Oops I broke the laws of math.

[-zeroSKILL-]

Re: Oops I broke the laws of math.

show your work

[Flaming_Dingleberry]

Re: Oops I broke the laws of math.

Stop at $5, if you don't get to $5 it isn't worth it.

I mean gee whiz, just get a job and earn $8 an hour.

[stargroup]

Re: Oops I broke the laws of math.

now see rubix, there's a huge jump in difficulty there

I was hoping for something, you know, around the middle

also I don't really have the time to solve these problems until november, so save these problems for me

[leonid]

Re: Oops I broke the laws of math.

I have a strategy with expected gain of about $0.963. How far is this from the optimal?

[MrRubix]

Re: Oops I broke the laws of math.

leonid has just proven that 2 = 52 O.O


Some more trickier problems:

1. Let's see if any of you are good with stochastic calculus -- tell me about the integral from 0 to T of w(t) dt, where w(t) is a standard Brownian motion.

2. This one is fun -- I am pretty sure it's an old classical problem, so resist the urge to Google it, because figuring it out is a lot of fun. There is a matriarchal town where the women believe in this prophecy. A stranger will show up and simply say "yes" or "no" -- where this answer is meant to indicate whether or not any of the men in the town have been cheating on their wives. The women agree to a rule given the stranger's announcement: If a woman, on any day, can deduce that her husband is a cheater, she will kick him out of the house by 10 a.m. the next morning. This action can also be seen by everyone else in the town. It's also given that every woman in the town is observant enough to know whether any other man (except her own) is faithful to his wife or not, but no woman can share such info with another. The stranger arrives and says "yes." On the morning of the 10th day following the stranger's arrival, some men are kicked out into the street. How many of them are there?

3. Leonid and Rubix are alternating rolling a pair of dice, stopping either when Leonid rolls the sum of 9 or when Rubix rolls the sum of 6. Assuming that Leonid rolls first, find the probability that Leonid has the final roll.

[ieatyourlvllol]

Re: Oops I broke the laws of math.

1. Obtain red crayon
2. Draw cards
3. ????
4. PROFIT!!!

[leonid]

Re: Oops I broke the laws of math.

I've already solved the third problem on the other thread

[MrRubix]

Re: Oops I broke the laws of math.

blah blah blah i wanted a hard problem, got one, and now i am a huge vagina

Come on man, sack up and at least give it a try. It is hard (it took me literally all day to solve before I was certain of my answer), but it isn't impossible.

[MrRubix]

Re: Oops I broke the laws of math.

I've already solved the third problem on the other thread

Too lazy to check, what did you get?

[leonid]

Re: Oops I broke the laws of math.

@Rubix 9/19

I'm having trouble proving whether a certain rule is optimal. Would be good if I knew the optimal expected gain beforehand

[Flaming_Dingleberry]

Re: Oops I broke the laws of math.

MrRubix, here's a problem that was given to all six-seven periods of a class I was in. I was the only one to solve it within the week and I want you to solve it. This is probably ****ing easy as hell, but still, it's the hardest math problem I retained and know the answer to lmfao.

There are 12 bags of gold, one bag has fake gold in it, you don't know whether the fake gold is lighter or heavier than real gold, you have a scale, you can only use it three times, what variations of weighing the gold will tell you which bag is fake gold?

Everyone else is welcome to try to solve my crappy algebra problem.

[leonid]

Re: Oops I broke the laws of math.

I've already solved that question in the past, so I won't spoil it..

[Flaming_Dingleberry]

Re: Oops I broke the laws of math.

FFRers are smarter than my high school xD

Good thing I was destined to be an FFRer.

That's why I was able to solve it of course.

[MrRubix]

Re: Oops I broke the laws of math.

MrRubix, here's a problem that was given to all six-seven periods of a class I was in. I was the only one to solve it within the week and I want you to solve it. This is probably ****ing easy as hell, but still, it's the hardest math problem I retained and know the answer to lmfao.

There are 12 bags of gold, one bag has fake gold in it, you don't know whether the fake gold is lighter or heavier than real gold, you have a scale, you can only use it three times, what variations of weighing the gold will tell you which bag is fake gold?

Everyone else is welcome to try to solve my crappy algebra problem.

Split the 12 bags into three groups of four where each sub-group has a single bag and a set of three bags, which we'll denote as X1 and X3, Y1 and Y3, and Z1 and Z3.

(Weighing 1) Compare: X1+X3 to Y1+Y3 (If equal, group Z has irregular bag)
If this happens: (Weighing 2) Compare: Y3 to Z3
If Z3 heavier/lighter, (Weighing 3) compare two bags within Z3 to deduce the irregular.
If Y3=Z3 though, then (Weighing 3) compare Y1 to Z1 to see whether Z1 is heavier/lighter.
But if Weighing 1 gave an imbalance, then compare (Weighing 2) X1+Y3 to Y1+Z3.
If they are equal, then the irregular bag is in X3, so (Weighing 3) comparing any two there will single the irregular bag.
But, otherwise, (Weighing 3) comparing X1 to Z1 will finish things off if X1+Y3 was heavier, or (Weighing 3) comparing two bags within Y3 will single the irregular bag out if X1+Y3 was heavier.

[MrRubix]

Re: Oops I broke the laws of math.

@Rubix 9/19

I'm having trouble proving whether a certain rule is optimal. Would be good if I knew the optimal expected gain beforehand

Yes, 9/19 is correct -- good job!