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On June 17 2005 14:22 baal wrote:Show nested quote +On June 17 2005 14:18 Polis wrote:
You got 12 ball's, one of the weight less OR more then the others. You have balance and you can use it 3 times.
Find the diferent ball. Easy, you put half and half, 6 remaining, half and half 3 remaining, then you put only 2, if they weight the same is the other one.
Nah, cause you don't know if it's lighter or heavier, therefore you can't tell which of the groups of six to split for the second measurement, etc. Someone posted this a while back and a bunch of us banged on it for a while 
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Ok ill do the ball one again. Label them 1,2,3,4,5,6,7,8,9,10,11,12
first you weigh 1,2,3,4v5,6,7,8
If unequal, we know the unequal ball is among the last 4.
Now weigh 1,2,9v5,10,11
If equal, we know 12 is unequal, one weighing determines lighter or heavier.
If unequal, odd ball is among 9,10,11. Suppose WLOG 1,2,9 was heavier. So 9 is potentially heavy, 10,11 potentially light. 3rd weighing: 8,10 v 11,12 If stays the same, 9 is heavy. If 10 side up, it is light, if 11 side up, 11 is light.
That covers when the 4x4 to start out is equal. I dont feel like doing the rest, maybe someone who has never done it can jump off from here and do the other case
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Belgium6772 Posts
On June 17 2005 14:27 wasted wrote:
the eyes riddle seems pretty difficult.. i'll give it a shot, i doubt it's correct, but i need a hint if im thinking in the right direction
Blue eyes present during the meeting: 125
Are there more blue or brown eyes in the meeting? same amount
Number of nights in which suicides happened: 250
Which mathematical concept made them kill themselves? statistical equal distribution
basic idea is, that you know br=num_of_browneyes, bl=num_of_blueeyes, and you assume that br=bl. your own eyecolor is x=unknown, so if it's like br=bl-1 situation, you "know" that you are bl, and kill yourself. the next night for the next person to think about it, it's bl=br, but you know what the eyecolor of the person who killed himself was. so you know that you must belong to the other group and kill yourself. da capo
No, this isnt the right way =)
But I'll give you a hint: The mathematical concept is called induction. With other words: Proving something by proving the opposide is wrong.
If you cant find it after this I'll post the answer, its quite hard
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On June 17 2005 14:03 LTT wrote:
Because if he doesn't agree, he is going to end up with nothing, and 1 coin is better than nothing.
if he doesn't agree, the first pirate gets executed and they can work for a better solution
whoever gets a very small share will be unhappy with the first guy getting more and vote against... as long as the first guy gets more than others, they logically shouldn't vote for it
I don't really see what perspective you are considering
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On June 17 2005 14:34 Xeofreestyler wrote:Show nested quote +On June 17 2005 14:27 wasted wrote:
the eyes riddle seems pretty difficult.. i'll give it a shot, i doubt it's correct, but i need a hint if im thinking in the right direction
Blue eyes present during the meeting: 125
Are there more blue or brown eyes in the meeting? same amount
Number of nights in which suicides happened: 250
Which mathematical concept made them kill themselves? statistical equal distribution
basic idea is, that you know br=num_of_browneyes, bl=num_of_blueeyes, and you assume that br=bl. your own eyecolor is x=unknown, so if it's like br=bl-1 situation, you "know" that you are bl, and kill yourself. the next night for the next person to think about it, it's bl=br, but you know what the eyecolor of the person who killed himself was. so you know that you must belong to the other group and kill yourself. da capo No, this isnt the right way =) But I'll give you a hint: The mathematical concept is called induction. With other words: Proving something by proving the opposide is wrong. If you cant find it after this I'll post the answer, its quite hard
that's contradiction
induction is when you build up for all numbers by showing a connection between n and n+1
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On June 17 2005 14:35 MPXMX wrote:Show nested quote +On June 17 2005 14:03 LTT wrote:
Because if he doesn't agree, he is going to end up with nothing, and 1 coin is better than nothing. if he doesn't agree, the first pirate gets executed and they can work for a better solution whoever gets a very small share will be unhappy with the first guy getting more and vote against... as long as the first guy gets more than others, they logically shouldn't vote for it I don't really see what perspective you are considering
msg me on aim, beanbags99, ill explain it
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would be cool, but I don't use AIM
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Belgium9947 Posts
On June 17 2005 14:36 BigBalls wrote:Show nested quote +On June 17 2005 14:34 Xeofreestyler wrote:On June 17 2005 14:27 wasted wrote:
the eyes riddle seems pretty difficult.. i'll give it a shot, i doubt it's correct, but i need a hint if im thinking in the right direction
Blue eyes present during the meeting: 125
Are there more blue or brown eyes in the meeting? same amount
Number of nights in which suicides happened: 250
Which mathematical concept made them kill themselves? statistical equal distribution
basic idea is, that you know br=num_of_browneyes, bl=num_of_blueeyes, and you assume that br=bl. your own eyecolor is x=unknown, so if it's like br=bl-1 situation, you "know" that you are bl, and kill yourself. the next night for the next person to think about it, it's bl=br, but you know what the eyecolor of the person who killed himself was. so you know that you must belong to the other group and kill yourself. da capo No, this isnt the right way =) But I'll give you a hint: The mathematical concept is called induction. With other words: Proving something by proving the opposide is wrong. If you cant find it after this I'll post the answer, its quite hard that's contradiction induction is when you build up for all numbers by showing a connection between n and n+1
he made a mathematical term clear to you in english, thats already quite a prestation
I'd want to see you do that in another language
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Maybe im not being an asshole like someone else and im trying to help his english cause he already said once he has trouble in it?
