Question 10
$A$ and $B$ play a game. Each has $10$ tokens numbered from $1$ to $10$. The board is two rows of squares. The first row is numbered $1$ to $1492$ and the second row is numbered $1$ to $1989$. On the $n$th turn, $A$ places his token number $n$ on any empty square in either row and $B$ places his token on any empty square in the other row. $B$ wins if the order of the tokens is the same in the two rows, otherwise $A$ wins. Which player has a winning strategy? Suppose each player has $k$ tokens, numbered from $1$ to $k$. Who has the winning strategy? What if both rows are all the integers? Or both all the rationals?