You play the following game with a friend. You share a pile of chips, and you take turns
removing between one and four chips from the pile. (In particular, at least one chip must be
removed on each turn.) The game ends when the last chip is removed from the pile; the one
who removes it is the loser.
It is your turn, and there are 2014 chips in the pile. How many chips should you remove to
guarantee that you win, assuming you then make the best moves until the game is over? Choose the correct choice:
A) 1
B) 2
C) 3
D) 4
E) there is no way to guarantee a win, even with the best play
The key to winning this game is that if you leave your opponent with 5k +1 chips,   for any integer k 0, then you win. When your opponent removes r chips, you remove 5-r,   and so there are now 5(k- 1) + 1 chips left, and you keep using this strategy until there is   only one chip left, at which point your opponent takes it and loses.   So, you should take 3 chips to leave 2011 = 5 402 + 1.   correct answer 3
<result>C</result>
You play the following game with a friend. You share a pile of chips, and you take turns
removing between one and four chips from the pile. (In particular, at least one chip must be
removed on each turn.) The game ends when the last chip is removed from the pile; the one
who removes it is the loser.
It is your turn, and there are 2014 chips in the pile. How many chips should you remove to
guarantee that you win, assuming you then make the best moves until the game is over?