This is a very nice “game puzzle” and I would encourage all of you to actually play the game, especially children. The puzzle is from “The Moscow Puzzles” by Boris A. Kordemsky, Chapter X. This puzzle is relevant for all age groups:
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 the first player win if there are 30 matches instead of 11?
(C) [For adults] Can the first player win in general, where n are the total number of matches and a player can pick up anywhere from 1 to p matches at a time (p less than or equal to n)?
Note: As always, please send your answers directly to me at firstname.lastname@example.org