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?
