Eleven matches

On the table are 11 matches (or other objects). The first player picks up 1, 2, or 3 matches. The second player picks up 1, 2, or 3, and so on. The player who picks up the last match loses.
(A) Can the first player always win?
(B) Can he if there are 30 matches instead of 11 ?
(C) Can he in general, with n matches to be picked up 1 through p at a time (p not greater than n) ?

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