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On November 23 2004 14:00 twsan wrote:
I have a followup question:
Somewhere in Northern Eurasia, a group of 20 lemmings is planning a special group suicide this year. Each of the lemmings will be placed in a random position along a thin, 100 meter long plank of wood which is floating in the sea. Each lemming is equally likely to be facing either end of the plank. At time t=0, all the lemmings walk forward at a slow speed of 1 meter per minute. If a lemming bumps into another lemming, the two both reverse directions. If a lemming falls off the plank, he drowns. What is the longest time that must elapse till all the lemmings have drowned?
Ah ah. Just figured it out. <3 It's great.
I'm not gonna spoil the answer tho.
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Catyoul
France2377 Posts
For tail or for head KarlSberg ? 
(though I'm pretty sure you have the right answer)
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On November 23 2004 13:55 KarlSberg~ wrote:
GJ not much more to say...
WTF that does not make any sense.
The trains meet at the same time, but the fly flies at speeds greater than both trains. Therefore let us say that the distance is 90KM, the trains are going at 10 KM/H each and the fly flies at 20 KM/H
The fly will meet train 1 60 KM from its departure, while train 1 and train 2 are 30 KM from their respective departures, and 30KM away from each other. The fly flies back to train 2 which, and fly another 20 KM, by which time the trains are 10 KM away from each other. In theory, the distance the fly will fly is infinite, since any return trip from its previous destination will always be 1/3 of its previous time, as the fly is faster than the trains, and the number becomes infinitely divisible :/
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On November 23 2004 00:09 Luhh wrote:
The hand has already been dealt! (the woman doesn't go upstairs, shag her husband and spit out another child. She had already given birth to the children. Those of you who thinks it's a 50/50 chance simply fail to see this.)
[...]
So please, think again :-/
Some people who think it is 50% probably fail to see this. Still the answer is 50%. I'm getting bored with self sufficient people who can't understand the (beautiful) logic which leads to 2/3 can't be used in this example.
I wonder what would happen if breathing wasn't a reflex but required active thought
Why do stupid people always have to show agressivity?
By the way I think you would probably die in suffocation if you really want an answer.
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Catyoul
France2377 Posts
An infinite sum of numbers can give a finite number Moltke 
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On November 23 2004 14:15 Catyoul wrote:For tail or for head KarlSberg ? (though I'm pretty sure you have the right answer)
Tail :p
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Catyoul
France2377 Posts
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On November 23 2004 14:15 MoltkeWarding wrote:
In theory, the distance the fly will fly is infinite, since any return trip from its previous destination will always be 1/3 of its previous time, as the fly is faster than the trains, and the number becomes infinitely divisible :/
Not quite, the fly will go back and forward an infinite number of times, still the total distance is finite. If you add 1/3 of what you previously added an infinite number of time, you get a finite result.
That's pretty advanced maths tho.
A pretty well known example showing that is:
You fire an arrow to a target. It will first travel half of the way.
From there it will travel half of the remaining distance.
When it reaches 3/4 it will then travel half of the remaining quarter.
etc...
That means you add D/2 + D/4 + D/8 + D/16 ...
In the end you get D.
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On November 23 2004 14:18 Catyoul wrote:An infinite sum of numbers can give a finite number Moltke
The number can only be expressed thus: 90*(1/3)^[i-(i-1)]+90*(1/3)^[i-(i-2)]+90*(1/3)^[i-(i-3)]....+90*(1/3)^[i-(0)]
Where i = infinite
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On November 23 2004 14:22 KarlSberg~ wrote:Show nested quote +On November 23 2004 14:15 MoltkeWarding wrote:
In theory, the distance the fly will fly is infinite, since any return trip from its previous destination will always be 1/3 of its previous time, as the fly is faster than the trains, and the number becomes infinitely divisible :/ Not quite, the fly will go back and forward an infinite number of times, still the total distance is finite. If you add 1/3 of what you previously added an infinite number of time, you get a finite result. That's pretty advanced maths tho.
The point is, without a reference of relative speeds and positions, even the formulation such as the one I gave is impossible.
"When the trains meet, what distance will the fly have flied?"
The answer must be: Insufficient data :/
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Catyoul
France2377 Posts
On November 23 2004 14:22 MoltkeWarding wrote:
The number can only be expressed thus: 90*(1/3)^[i-(i-1)]+90*(1/3)^[i-(i-2)]+90*(1/3)^[i-(i-3)]....+90*(1/3)^[i-(i-0)]
Where i = infinite
What does infinite do in exponent there ?
