TWCP OTD (The Who Cares Puzzle Of The Day) - 15th of February, 2017
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WORKS LIKE AN ANT There is a meter long rope tight between two poles. An ant starts running at the speed of 1 cm/s from one end of the rope to the other. At same time the poles are moving back a 1/2 m/s each, stretching the rope (the rope is magical and can be stretched infinitely). Will the ant ever arrive?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Yes. The actual speeds are irrelevant to the solution as well. Each time the ant moves, more of the rope expands behind the ant than the previous move and less in front. Eventually when the ant reaches the mid-way point the rope is expanding equally in front and behind. As it moves closer to its destination more and more of the rope is expanding behind the ant. This means that eventually the ant will reach its destination because eventually less rope will expand in front of the ant than the ant can travel which will land the ant at his destination :thumbsup:
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WORKS LIKE AN ANT There is a meter long rope tight between two poles. An ant starts running at the speed of 1 cm/s from one end of the rope to the other. At same time the poles are moving back a 1/2 m/s each, stretching the rope (the rope is magical and can be stretched infinitely). Will the ant ever arrive?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
I say the ant will certainly arrive. Even if we say the ant is moving after the poles, even though they are separating at the same speed the ant is covering at least a part of the gap. As the gap is getting larger at the same rate as the ant is moving, because the ant is not at the end part of the expansion must be on the part already travelled. So if the gap increases uniformly the extra distance still to travel each second will always be less than 1cm.
veni bibi saltavi
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Yes. The actual speeds are irrelevant to the solution as well. Each time the ant moves, more of the rope expands behind the ant than the previous move and less in front. Eventually when the ant reaches the mid-way point the rope is expanding equally in front and behind. As it moves closer to its destination more and more of the rope is expanding behind the ant. This means that eventually the ant will reach its destination because eventually less rope will expand in front of the ant than the ant can travel which will land the ant at his destination :thumbsup:
Or in other words - it will be a very-very old ant when getting off the rope...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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I say the ant will certainly arrive. Even if we say the ant is moving after the poles, even though they are separating at the same speed the ant is covering at least a part of the gap. As the gap is getting larger at the same rate as the ant is moving, because the ant is not at the end part of the expansion must be on the part already travelled. So if the gap increases uniformly the extra distance still to travel each second will always be less than 1cm.
veni bibi saltavi
Can you explain it magyarul?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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The poles are moving away from each other at 500 cm/s?
My mistake... I somehow stopped at the 'each other' part and cleared the '500 cm/s'... It is away - yes, but only at 50 cm/s... (but that's probably irrelevant anyway)
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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1/2 m = 50 cm... And I meant that and not 0.5 cm...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
That's why I said 'I think' and not 'I correctly think'. :-O :laugh:
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment "Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst "I don't drink any more... then again, I don't drink any less." - Mike Mullikins uncle
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WORKS LIKE AN ANT There is a meter long rope tight between two poles. An ant starts running at the speed of 1 cm/s from one end of the rope to the other. At same time the poles are moving back a 1/2 m/s each, stretching the rope (the rope is magical and can be stretched infinitely). Will the ant ever arrive?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
The ant never makes it to the end of the rope. The waveform set up by the flexing of the rope makes the ant dizzy and so he falls off. On his way to the ground he intercepts the path of an arrow that a tortoise has been struggling to run away from for quite some time.
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Or in other words - it will be a very-very old ant when getting off the rope...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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Can you explain it magyarul?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Egyszer volt egy kiss hangyat, egyszer nem volt. ;P
veni bibi saltavi
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Egyszer volt egy kiss hangyat, egyszer nem volt. ;P
veni bibi saltavi
Once there was a kiss ants, not once was
Not sure if it's Google's Hungarian translator that's broken, or your Hungarian. :laugh:
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
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The ant never makes it to the end of the rope. The waveform set up by the flexing of the rope makes the ant dizzy and so he falls off. On his way to the ground he intercepts the path of an arrow that a tortoise has been struggling to run away from for quite some time.
If the arrow doesn't get him, the bowl of petunias probably will. :-D
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
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Once there was a kiss ants, not once was
Not sure if it's Google's Hungarian translator that's broken, or your Hungarian. :laugh:
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
I missed an auto correct, kis not kiss. Once there was a little mouse, once there wasn't. Every Hungarian folk tale starts this way.
veni bibi saltavi
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Jon McKee wrote:
Approximately 8.547e+35 years if my math is correct
So, that's still younger than @OriginalGriff then.
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WORKS LIKE AN ANT There is a meter long rope tight between two poles. An ant starts running at the speed of 1 cm/s from one end of the rope to the other. At same time the poles are moving back a 1/2 m/s each, stretching the rope (the rope is magical and can be stretched infinitely). Will the ant ever arrive?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Yes. The ant does not even need to move. Just stay there. Eventually, destination pole will touch the origin pole due to stretching and Earth being spherical (almost). At that point, just switch lanes. :cool:
"It is easy to decipher extraterrestrial signals after deciphering Javascript and VB6 themselves.", ISanti[^]
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Jon McKee wrote:
Approximately 8.547e+35 years if my math is correct
So, that's still younger than @OriginalGriff then.
No, I only feel that old...
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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My mistake... I somehow stopped at the 'each other' part and cleared the '500 cm/s'... It is away - yes, but only at 50 cm/s... (but that's probably irrelevant anyway)
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
SO, each second the ant moves 1cm closer to his goal, which moves approx 50cm further away from him in the same second.(actually, I think in the first second it move 99.5cm away). So, no, he's never going to reach it.
Truth, James
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WORKS LIKE AN ANT There is a meter long rope tight between two poles. An ant starts running at the speed of 1 cm/s from one end of the rope to the other. At same time the poles are moving back a 1/2 m/s each, stretching the rope (the rope is magical and can be stretched infinitely). Will the ant ever arrive?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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WORKS LIKE AN ANT There is a meter long rope tight between two poles. An ant starts running at the speed of 1 cm/s from one end of the rope to the other. At same time the poles are moving back a 1/2 m/s each, stretching the rope (the rope is magical and can be stretched infinitely). Will the ant ever arrive?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
The ant will reach the end -- the part of the whole path he covers in a second is 0.01 / (1 + t), where t is time in seconds (the covered part doesn't decrease since the line extends uniformly). So the total part he has covered up to the time t is 0.01 * ln(1 + t), meaning he crosses whole path in exp(100) - 1 seconds (approx. 10^36 years).
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speed of rope at distance x from centre is x/(t+1) (ant starts at x=-50, t=0) speed of ant is x/(t+1)+1 = dx/dt x=c(t+1)+(t+1)log(t+1) so -50=c ant arrives: 50=-50(t+1)+(t+1)log(t+1) let u=t+1 50(u+1)=u log u if u=exp(50), u log u = 50.u which is near enough
