ;)
Posted March 14, 2019
And now I'm embarassed for notchecking your solution thoroughly...
I looked at the final answer, saw the word "induction" and skipped the maths.

But yeah, in general the first drunk either

sits in his own seat. Probability 1/n. Problem solved.
sits in last guy's seat. Probability same 1/n. Problem unsolvable.
sits in someone else's seat. Say kth person.

If the last option happens, then all people up to k sit in their own seats and k becomes... the new drunk. Again, he either sits in the original drunk's seat. Or in the last seat. Or in someone else's who becomes the new new drunk... etc

So for any n there is an equal chance of solving it, making it unsolvable or reducing it to an equivalent problem with a smaller number of people.
Posted March 14, 2019
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ZFR: And now I'm embarassed for notchecking your solution thoroughly...
and you call yourself the king of maths... tut tut tut...
Posted March 14, 2019
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ZFR: And now I'm embarassed for notchecking your solution thoroughly...
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JoeSapphire: and you call yourself the king of maths... tut tut tut...
I never do.

But who am I to argue against everyone else's opinion.
Posted March 14, 2019
It's legitimately distressing to me that I can no longer follow the math. I feel like less of a man.

I brute-forced n=2, 3, and 4, and they all came up 50%.
Posted March 14, 2019
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yogsloth: It's legitimately distressing to me that I can no longer follow the math. I feel like less of a man.

I brute-forced n=2, 3, and 4, and they all came up 50%.
(you can make yourself feel better by claiming to have checked someone's working and telling them it all adds up. Makes you look very smartbrains.)
Posted March 14, 2019
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yogsloth: It's legitimately distressing to me that I can no longer follow the math. I feel like less of a man.
I feel you. Someone asked me a relatively basic algebra type problem a few months ago, and I had to sit down and really think through the math to get the right answer.
Posted March 14, 2019
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JoeSapphire: (you can make yourself feel better by claiming to have checked someone's working and telling them it all adds up. Makes you look very smartbrains.)
Mmmhmm, mmmhmm, yup. Sounds right to me.
Posted March 14, 2019
Viiiiiiiiiiiiiiiiiteeeeeeeeeeeeeeeeeeeek
Posted March 15, 2019
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ZFR: Viiiiiiiiiiiiiiiiiteeeeeeeeeeeeeeeeeeeek
Good news everybody! I've found the trail of our missing mod.
Someone just needs to go and threaten the seller until they tell us who the buyer was.
Posted March 15, 2019
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SirPrimalform:
"Very good used condition no original packaging or instructions.


That's him!!!
Posted March 15, 2019
if we can just post in this thread 3000 more times we can get the reply count to spell 'boob'


Well, 2999 now.



Go!
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This is my favourite topic
Community
General discussion[Forum game] Forum Mafia - Administration and general discussion(8542 posts)(8542 posts)
(8542 posts)