Oops I broke the laws of math. - Page 8

MrRubix · 10-20-2009, 12:40 AM

It isn't just similar.

**Ghakimx** · 10-20-2009, 12:44 AM

What does your signature mean, Rubix

MrRubix · 10-20-2009, 12:45 AM

only leonid so far has figured out my signature

**emerald000** · 10-20-2009, 12:51 AM

Rubix cube code. Doesn't need a genius to know what it is.

stargroup · 10-20-2009, 12:54 AM

lmfao rubix giving us baby problems

I could've proved that using combinatorics easily

leonid · 10-20-2009, 12:55 AM

I was too stupid to think of other ways than proving by induction

MrRubix · 10-20-2009, 12:58 AM

Quote:

Originally Posted by stargroup

lmfao rubix giving us baby problems

I could've proved that using combinatorics easily

Every time I ever give hard problems on this forum, nobody ever solves them. I like to give fun problems that I am pretty sure at least one person will know how to solve.

MrRubix · 10-20-2009, 01:00 AM

stargroup: Just for you, a hard problem that nobody on this forum (except me) has solved yet:

You have a standard 52-card deck. For every red card you draw, you earn a dollar. For every black card you draw, you lose a dollar. Drawn cards cannot be reinserted back into the deck. You can stop at any time and leave with your earnings (or losses, if you feel inclined to be retarded and not simply draw the entire deck). Given this game, devise an optimal stopping rule -- and, given this stopping rule, what is your expected payout from this game?

Have fun >:] This is a hard problem.

leonid · 10-20-2009, 01:01 AM

**** I forgot about solving that problem

Now I'm too busy to attempt it so I guess I'll hand it over to bufang

leonid · 10-20-2009, 01:04 AM

Here's the optimal strategy.

Draw one card. If it's red, stop. Otherwise, draw entire deck.

Did I mention every deck in Korea has two cards in total

**-zeroSKILL-** · 10-20-2009, 01:06 AM

show your work

**Flaming_Dingleberry** · 10-20-2009, 01:13 AM

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 · 10-20-2009, 01:19 AM

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 · 10-20-2009, 01:25 AM

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

MrRubix · 10-20-2009, 01:27 AM

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 · 10-20-2009, 01:28 AM

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

leonid · 10-20-2009, 01:29 AM

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

MrRubix · 10-20-2009, 01:30 AM

Quote:

Originally Posted by stargroup

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 · 10-20-2009, 01:32 AM

Quote:

Originally Posted by leonid

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

Too lazy to check, what did you get?

leonid · 10-20-2009, 01:33 AM

@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

10-20-2009, 12:40 AM	#141
MrRubix FFR Player Join Date: Dec 1969 Location: New York City, New York Posts: 8,340	Re: Oops I broke the laws of math. It isn't just similar. __________________ https://www.youtube.com/watch?v=0es0Mip1jWY

10-20-2009, 12:44 AM	#142
Ghakimx Cutie&Handshaking Sounds Join Date: Mar 2009 Location: Xingapore Posts: 1,594	Re: Oops I broke the laws of math. What does your signature mean, Rubix __________________ I AM ASHAMED OF MY STUPIDITY AND MUST COMMIT SEPPUKU. FORGIVE ME, FFR. Ninjas NEVER die. Now on a 30 kill streak.

10-20-2009, 12:45 AM	#143
MrRubix FFR Player Join Date: Dec 1969 Location: New York City, New York Posts: 8,340	Re: Oops I broke the laws of math. only leonid so far has figured out my signature __________________ https://www.youtube.com/watch?v=0es0Mip1jWY

10-20-2009, 12:51 AM	#144
emerald000 the Mathemagician~ Join Date: Nov 2005 Location: Quebec City Age: 33 Posts: 1,320	Re: Oops I broke the laws of math. Rubix cube code. Doesn't need a genius to know what it is.

10-20-2009, 12:54 AM	#145
stargroup FFR Player Join Date: Jun 2007 Posts: 974	Re: Oops I broke the laws of math. lmfao rubix giving us baby problems I could've proved that using combinatorics easily __________________ (´･ω･`)

10-20-2009, 12:55 AM	#146
leonid I am leonid Join Date: Oct 2008 Location: MOUNTAIN VIEW Age: 34 Posts: 8,080	Re: Oops I broke the laws of math. I was too stupid to think of other ways than proving by induction __________________ Proud member of Team No

10-20-2009, 01:00 AM	#148
MrRubix FFR Player Join Date: Dec 1969 Location: New York City, New York Posts: 8,340	Re: Oops I broke the laws of math. stargroup: Just for you, a hard problem that nobody on this forum (except me) has solved yet: You have a standard 52-card deck. For every red card you draw, you earn a dollar. For every black card you draw, you lose a dollar. Drawn cards cannot be reinserted back into the deck. You can stop at any time and leave with your earnings (or losses, if you feel inclined to be retarded and not simply draw the entire deck). Given this game, devise an optimal stopping rule -- and, given this stopping rule, what is your expected payout from this game? Have fun >:] This is a hard problem. __________________ https://www.youtube.com/watch?v=0es0Mip1jWY

10-20-2009, 01:01 AM	#149
leonid I am leonid Join Date: Oct 2008 Location: MOUNTAIN VIEW Age: 34 Posts: 8,080	Re: Oops I broke the laws of math. **** I forgot about solving that problem Now I'm too busy to attempt it so I guess I'll hand it over to bufang __________________ Proud member of Team No

10-20-2009, 01:04 AM	#150
leonid I am leonid Join Date: Oct 2008 Location: MOUNTAIN VIEW Age: 34 Posts: 8,080	Re: Oops I broke the laws of math. Here's the optimal strategy. Draw one card. If it's red, stop. Otherwise, draw entire deck. Did I mention every deck in Korea has two cards in total __________________ Proud member of Team No

10-20-2009, 01:13 AM	#152
Flaming_Dingleberry Everybody gets one. Join Date: Jul 2006 Location: Fuckin space bro Posts: 1,008	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.

10-20-2009, 01:19 AM	#153
stargroup FFR Player Join Date: Jun 2007 Posts: 974	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 __________________ (´･ω･`)

10-20-2009, 01:25 AM	#154
leonid I am leonid Join Date: Oct 2008 Location: MOUNTAIN VIEW Age: 34 Posts: 8,080	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? __________________ Proud member of Team No

10-20-2009, 01:27 AM	#155
MrRubix FFR Player Join Date: Dec 1969 Location: New York City, New York Posts: 8,340	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. __________________ https://www.youtube.com/watch?v=0es0Mip1jWY

10-20-2009, 01:28 AM	#156
ieatyourlvllol FFR Player Join Date: Sep 2006 Location: it's a mystery oooo Posts: 3,221	Re: Oops I broke the laws of math. 1. Obtain red crayon 2. Draw cards 3. ???? 4. PROFIT!!!

10-20-2009, 01:29 AM	#157
leonid I am leonid Join Date: Oct 2008 Location: MOUNTAIN VIEW Age: 34 Posts: 8,080	Re: Oops I broke the laws of math. I've already solved the third problem on the other thread __________________ Proud member of Team No

10-20-2009, 01:33 AM	#160
leonid I am leonid Join Date: Oct 2008 Location: MOUNTAIN VIEW Age: 34 Posts: 8,080	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 __________________ Proud member of Team No

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