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** STICKY ** League of Reason? PROVE YOURSELF!

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** STICKY ** League of Reason? PROVE YOURSELF!
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PulsarUser avatarPosts: 872Joined: Tue Feb 24, 2009 5:52 pmLocation: Belgium

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Yep, that's basically the same idea. Very nice puzzle, it would be a good question for math students.
I know that you believe you understand what you think I said, but I'm not sure you realize that what you heard is not what I meant. - Robert McCloskey

Science doesn’t know everything … religion doesn’t know ANYTHING.
Fri Jul 16, 2010 11:37 pm
MutoPosts: 21Joined: Sat Jun 12, 2010 1:04 amLocation: Austria Gender: Pinecone

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

@Case:

Because of the symmetry of the cube we can have 4 different positions.

Position 0: At the start.
Position 1: 2 edges away from the pinecone
Position 2: 1 edge away from the pinecone.
Position 3: At the pinecone

One quickly dicovers that each of TC desperate movement can be interpreted as adding one or subtracting on from the current position with a certain probability:
If he is at zero every change in position bring him to 1 with probability 1.
If he is at 1 he either gets to 2 with probability 2/3 or to 0 with probability 1/3.
If he is at 2 he either gets to 3 with probability 1/3 or to 1 with probability 2/3.

Now we are interested in the probaibility that TC first tastes his pinecone after the covering the length l.
Since l must be odd l =2*n+1 with n positive.
We know that after the first movement he is at 1 and to movements before he arrives at the pinecone he is at 1.
If he moves in between and it adds 1 the next movement must subtract 1. This event has probability 4/9
If he moves in between and it subtracts 1 the next movement must add 1. This event has probability 1/3

In those 2n-2 movements he has n-1 opportunities to either move up or down.
Hence there are n-1 over k paths so that he moves up 1 position k times. the corresponding path (not counting the movement at the start and the two in the end ) has the probability (1/3)^(n-1-k) * (4/9)^k. If we now sum over all the paths we can use the binomial theorem and arrive at the result that(now counting the end parts) the probability of TC arriving at the pinecone for the first time after 2n +1 steps is 2/9*(7/9)^(n-1). After a bit of algebra we see that TC needs astonishing 45 minutes to have his meal.

Hope this is the solution( the algebra part is a bit tricky I migh have made a mistake.
Sat Jul 17, 2010 1:50 am
CaseUser avatarPosts: 1080Joined: Sun Feb 28, 2010 9:40 pm Gender: Cake

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Well, that's sort of the correct answer. The +5m from the initial move leaves us with 50 minutes. ^^
I am determined that my children shall be brought up in their father's religion, if they can find out what it is.
Charles Lamb (1775 - 1834)

Atheism is a non-prophet organization.
Sat Jul 17, 2010 6:20 am
ArthurWilbornPosts: 964Joined: Sat Jun 19, 2010 4:46 pm

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Case wrote:Next: TruthfulChristian has been locked in virtual reality again and this time, he roams the grid of a cube (you know... 8 vertices, 12 lines). He's at one end of the cubic grid while a tasty pinecone lounges at the other side. TC moves at random from one vertex to one of the connected vertices, this process takes 5 minutes. How long will it take him, on average, to get to the tasty pinecone?


Alternate solution.

Five minutes are spent moving from state 1 to state 2.

SUM(10 * (1/3)^n) minutes are spent on average wandering back and forth between state 1 and state 2 for each visit to state 2. As n approaches infinity, this sum approaches five.

Five minutes are spent moving from state 2 to state 3.

SUM((10 + 5) * (2/3)^n) minutes are spent on average wandering back and forth between states 1 to 3. As n approaches infinity, this sum approaches thirty minutes.

Five minutes are spent moving from state 3 to state 4, where we finish.

5 + 5 + 5 + 30 + 5 = 50 minutes on average
Mon Jul 19, 2010 8:10 pm
nemesissUser avatarPosts: 1259Joined: Sun Sep 13, 2009 7:29 pm

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Muto wrote:@ case: 961

Here is my callenge: (I hope it wasn't allready there):

We have two women sitting and talking:

Q: How old are your three children?

A:If you multiply their ages you get 36.

Q: I am not satisfyed. Can you give me more information?

A: Yes, if you add their ages you get the number on the sign across the street.

Q: I need more information to determine their age.

A: My oldest daughter has beautiful eyes.

After this discussion the questioner knows the age of the children.
Can anyone else determine it as well?

