title: Combinatorial Game. Who wins if both players play optimally
body: <blockquote>
    <p>Players <em>A</em> and <em>B</em> play a game optimally and move alternately. They
    start with 1. Each player in his turn multiplies the current number
    with any integer from [2,9]. If after a player's turn, the number is
    more than or equal to <strong>n</strong>, he wins.</p>
    
    <p>A starts. Given <strong>n</strong>, who wins?</p>
  </blockquote>
  
  <p>For example,</p>
  
  <p>Numbers 2,3..,9 are winning numbers (Player A will win)</p>
  
  <p>Numbers 10,11,..,18 are losing numbers (Player A will lose)</p>
  
  <p>Numbers 19,20,..,162 are winning numbers</p>
  
  <p>What would be the winning strategy? How can the Sprague-Grundy theorem be applied to solve this?</p>