Let's look at this one and see if you can find a strategy for it:

**Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.**

Is there a guaranteed winning strategy for Player 1?

Is there a guaranteed winning strategy for Player 2?

source:

```
Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.
— Chris Lusto (@Lustomatical) July 16, 2015
```

How does his later comment help? "It’s equivalent to tic-tac-toe since any row/col/diagonal in a 3x3 magic square sums to 15, but more mathematically interesting."
Consider the game in which two players alternate placing quarters on a large square table. The rules are that your quarter must be placed down fully on the table; no overlapping with others, and no hanging off of the edge. The first player to have no legal move loses.

ReplyDeleteThe game described above can be won by Player 1: Take the center point on move one, and then mirror the opponent's moves thereafter.

This is a more general "strategy-stealing" idea, but it can be applied to the game at hand, too:

Player 1 should pick 5, and, thereafter, mirror their opponent's n by picking 10-n.

See also: http://math.stackexchange.com/a/366088