Abby and Brian play the following game: They first choose a positive integer N. Then they write numbers on a blackboard in turn. Abby starts by writing a 1. Thereafter, when one of them has written the number n, the other writes down either n+1 or 2n, provided that the number is not greater than N. The player who writes N on the blackboard wins.
(a) Determine which player has a winning strategy if N=2011.
(b) Find the number of positive integers N⩽2011 for which Brian has a winning strategy.(This is based on ISL 2004, Problem C5.) combinatorics proposedcombinatorics