$\textbf{Cards Game (Sum Fifteen)}$
There are nine cards laid out on a table, numbered $1$ through $9$. Two players, Joe and John, take turns to pick up one card a time (and once a card is picked up, it is out of play). As soon as one of these two players has the sum of three of cards equal $15$ , that player wins. Who will win if both players adopt the best strategy?
$\textbf{Solution}$
The result will be a tie if both players play optimally.
$\textbf{Analysis}$
This problem is equivalent to playing a tic-tac-toe game by placing these nine numbers in the following form. The sums of the three horizontal lines, three vertical lines and two diagonals are all $15$. Meanwhile, these eight combinations are the only combination of three distinct numbers between $1$ and $9$ summing to $15$. Hence, picking up three cards to win the game is equivalent to wining this tic-tac-toe game.
It is well known that a tic-tac-toe will results a tie if both players make no mistake. This means the answer to the original question is a tie.
$\textbf{Note}$
This problem is a typical one that uses the modelling method. The essence of this method is to transform the given problem to an easier-to-solve or well known equivalent one.