3 ducks have landed in a circular pond. What is the probability there is a diameter such that the semicircle on one side contains all of them?
Repeat for 4 ducks.
Note: consider the ducks to be randomly chosen points in a circle.
(In reply to
The duck sequence by Math Man)
In my solution I already formulated P(d) = d/2^(d-1), valid starting at d=2. So the sequence continues as 1, 3/4, 1/2, 5/16, 3/16, 7/64, 1/16, 9/256, .....
The numerators for the sequence 1, 3, 1, 5, 3, 7, 1, 9, ... which is OEIS A000265 "Remove all factors of 2 from n; or largest odd divisor of n; or odd part of n."
The denominators form the sequence 1, 4, 2, 16, 16, 64, 16, 256, ... which is OEIS A084623 "Numerator of 2^(n-1)/n." f(n)=2^(n-1)/n is literally the reciprocals of p(d)=d/2^(d-1).
re: The duck sequence
