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        riddles >> hard >> DUCK IN THE POND
        
(Message started by: pa0pa0 on Aug 4^th, 2002, 2:58am)

Title: DUCK IN THE POND
Post by pa0pa0 on Aug 4^th, 2002, 2:58am

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.

Title: Re: DUCK IN THE POND
Post by mook on Aug 4^th, 2002, 8:51am

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.

Title: Re: DUCK IN THE POND
Post by Chronos on Aug 6^th, 2002, 12:36am

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.

Title: Re: DUCK IN THE POND
Post by srn347 on Aug 28^th, 2007, 8:47pm

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.

Title: Re: DUCK IN THE POND
Post by towr on Aug 29^th, 2007, 1:04am

on 08/28/07 at 20:47:10, srn347 wrote:

Are you quite, quite sure, about that?
If it were that obvious, would this even be a puzzle?

Title: Re: DUCK IN THE POND
Post by mikedagr8 on Aug 29^th, 2007, 1:06am

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.

Title: Re: DUCK IN THE POND
Post by srn347 on Aug 29^th, 2007, 11:22am

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.

Title: Re: DUCK IN THE POND
Post by towr on Aug 29^th, 2007, 11:30am

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.

Title: Re: DUCK IN THE POND
Post by Aryabhatta on Aug 29^th, 2007, 11:34am

Easy. The duck, without batting an eyelid, will use telekinesis to make the bread come to it.

Sorry, couldn't resist. :P

Title: Re: DUCK IN THE POND
Post by mikedagr8 on Aug 29^th, 2007, 5:16pm

Isn't this the same or very similar as the lion and lion tamer problem? The one where Barukh proved everyone incorrect? ::)

Title: Re: DUCK IN THE POND
Post by srn347 on Aug 29^th, 2007, 5:25pm

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?

Title: Re: DUCK IN THE POND
Post by mikedagr8 on Aug 29^th, 2007, 5:26pm

No, the tamer is always able to escape due to their relative speeds.