1990 IMO Problems/Problem 5
5. Given an initial integer , two players,
and
, choose integers
, . . . alternately according to the following rules:
Knowing
\mathbb{A}
n_{2k+1}
n_{2k}\leq n_{2k+1}\leq n_{2k}^2
n_{2k+1}
\mathbb{B}
n_{2k+2}
\frac{n_{2k+1}}{n_{2k+2}}
\mathbb{A}
\mathbb{B}
n_{0}
\mathbb{A}
\mathbb{B}$ have a winning strategy?
(c) Neither player have a winning strategy?