Let S be a set of some positive integers.
We'll call S autonomous if the number of elements in S is itself an element of S. e.g. the set {2,3,5} is autonomous, as is the set {2,7}, but the sets {1, 4} or {2,4,5} are not.

Determine a general formula for the number
of autonomous subsets of {1, 2, 3, ... , n}.

(In reply to computer assisted solution by Charlie)

Please read the question one more time, find few samples e.g.

f(0) undefined , f(1)=1  etc and then deduce and explain the formula.

The computer is totally unneeded - you have just misunderstood the text, once you get it cleared it is a d1 or d2 puzzle.

Posted by Ady TZIDON on 2014-07-29 23:53:21