Note: The women are good at mathematics/logic. The age of each child is a positive integer.


the solution lies in between the lines;
the sign across the street, which could be a significant be... is a speed limit sign where the speed limit is 10mph.
from that we have the formula;

X*Y*Z=36
X+Y+Z=10

from the third answer we can assume that among the ages, that there is only one who is the oldest.
the answer is;
kid #1 = 3 years old
kid #2 = 3 years old
kid #3, aka the oldest daughter = 4 years old

additionally, a positive integer is a given.
ever seen a child that has an age -1? that would mean the kid wasn't even born.
Wed Jul 21, 2010 10:24 pm
UndeathUser avatarPosts: 61Joined: Mon Jun 07, 2010 5:47 pmLocation: Copenhagen, Denmark Gender: Pinecone

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

nemesiss wrote:the solution lies in between the lines;
the sign across the street, which could be a significant be... is a speed limit sign where the speed limit is 10mph.
from that we have the formula;

X*Y*Z=36
X+Y+Z=10

from the third answer we can assume that among the ages, that there is only one who is the oldest.
the answer is;
kid #1 = 3 years old
kid #2 = 3 years old
kid #3, aka the oldest daughter = 4 years old
Close, but not quite. The sign says 13, not 10, and the reason for this is that there must be some ambiguity in the answer even when you know the number on the sign. If the sign says 10, then there is only one possible combination with a product of 36 (3,3,4). If you have a sum of 13, there are two combinations: 1,6,6 and 2,2,9. The third piece of information is necessary to distinguish between the two - there must be an oldest daughter, so the correct answer is 2,2,9.


nemesiss wrote:additionally, a positive integer is a given.
ever seen a child that has an age -1? that would mean the kid wasn't even born.
Ah, but if you do not specify the age as a positive integer, one of the children could be age 0, or a fractional age.
Support bacteria - they're the only culture some people have.
Scientists never grow up, they just get bigger toys.
Last edited by Undeath on Wed Jul 21, 2010 11:18 pm, edited 1 time in total.
Wed Jul 21, 2010 10:58 pm
SchrodingersFinchLeague LegendUser avatarPosts: 275Joined: Sat Feb 21, 2009 10:25 pmLocation: Finland Gender: Male

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

nemesiss wrote:the solution lies in between the lines;
the sign across the street, which could be a significant be... is a speed limit sign where the speed limit is 10mph.
from that we have the formula;

X*Y*Z=36
X+Y+Z=10

from the third answer we can assume that among the ages, that there is only one who is the oldest.
the answer is;
kid #1 = 3 years old
kid #2 = 3 years old
kid #3, aka the oldest daughter = 4 years old

additionally, a positive integer is a given.
ever seen a child that has an age -1? that would mean the kid wasn't even born.

Wrong. You see all possible solutions for x*y*z = 36 are:
1, 1, 36
1, 2, 18
1, 3, 12
1, 4, 9
1, 6, 6
2, 2, 9
2, 3, 6
3, 3, 4

And only 3 + 3 + 4 = 10, which would make the last bit of information ("my oldest daughter has beautiful eyes") unneccessary. But since the woman said: "I need more information to determine their age", it must be necessary. Therefore, the number on the sign must come up in the sums at least twice.

The sums are respectively:
38
21
16
14
13
13

11
10

So it must be either 1, 6, 6 or 2, 2, 9. However, in the way Muto phrased the question, it's impossible to tell which one it is.
"My oldest daughter has beautiful eyes" only tells us that there are at least two girls, one older than the other. It could be that the girls' ages are 1 and 6, or 2 and 9. But if all three are girls, the answer is obviously 2, 2, 9.

edit: Undeath beat me to it.
"Religion is a culture of faith; science is a culture of doubt."
- Richard P. Feynman
Wed Jul 21, 2010 11:00 pm
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MutoPosts: 21Joined: Sat Jun 12, 2010 1:04 amLocation: Austria Gender: Pinecone

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Sorry for the ambiguity. 9,2,2 is correct if you assume that the oldest daughter is the oldest kid.
Thu Jul 22, 2010 12:51 am
DeathofSpeechUser avatarPosts: 220Joined: Tue Jul 20, 2010 2:28 pmLocation: I can't know with certainty Gender: Tree

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Here's an oldy but goodie.

A logician sends his son off to school.
A week later his son writes back to to him and the letter says only:

Father,
I require an uniquely valuable additional text please.

_SE.ND
+MO.RE
MON.EY

How much does he require?
Reason Bran, with two scoops of Objectivity in every box and loaded with Bran fiber goodness...
...you'll never be full of shit again.


Science - You can see why it works.
Religion - You can't see why it doesn't work
Thu Jul 22, 2010 12:17 pm
nemesissUser avatarPosts: 1259Joined: Sun Sep 13, 2009 7:29 pm

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

DeathofSpeech wrote:Here's an oldy but goodie.

