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Topic: DUCK IN THE POND (Read 1604 times) |
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pa0pa0
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DUCK IN THE POND
« on: Aug 4th, 2002, 2:58am » |
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As it stands this riddle is singularly pointless, so let us imagine that there are pieces of bread all the way around the edge of the pond (perhaps put there as bait by the cat), and the duck is trying to grab a piece of bread without the cat grabbing him.
The cat can move 4 times as fast as the duck. Let the radius of the pond be 4R. Imagine a circle, concentric with the pond, of radius R. Let us call the inside of this circle the zone of safety, because inside this circle, the duck can achieve the same angular velocity (about the centre) as the cat, with speed to spare for moving outwards (albeit with less and less speed to spare as it approaches the edge of the zone.)
The duck's feeding strategy has two phases:
(1) Starting at the centre, move outwards towards the edge of the zone of safety, all the while staying diametrically opposite the cat.
The cat (if it keeps circling the pond at full speed) can prevent the duck from actually reaching the edge of the zone, but we have:
(2) When sufficiently near the edge of the zone of safety, make a radial dash for the shore and grab some bread. How near? Well, if it was starting *at* the edge of the zone of safety, the duck (moving with speed 1, say) would take time 3R to reach the shore, while the cat (moving with speed 4) will take time pi*R to reach the duck's arrival point, so there is clearly a margin of around (pi - 3)*R from within which the duck can safely start its dash.
The duck can use the fact that there is this margin, to grab some bread even if the bread is not distributed all the way around the pond, but is in clumps. Working out how near to each other the clumps have to be, for the duck to succeed, would make this riddle somewhat harder.
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mook
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Re: DUCK IN THE POND
« Reply #1 on: Aug 4th, 2002, 8:51am » |
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Your explanation is somewhat confusing to me, so let me see if I'm tracking. Let's say cat is on south end of pond, duck in center of pond. If duck swims due north and cat runs around pond, cat gets to north side of pond first because he travels the same distance covered by the duck times pi. since this distance is less than four times as far, the cat gets there first.
But if the cat travels to the north side in an easterly direction, then the duck can change his angle of approach towards the northwest shore enough to allow him the extra time to get his bread. Same way slower defensive backs catch randy moss from behind.
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Chronos
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Re: DUCK IN THE POND
« Reply #2 on: Aug 6th, 2002, 12:36am » |
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Very clever, pa0pa0, and I agree that your answer would be the right one if we had, say, a newt and a cat. But we have a duck and a cat, and that makes the riddle much easier.
It doesn't matter how fast the cat can travel horizontally, because the duck can fly. In fact, that's what any duck would do in this situation, ducks being notoriously bad at analytitical geometry.
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srn437
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the dark lord rises again....
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Re: DUCK IN THE POND
« Reply #3 on: Aug 28th, 2007, 8:47pm » |
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Let's just say it's wings were genetically altered or something so they can still be used for swimming but not flying. The cat moves pi times the ducks distance and moves 4 times as fast so it will always get there faster. Even if the duck is strategic he can't get there.
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towr
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Re: DUCK IN THE POND
« Reply #4 on: Aug 29th, 2007, 1:04am » |
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on Aug 28th, 2007, 8:47pm, srn347 wrote:| Let's just say it's wings were genetically altered or something so they can still be used for swimming but not flying. The cat moves pi times the ducks distance and moves 4 times as fast so it will always get there faster. Even if the duck is strategic he can't get there. |
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Are you quite, quite sure, about that?
If it were that obvious, would this even be a puzzle?
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mikedagr8
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Re: DUCK IN THE POND
« Reply #5 on: Aug 29th, 2007, 1:06am » |
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Of course it would, it would be as stupid as "John, what is your name?" 
It would just be stupid, but it would still be a puzzle, like my common standard riddle in the what am i section.
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srn437
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Re: DUCK IN THE POND
« Reply #6 on: Aug 29th, 2007, 11:22am » |
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It is not a stupid puzzle! They intend on making you think the cat always getting there first can be used as an advantage of the duck by always going some other way. But that is not the case.
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towr
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Re: DUCK IN THE POND
« Reply #7 on: Aug 29th, 2007, 11:30am » |
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The duck can get to the bread.
If you can't see how, well, your loss. I mean, it's written right there above in this thread.
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| « Last Edit: Aug 29th, 2007, 11:30am by towr » |
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Aryabhatta
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Re: DUCK IN THE POND
« Reply #8 on: Aug 29th, 2007, 11:34am » |
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Easy. The duck, without batting an eyelid, will use telekinesis to make the bread come to it.
Sorry, couldn't resist. 
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| « Last Edit: Aug 29th, 2007, 11:35am by Aryabhatta » |
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mikedagr8
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Re: DUCK IN THE POND
« Reply #9 on: Aug 29th, 2007, 5:16pm » |
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Isn't this the same or very similar as the lion and lion tamer problem? The one where Barukh proved everyone incorrect?
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srn437
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the dark lord rises again....
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Re: DUCK IN THE POND
« Reply #10 on: Aug 29th, 2007, 5:25pm » |
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Identical, yes. The same, no. This is more identical than the lion tamer one. By the way, can the lion get the tamer or vice-verca?
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mikedagr8
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Re: DUCK IN THE POND
« Reply #11 on: Aug 29th, 2007, 5:26pm » |
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No, the tamer is always able to escape due to their relative speeds.
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