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On November 23 2004 14:26 Catyoul wrote:Show nested quote +On November 23 2004 14:22 MoltkeWarding wrote:
The number can only be expressed thus: 90*(1/3)^[i-(i-1)]+90*(1/3)^[i-(i-2)]+90*(1/3)^[i-(i-3)]....+90*(1/3)^[i-(i-0)]
Where i = infinite What does infinite do in exponent there ?
90*1/3^1+90*1/3^2....+90*1/3^i
i-(i-0) should read i-i 
Edit: i-i should read i-0
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If I understand well the formula you wrote, you are right Moltke, but believe it or not, the sum is finite.
Considering the problem the way twsan put it shows what the result is. Finding the result by calculating the sum you wrote would lead to the same result. (in a much longer time)
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Catyoul
France2377 Posts
Well yeah I had seen they canceled each other, now that you've written your last term (90*1/3^i) I understand where you got that from ^^
Technically you can't write 90*1/3^infinite, it's not a number, it defines nothing. The limit of 90*1/3^n when n goes to infinite exists though and it is 0.
The limit of 90*(1/3)^1+90*(1/3)^2+90*(1/3)^3+....+90*(1/3)^n when n goes to infinite exists too (meaning it doesn't diverge, it converges to a number) and it can be calculated. One methode for example : if you have a sum of 1 + q + q^2 + q^3 + ... + q^n, with q different from 1, you can prove pretty quickly that its value is (1-q^n) / (1-q). If q is smaller than 1 (in absolute value) then q^n -> 0 when n -> infinite, and the series (the sum of 1 + q + ...) tends to 1 / (1-q)
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On November 23 2004 14:12 KarlSberg~ wrote:Show nested quote +On November 23 2004 14:00 twsan wrote:
I have a followup question:
Somewhere in Northern Eurasia, a group of 20 lemmings is planning a special group suicide this year. Each of the lemmings will be placed in a random position along a thin, 100 meter long plank of wood which is floating in the sea. Each lemming is equally likely to be facing either end of the plank. At time t=0, all the lemmings walk forward at a slow speed of 1 meter per minute. If a lemming bumps into another lemming, the two both reverse directions. If a lemming falls off the plank, he drowns. What is the longest time that must elapse till all the lemmings have drowned? Ah ah. Just figured it out. <3 It's great. I'm not gonna spoil the answer tho.
Can lemmings stack? :D You can't have a perfect problem here. If they don't stack, then they must occupy space, such as 20 cm width, in which case it would figure into the calculations. If they can stack, the answer is infinite :D
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If they don't occupy any space, the answer is much simpler than if they did. But not infinite.
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On November 23 2004 14:37 Catyoul wrote:
Well yeah I had seen they canceled each other, now that you've written your last term (90*1/3^i) I understand where you got that from ^^
Technically you can't write 90*1/3^infinite, it's not a number, it defines nothing. The limit of 90*1/3^n when n goes to infinite exists though and it is 0.
The limit of 90*(1/3)^1+90*(1/3)^2+90*(1/3)^3+....+90*(1/3)^n when n goes to infinite exists too (meaning it doesn't diverge, it converges to a number) and it can be calculated. One methode for example : if you have a sum of 1 + q + q^2 + q^3 + ... + q^n, with q different from 1, you can prove pretty quickly that its value is (1-q^n) / (1-q). If q is smaller than 1 (in absolute value) then q^n -> 0 when n -> infinite, and the series (the sum of 1 + q + ...) tends to 1 / (1-q)
I can't use I as a variable whereas you can use N?
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Catyoul
France2377 Posts
In your formulation i is not a variable, it is infinite
In my case n is an arbitrary integer
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Just think about what is happening when 2 lemmings meet each other.
What is the situation just before?
What is the situation just after?
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On November 23 2004 14:40 KarlSberg~ wrote:
If they don't occupy any space, the answer is much simpler than if they did. But not infinite.
If they stack they cant move, the time that they would be turning around in = 0
timexvelocity=distance
0sx1m/s=0m
They would never move :/
If you need visual proof go see that Nada rep where a SCV got stacked inside a tank. He unsieged the tank, but neither could move.
In that case the SCV was going at SCV velocity, tank going at Tank velocity. When SCV contacts tank they turn and move. However they occupied the same space so when they turned they contacted each other again and kept spinning in circles indefinitely while neither changed their position. Nada could not get unstuck on the ramp and nada had to kill them both
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EPT