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On June 17 2005 14:34 Xeofreestyler wrote:No, this isnt the right way =) But I'll give you a hint: The mathematical concept is called induction. With other words: Proving something by proving the opposide is wrong. If you cant find it after this I'll post the answer, its quite hard
hmm, well so everyone makes the assumption "i have XYZ_colored eyes" and contradicts that assumption thus proving (s)he has the other color? dont think i will get that anytime soon, so if i'm the only person thinking about this, i give up and you can reveal the answer 
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On June 17 2005 14:09 BigBalls wrote:
pretty easy problem, prove answer is correct
Basketball player S's team statistician keeps track of the number, S(n) of successfull free throws S has made in his first n attempts of the season. Early in the season, S(n) was less than 80% of n but by the end of the season, S(n) was more than 80%. Is it necessarily true that at one point in the season S(n) was exactly 80% of n?
This is one I haven't heard... I guess for 80% it is necessarily true... because 80% means you have exactly 4 makes for each miss. It's impossible to improve to >= 80% with a miss, only a make. Assume you have X misses and Y makes. So at the point where you go to or above 80%, you are going from (X,Y) to (X,Y+1) and from Y < 4X to either Y > 4X or Y=4X. But that's not possible without going through Y = 4X, because X and Y both increment by ones and are both integers.
Really convoluted wording I just made... but I convinced myself...
It's a cool problem. I guess the same thing holds for every percentage which can be expressed as N/(N+1) with N a positive integer?
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Belgium6772 Posts
Bigballs,rage, chill. Thats just the definition I heard for induction and it seemed to be the correct answer for the riddle too... Anyway;
They know they are mixed, with blue-eyed people and brown-eyed people, so there must be at least one of each. When the spaceship crashed, from the math book they learned about mathematical induction. Therefore, they knew that if there was only one brown-eyed person, the brown-eyed person would find out cos* eye color from the fact that everybody else had blue eyes, and kill cosself. If there were two brown-eyed people, each would expect the other to kill themself, and, upon finding the other alive the next morning, realize that the other person saw someone with brown eyes, which must be them, and both would die the second night. If there were three brown-eyed people, each would assume the situation in the previous sentence was taking place, until they saw that the other two were alive on the third day, at which time they would realize that there was another brown-eyed person, who must be themself, so all three would kill themselves on the third night. And so on. Since it took until the 250th night, 250 brown-eyed people killed themselves. Upon awakening the next morning and finding all of the brown-eyed people dead, the blue-eyed people would know that they had blue eyes and kill themselves the next night, leaving the planet unpopulated in just two nights of suicides.
Number of blue eyes? -249
Number of nights in which suicides happened after the meeting: -2
Are there more blue or brown eyes in the meeting? -brown
Which mathematical concept made them kill themselves? -Mathematical induction
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On June 17 2005 14:25 One Page Memory wrote:
And one old, not very difficult, but as far as I remember Newton gave a wrong answer first. Here it is:
There is a lake, a boat in it, and a stone in the boat. What will happen if the the stone is taken from the boat and put in the lake?
a) the level of the lake increases;
b) the level of the lake decreases;
c) the level of the lake stays the same;
Id say the the weight/volume (i forget what's the english for this, density?) of the stone is bigger than that of water. So the stone is able to push up more water when in the boat than when it replaces it's own volume with stone in the water. So the water level will decrease...
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On June 17 2005 14:27 BigBalls wrote:
There are 4 people who are trying to cross a bridge. One person walks across at 1 second, one at 2, one at 5, one at 10.
