2 In this question INT( $m$ ) means the integer part of $m$. Thus INT(3.5) $= 3$ and INT(4) $= 4$.\\
A game for two players starts with a number, $n$, of counters. Players alternately pick up a number of counters, at least 1 and not more than half of those left. The player forced to pick up the last counter is the loser. Arif programs his computer to play the game, using the rule "pick up INT(half of the remaining counters), or the last counter if forced".\\
(i) You are to play against Arif's computer with $n = 5$ and with Arif's computer going first. What happens at each turn?\\
(ii) You are to play against Arif's computer with $n = 6$ and with Arif's computer going first. What happens at each turn?\\
(iii) Now play against Arif's computer with $n = 7$ and with Arif's computer going first. Describe what happens.

\hfill \mbox{\textit{OCR MEI D1 2009 Q2 [8]}}