A logician sends his son off to school.
A week later his son writes back to to him and the letter says only:

Father,
I require an uniquely valuable additional text please.

_SE.ND
+MO.RE
MON.EY

How much does he require?


10652

the code is: 9567 +1085 = 10652
Thu Jul 22, 2010 7:46 pm
DeathofSpeechUser avatarPosts: 220Joined: Tue Jul 20, 2010 2:28 pmLocation: I can't know with certainty Gender: Tree

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

nemesiss wrote:
DeathofSpeech wrote:Here's an oldy but goodie.

A logician sends his son off to school.
A week later his son writes back to to him and the letter says only:

Father,
I require an uniquely valuable additional text please.

_SE.ND
+MO.RE
MON.EY

How much does he require?


10652

the code is: 9567 +1085 = 10652



Sigh... yeah well that's what I get for bringing a cute puzzle to a party serving N dimensional cake. :lol:
Reason Bran, with two scoops of Objectivity in every box and loaded with Bran fiber goodness...
...you'll never be full of shit again.


Science - You can see why it works.
Religion - You can't see why it doesn't work
Fri Jul 23, 2010 10:05 pm
CaseUser avatarPosts: 1080Joined: Sun Feb 28, 2010 9:40 pm Gender: Cake

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Sigh... yeah well that's what I get for bringing a cute puzzle to a party serving N dimensional cake. :lol:
Hehehe.

New riddle. :D
Five bankers are on their way home, they just settled a deal that will get them 1'000'000'000 $. Each banker may make a proposal as to how much $ each of the bankers gets. A proposal is accepted if the majority votes in favor of it. If a proposal is rejected, the one whose proposal was rejected will be assasssinated on the spot. The bankers are extremely clever, very bloodthirsty and not generous at all. Banker #5 may make the first proposal.

What is his proposal - and what are his reasons for making it?
I am determined that my children shall be brought up in their father's religion, if they can find out what it is.
Charles Lamb (1775 - 1834)

Atheism is a non-prophet organization.
Fri Jul 23, 2010 11:58 pm
ArthurWilbornPosts: 964Joined: Sat Jun 19, 2010 4:46 pm

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Case wrote:
Sigh... yeah well that's what I get for bringing a cute puzzle to a party serving N dimensional cake. :lol:
Hehehe.

New riddle. :D
Five bankers are on their way home, they just settled a deal that will get them 1'000'000'000 $. Each banker may make a proposal as to how much $ each of the bankers gets. A proposal is accepted if the majority votes in favor of it. If a proposal is rejected, the one whose proposal was rejected will be assasssinated on the spot. The bankers are extremely clever, very bloodthirsty and not generous at all. Banker #5 may make the first proposal.

What is his proposal - and what are his reasons for making it?


Assuming the suggestion passes next to #4 and #3 in turn, #5 should suggest that #1 and #2 receive no money, that #3 receive 50%, #4 nothing, and himself the remainder. This is the maximum amount that #3 and #4 could be expected to walk away with if they tried a similar tactic after allowing the previous members to die, and therefore it in their interest to agree. #5 is lucky to walk away with his life and at least some money.

Work backward. If only #1 and #2 are left, presumably they split the money 50/50.

With three people, only two votes count. #2 knows he won't get more then 50%, so #2 and #3 split the money.

With four people, three votes count. #4 is screwed; #2 and #3 know they can split the money if he dies. The best he can do is give them the money and hope they don't kill him.

With five people, three votes count. #3 knows he can get half, and #4 knows he can't get anything. #5 only has to buy off #3.
Sat Jul 24, 2010 2:04 am
MuslimPonderingsPosts: 6Joined: Sun Jun 27, 2010 5:08 pm

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Case wrote:
Five bankers are on their way home, they just settled a deal that will get them 1'000'000'000 $. Each banker may make a proposal as to how much $ each of the bankers gets. A proposal is accepted if the majority votes in favor of it. If a proposal is rejected, the one whose proposal was rejected will be assasssinated on the spot. The bankers are extremely clever, very bloodthirsty and not generous at all. Banker #5 may make the first proposal.

What is his proposal - and what are his reasons for making it?


Proposal:

#1 and #2 should get nothing and should be killed (if that is allowed :D). #5, should get nothing but can borrow the money until it is decided how the money is to be shared between #3 and #4.

