NO-ABEL 2002 Problem 4

An integer is given $N> 1$ . Arne and Britt play the following game: (1) Arne says a positive integer $A$ . (2) Britt says an integer $B> 1$ that is either a divisor of $A$ or a multiple of $A$ . ( $A$ itself is a possibility.) (3) Arne says a new number $A$ that is either $B - 1, B$ or $B + 1$ . The game continues by repeating steps 2 and 3. Britt wins if she is okay with being told the number $N$ before the $50$ th has been said. Otherwise, Arne wins. a) Show that Arne has a winning strategy if $N = 10$ . b) Show that Britt has a winning strategy if $N = 24$ . c) For which $N$ does Britt have a winning strategy?