The Fox, Duck and Circular Pond Puzzle

Puzzle on Fox, A Duck and A Circular Pond

In this puzzle, there is a situation where we have a fox, a duck and a circular pond. Read the premise, rule, and objective carefully.

Premise – A Duck persuaded by a Fox escapes by sitting in the center of a circular pond with a radius of r.

Rule – The Duck can only fly on land and cannot fly on the water. Fox is also unable to swim. The Fox has a four-fold faster speed than the Duck.

Objective – Is it possible for the Duck to reach the edge of the pond and fly away from the earth if both the Duck and the Fox are perfectly intelligent?

Puzzle on Fox, A Duck and A Circular Pond
A Duck being pursued by a Fox escapes by sitting in the center of a circular pond with radius r
  • The Duck cannot swim directly away from the Fox because for this the duck would require to swim a distance of r and the Fox can cover half the diameter of the pond, i.e. (pi * r).
  • As it is given that Fox’s speed is four times that of the Duck, he will be able to catch the duck, as we know from (pi * r) (4 * r).
  • The duck could swim in concentric circles near the pond’s center as a solution to this challenge.
  • As a result, the Duck will cover the pond’s little diameter while the Fox will have to cover the pond’s greater circumference.
  • The Duck will use the above approach to create tiny concentric circles around the center, and the Fox will be unable to keep up with the Duck since he will have to cover the entire pond.
  • Because Fox’s speed is four times that of the Duck, the Duck must move in a concentric circle with a radius of r/4 to cover the same distance as the Fox.
  • The duck will gain some distance over Fox after some time if he continues within that concentric circle, and the Fox will be unable to keep up with the Duck.

When the Fox is 180 degrees behind the Duck, the Duck will cross the remaining distance (3*r / 4) because the distance covered by the Fox is less than the distance covered by the Duck (pi * r) > 4 * (3r/4).

Finally, The Duck would be able to fly away from the pond’s edge.

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