No it cannot .
Minimum distance the duck has to go is the radius of the circle   in order to make the fox run to maximum distance ( half of the circle) to reach the duck .
In that situation also the ratio of the distance between fox and duck are 3.14: 1 ( pi : 1) .  which is smaller than 4:1  the speed ratio between them .

So  no matter where the Duck goes , the fox can catch it  and  Guess what !  bon appetit!!! 

Let the holes be A,B,C,D  and  E.  Start from  any one end . Say A . look in it first  day  and the next day . if you  don’t find him , look in the next hole for the next  two days  continue this process  up to E   you will  get him  with a maximum of 8 days or less..

Answer- 40 

EXPLANATION-
26+2 = 28 , 28+3 = 31, 31+4 = 35 , 35+5 = 40

He just said pointing  some Adam and Robert ” they both have 4534703 hairs on head  if you have doubt , go and count !!! ” and you are trapped!! :p

“If I can write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50.” he just asked the boys  weight so that he can write exactly the weight of the boy in the paper .   challenge in the bet is  whether he knows how to write or not . nothing else…

7+3= 5*2
8+6 = 7*2
2+10 = 6*2
similarly,  4+2 = 3* 2

so 3 may be the answer