Reason:

#3 and #4 will vote with #5 because they will see it as advantageous to reduce the number of claimants: rejecting the proposal would only reduce by one claimant but accepting the proposal reduces by three.
#3 and #4 will not make proposals in fear the other banker will vote with #5 to reject the proposal and claim all the money upon assassination.
This means #5 will indefinitely retain use of the money.
Sat Jul 24, 2010 2:49 am
CaseUser avatarPosts: 1080Joined: Sun Feb 28, 2010 9:40 pm Gender: Cake

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Noooo. :mrgreen:
I am determined that my children shall be brought up in their father's religion, if they can find out what it is.
Charles Lamb (1775 - 1834)

Atheism is a non-prophet organization.
Sat Jul 24, 2010 3:39 am
ArthurWilbornPosts: 964Joined: Sat Jun 19, 2010 4:46 pm

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Case wrote:Noooo. :mrgreen:


This problem is not very well posed.

Assuming:

The order which the people making the suggestion is known
That a suggestion must be made
That "bloodthirsty" means "will kill if given the opportunity"
That they will not kill eachother except by failure to reach a majority vote
Their desire to live is greater then their greed

Given those assumptions, #5 will suggest he keep all the money and explain to #3 and #4 that #1 will kill them if they lose #5's vote. They at least keep their lives.
Sat Jul 24, 2010 3:50 am
Aught3ModeratorUser avatarPosts: 4290Joined: Fri Feb 27, 2009 3:36 amLocation: New Zealand Gender: Male

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

First though after reading it is that he should get 3 and 4 to split the money evenly. Bankers 3 and 4 will vote for the proposal as they won't want a turn at being assassinated should they reject the proposal. Banker 5 will also vote for the motion as he doesn't want to be killed. With the majority vote the proposal is accepted and everyone walks away with their lives but only two get any money.
Wanderer, there is no path, the path is made by walking.
Sat Jul 24, 2010 3:52 am
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CaseUser avatarPosts: 1080Joined: Sun Feb 28, 2010 9:40 pm Gender: Cake

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

This problem is not very well posed.

Yes it is... you just have to read carefully.

As for the assumptions:
The order which the people making the suggestion is known -> it's irrelevant, because the bankers have no identities; but for the sake of the argument we can assume it is.
That a suggestion must be made -> yes
That "bloodthirsty" means "will kill if given the opportunity" -> yes
That they will not kill eachother except by failure to reach a majority vote -> assassination only takes place after a proposal has been rejected, only the person who made it, dies
Their desire to live is greater then their greed -> I'll just quote myself: "The bankers are extremely clever".

As for your proposals - no and no. It's a bit hard to say why, without giving clues.
I am determined that my children shall be brought up in their father's religion, if they can find out what it is.
Charles Lamb (1775 - 1834)

Atheism is a non-prophet organization.
Sat Jul 24, 2010 4:42 am
DeathofSpeechUser avatarPosts: 220Joined: Tue Jul 20, 2010 2:28 pmLocation: I can't know with certainty Gender: Tree

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Case wrote:
Sigh... yeah well that's what I get for bringing a cute puzzle to a party serving N dimensional cake. :lol:
Hehehe.

New riddle. :D
Five bankers are on their way home, they just settled a deal that will get them 1'000'000'000 $. Each banker may make a proposal as to how much $ each of the bankers gets. A proposal is accepted if the majority votes in favor of it. If a proposal is rejected, the one whose proposal was rejected will be assasssinated on the spot. The bankers are extremely clever, very bloodthirsty and not generous at all. Banker #5 may make the first proposal.

What is his proposal - and what are his reasons for making it?


Banker #5 proposes that he himself receive no money.

With the other four craftily contriving each others deaths.
The last of them then makes a proposal which #5 rejects.
With no majority vote...
Leaving #5 the last man standing.

Details details

Okay...
Five proposes he get no money because he wants to live. the majority agree.
Four proposes that three and two be killed, the majority agree.
One proposes that Four be killed.
Four and Five reject the proposal. One is killed.
Four proposes anything.
Five rejects the proposal.
Four is killed.
Five proposes he take the entire sum with no opposition.
Reason Bran, with two scoops of Objectivity in every box and loaded with Bran fiber goodness...
...you'll never be full of shit again.


Science - You can see why it works.
Religion - You can't see why it doesn't work
Sat Jul 24, 2010 6:05 am
CaseUser avatarPosts: 1080Joined: Sun Feb 28, 2010 9:40 pm Gender: Cake

Post Re: ** STICKY ** League of Reason? PROVE YOURSELF!

Five proposes he get no money because he wants to live. the majority agree. Four proposes that three and two be killed, the majority agree, [etc...]

Erm, no, because this doesn't specify who gets what. Besides, if a proposal were to be accepted, the money is already distributed and no other proposal will be made. Furthermore, the bankers cannot suggest that anyone be killed.
I am determined that my children shall be brought up in their father's religion, if they can find out what it is.
Charles Lamb (1775 - 1834)

Atheism is a non-prophet organization.
Sat Jul 24, 2010 10:10 am
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