Greedy Math Games

There is a row of 2n coins on the table; each coin can have any positive integer value. Two players alternate turns. On a player’s turn she must take one of the two coins on either end of the row of remaining coins, so with each turn the row gets shorter by one. After all the coins have been taken, the player with the higher total value is the winner.

Let’s look at an example. Suppose the coins start out like this:

The first player (let’s call her Alice) can choose either the 3 or the 2. Let’s say she takes the 3. (3 is bigger than 2, right?) Now the table looks like this: … (The Math Less Traveled)