Question 121
There are 8 cards on the table numbered from 1 to 8. Two players, $A$ and $B$, play the following game. In each round:
* Player $A$ selects two cards from the table
* Player $B$, after seeing the two selected cards, chooses one to keep and discards the other
The game consists of four rounds with the restriction that:
* In rounds 1 and 2, $B$ cannot choose the larger number in both rounds
* In rounds 3 and 4, $B$ cannot choose the larger number in both rounds
Let $S$ be the sum of the numbers on the four cards $B$ holds after four rounds.
Find the largest integer $N$ such that no matter how $A$ selects cards in each round, $B$ can guarantee $S \ge N$.
* Player $A$ selects two cards from the table
* Player $B$, after seeing the two selected cards, chooses one to keep and discards the other
The game consists of four rounds with the restriction that:
* In rounds 1 and 2, $B$ cannot choose the larger number in both rounds
* In rounds 3 and 4, $B$ cannot choose the larger number in both rounds
Let $S$ be the sum of the numbers on the four cards $B$ holds after four rounds.
Find the largest integer $N$ such that no matter how $A$ selects cards in each round, $B$ can guarantee $S \ge N$.