Duck in the pond

Puzzle : A duck is swimming at the center of circular pond of radius r. given that It can fly only from land and so cannot fly from water . Furthermore, the fox cannot swim. The speed of fox is four times the speed of duck . How should the duck swim to evade the fox and fly eventually. assume both duck and fox to be perfectly smart.

solution ==>

the puzzle is really very simple just make sure that when duck reaches land, fox is not there but wait the fox is four times faster than duck

so duck needs a strategy

1) fox has to travel in circumference i.e. 2*pi*r. time taken by it to complete one circle = 2*pi*r/4v (where v is the speed of duck)

2) now notice that same time will be taken by duck if it swim in a smaller circle , the radius of that circle comes to be r/4

3) the question is solved by now , duck needs to swim in a circle radius slightly lesser than the r/4 and she can make sure that after certain time, she will be exactly opposite to fox

4) at this position duck should start moving towards the shore , distance 3r/4 , time taken is 3r/4v

5) fox also starts moving towards that point , time taken by fox will be pi*r/4v

clearly 3r is lesser than pi*r which is 3.14*r

6) thus duck will reach earlier and fly away