Question 173
2009 cards are in a row on a table. First of all, the top of all cards is white and the underside is black. The cards are numbered from $1$ to $2009$. Two players $A$ and $B$ take turns performing a turn, starting $A$. Each turn is that the player chooses a card number $k$ ($k \lt 1969$), the white side of which is on the top, and then the cards with the numbers $k, k+1, k+2, \ldots, k+40$ in their seats turns around. The last player to make a valid move wins the game.
a) You decide if this game necessarily ends.
b) Which of the two players has a winning strategy for?
a) You decide if this game necessarily ends.
b) Which of the two players has a winning strategy for?