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        riddles >> hard >> The Duck in the Pond
        
(Message started by: Eric Yeh on Aug 2^nd, 2002, 2:44pm)

Title: The Duck in the Pond
Post by Eric Yeh on Aug 2^nd, 2002, 2:44pm

OK, this one will be it for me for now -- I don't want to flood the boards overly much. If these go well, maybe I will post more later.

This is a somewhat easier one, for balance. But still one of my faves, and one that I used to use in interviews all the time:

A duck is in a circular pond with a menacing cat outside. The cat runs four times as fast as the duck can swim, but cannot enter the water. Can the duck get to the perimeter of the pond without the cat being on top of him?

Happy Puzzling,
Eric

Title: Re: NEW PROBLEM: The Duck in the Pond
Post by AlexH on Aug 3^rd, 2002, 4:54pm

Since noone else went for this one I'll bite.

Define our distance scale so that the radius of the circle is 1, and define time so that the duck's speed is also 1 and cats speed is 4. The duck can swim out to a point 1/4 - x from the center (x is any small positive number). The duck can swim around this circle faster than the cat can run around the pond because its circumference is less than 1/4 the circumference of the pond. This means he can position himself at the opposite side of this subcircle from the cat by racing around this inner circle faster than the cat can keep up (he could do this more efficiently but I'm just saying it can be done). Once he is opposite the cat, then his distance to the edge is 3/4+x, while the cat will have to run a distance of pi to make it to that point. As long as we pick x < (pi -3)/4 then the duck will make it there first.

Title: Re: NEW PROBLEM: The Duck in the Pond
Post by Eric Yeh on Aug 3^rd, 2002, 9:22pm

Yup -- nice job!

Best,
Eric

Title: Re: NEW PROBLEM: The Duck in the Pond
Post by jograd on Aug 4^th, 2002, 11:14pm

Easy, the duck can fly out of the pond.

:)

Title: Re: NEW PROBLEM: The Duck in the Pond
Post by Eric Yeh on Aug 5^th, 2002, 8:25am

OK, I forgot to mention that the cat also has a shotgun, but since he forgot to put in his contact lenses this morning, his vision is only good enough to shoot something out of a bright background. ;)

Title: Re: NEW PROBLEM: The Duck in the Pond
Post by EvolvedHumanoid on Aug 7^th, 2002, 2:55am

There is no way the duck can reach the edge of the pond.

Draw a straight line from the centerpoint of the pond, through the duck, to the edge of the pond. No matter where the duck is, where the line intersects the edge of the pond is where the cat should be.

The farthest the cat will ever have to run is exactly halfway around the pond (in the case that the duck crosses the center point).

Define the pond as having a radius of 1.
The circomference is 2 * pi * r. The farthest the cat ever has to run is (2*pi*r) / 2 or pi*r, which is well below 4.

Title: Re: NEW PROBLEM: The Duck in the Pond
Post by Willis on Aug 7^th, 2002, 4:43am

EvolvedHumanoid: Your counterargument only works if the duck always starts at the center of the pond. However, if you read above, you'll see that it's possible for the duck to be r/4 from the center (in fact, more than r/4, but r/4 suffices), and move more quickly about its "circle" than the cat can move around the pond. Therefore, it's possible for the duck to get opposite the cat at least r/4 from the center of the pond, which gives it the edge it needs.

Title: Re: NEW PROBLEM: The Duck in the Pond
Post by EvolvedHumanoid on Aug 7^th, 2002, 12:23pm

I should know better than to post at three in the morning.

I see my error now.