John and Rose play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If John goes first, which of the following is a value of n such that Rose can always win no matter how John plays? Choose the correct option
A) 7	B) 10	C) 11	D) 12	E) 16
If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).   Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.   The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.   Answer: 12.
<result>D</result>
John and Rose play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If John goes first, which of the following is a value of n such that Rose can always win no matter how John plays?