How do you win the matchstick game?

Question

You have between 14 and 28 matchsticks. You take turns with the computer taking 1, 2, or 3 sticks. You get the first turn. How do you win?

Answer 1

I presume that the "winner" is whoever takes the last matchstick.

Let's break this down. Obviously, if there are 1-3 sticks left, then the current player will win. If there are four sticks left, then the current player will lose - since any move will let the other player win.

Now, let's extend this.

If there are 5-7 sticks left on your turn, then you can guarantee yourself a win, by making sure your opponent is left with 4 sticks.
If there are 8 sticks left on your turn, then your opponent will win: any move you make will leave him with 5-7 sticks, which we know is a guaranteed win.

See what's going on? The winning strategy is to make sure your opponent is left with a number of sticks that's divisible by four. Once you can do that, you have a guaranteed win.

If the number of sticks is divisible by 4, and you have the first turn, then your opponent will win unless he makes a mistake.

Hopefully this explanation helps ya understand what's going on!