The bridge has holes in it, so each trip a flashlight must go across. Also, only two people may cross at once. Finally, a trip takes as long as it takes the slowest person to travel across.
Find a way to get everyone across in less than 18 seconds.
i assume this means:
there can only go 2 over at the same time, since the flashlight has to be returned, thus the following sequence must happen
side A <-> side B
4 <-> 0 // 2 from A to B = pass 1
2 <-> 2 // 1 from B to A = pass 2
3 <-> 1 // 2 from A to B = pass 3
1 <-> 3 // 1 from B to A = pass 4
2 <-> 2 // 2 from A to B = pass 5
0 <-> 4 // done
so, 5 passes and only 18 secs
5 and 10 can't go together, since one of them had to go back, which would kill the deadline.
if they have to go seperate, their trips will last fifteen secs
since you have to go back at least two times, you use at least another two secs, if you use 1 as the one who goes back. that leaves pass5, which will at least cost two seconds
that sums up to 19.
i'm curious how to do it quicker.
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huh aseq smarter then Newton )) RIGHT
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On June 17 2005 15:07 wasted wrote:Show nested quote +On June 17 2005 14:27 BigBalls wrote:
There are 4 people who are trying to cross a bridge. One person walks across at 1 second, one at 2, one at 5, one at 10.
The bridge has holes in it, so each trip a flashlight must go across. Also, only two people may cross at once. Finally, a trip takes as long as it takes the slowest person to travel across.
Find a way to get everyone across in less than 18 seconds. i assume this means: there can only go 2 over at the same time, since the flashlight has to be returned, thus the following sequence must happen side A <-> side B 4 <-> 0 // 2 from A to B = pass 1 2 <-> 2 // 1 from B to A = pass 2 3 <-> 1 // 2 from A to B = pass 3 1 <-> 3 // 1 from B to A = pass 4 2 <-> 2 // 2 from A to B = pass 5 0 <-> 4 // done so, 5 passes and only 18 secs 5 and 10 can't go together, since one of them had to go back, which would kill the deadline. if they have to go seperate, their trips will last fifteen secs since you have to go back at least two times, you use at least another two secs, if you use 1 as the one who goes back. that leaves pass5, which will at least cost two seconds that sums up to 19. i'm curious how to do it quicker.
be clever
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On June 17 2005 14:53 Xeofreestyler wrote:
Bigballs,rage, chill. Thats just the definition I heard for induction and it seemed to be the correct answer for the riddle too... Anyway;
They know they are mixed, with blue-eyed people and brown-eyed people, so there must be at least one of each. When the spaceship crashed, from the math book they learned about mathematical induction. Therefore, they knew that if there was only one brown-eyed person, the brown-eyed person would find out cos* eye color from the fact that everybody else had blue eyes, and kill cosself. If there were two brown-eyed people, each would expect the other to kill themself, and, upon finding the other alive the next morning, realize that the other person saw someone with brown eyes, which must be them, and both would die the second night. If there were three brown-eyed people, each would assume the situation in the previous sentence was taking place, until they saw that the other two were alive on the third day, at which time they would realize that there was another brown-eyed person, who must be themself, so all three would kill themselves on the third night. And so on. Since it took until the 250th night, 250 brown-eyed people killed themselves. Upon awakening the next morning and finding all of the brown-eyed people dead, the blue-eyed people would know that they had blue eyes and kill themselves the next night, leaving the planet unpopulated in just two nights of suicides.
Number of blue eyes? -249
Number of nights in which suicides happened after the meeting: -2
Are there more blue or brown eyes in the meeting? -brown
Which mathematical concept made them kill themselves? -Mathematical induction
guess i would have been the only survivor on that island since i couldn't think that deep
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On June 17 2005 13:21 LTT wrote:Show nested quote +On June 17 2005 13:20 Pistachio wrote:
Here's a better one:
Three woman go to their favorite restaurant and each order some food that costs £30 overall. So they each give £10 to the waiter who then gives it to the manager. The manager however decides to give £5 back to the women as a good will gesture since the women have been such loyal customers over the years. Now the waiter thinks he can make some money out of this so he secretely takes £2 for himself and only gives £1 back to each women.
This means each woman has payed £9 each, having originally payed £10 and gotten £1 back.
The waiter has £2 thus the overall money payed is 3x9 + 2 = £29.
So where'd the extra pound go? Old One. Order of Operations.
errr NO -.-
its simply that 3x9 + 2 makes no sense at all, its like saying something like this:
4 + 4 = 8
8 - 2 = 6
then:
8 - 4 = 6 <--- wooooot
its just confusing ppl so they dont think that what the waiter took has nothing to do with anything in 3x9.
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EPT
