There are five squares (one 3x3 and four 1x1) formed with 20 matchsticks, as shown in the illustration. Move two matchstick to get seven squares. Overlapping or breaking of matchsticks or "loose ends" are not allowed.

Here is a simple game for 2 people that you can always win (unless your opponent also knows the secret). Itâ€™s a tremendous confidence booster for children who can learn to defeat adults once they learn the 'trick'. Kid's love secrets; particularly ones adults don't know.
You start off with 15 matches laid out on the ground. In practice you can use any small objects. Stones or shells are ideal which means it is a great game to introduce on the beach when the kids are getting restless.
The rules are very simple. Each person takes turns to remove either 1, 2 or 3 matches. You win if your opponent is left with the last match.

Matchsticks Maths Fun!

An Example Game

Number of Matches

Number of Matches Removed

Number of matches Left

|| 15 || You remove 2 || 13 ||

|| 13 || Opponent removes 3 || 10 ||

|| 10 || You remove 1 || 9 ||

|| 9 || Opponent removes 2 || 7 ||

|| 7 || You remove 2 || 5 ||

|| 5 || Opponent removes 1 || 4 ||

|| 4 || You remove 3 || 1 Opponent looses! ||

How Does it Work?
When you start, you first remove 2 matches. You are then guaranteed to win.
From then on, each time your opponent plays you make the count removed by you and your opponent up to 4. If they take 1 you take 3 if they take 2 you take 2 etc. This means your opponent is always left with the last match.
The key to this game is TARGET NUMBERS. You arrange it so you leave your opponent with:

13, 9, 5 and finally 1 match.

Once you've removed the first 2 matches, you keep making up the total removed in that round to 4. Can you win if your opponent starts? Yes you can unless they understand how to win and begin with 2. If they start with 1: you take away another 1 bringing you to your target number of 13 left. If they start with 3, you remove another 3 making the target number 9.

A simple game like this is an example of what mathematicians call an Impartial, two-person game with Complete Information. Impartial means that rules for moving apply equally to both players (unlike Chess, for example, which not impartial, because the white player can only move white pieces, and black can only move black pieces). Complete information means that both players know the complete state of the game, in contrast to, for example, card games such as poker where one player does not know the cards held by the other player(s).

What if They Start and Remove 2?

Then you play randomly and try to reach a target number.

For Example:

START: 15 Matches Opponent removes 2 matches (leaving 13) You remove 2 (leaving 11) Opponent removes 1 (leaving 10) You can then remove 1 (leaving 9 - target number). You can now win.
Unless your opponent understands the trick they are almost certainly going to make a mistake and allow you to reach a target number before the end of the game. Now you've mastered the game, try it out on your friends and your children. But remember, don't use your new found skills to cheat strangers in bars or pubs to buy you drinks. This could be illegal where you live and besides, you might make some powerful enemies!

(Source http://www.mathsisfun.com/puzzles/matchstick-frame.html)

## The MatchStick Game

Here is a simple game for 2 people that you can always win (unless your opponent also knows the secret).Itâ€™s a tremendous confidence booster for children who can learn to defeat adults once they learn the 'trick'. Kid's love secrets; particularly ones adults don't know.You start off with

15 matcheslaid out on the ground. In practice you can use any small objects.Stones or shellsare ideal which means it is a great game to introduce on the beach when the kids are getting restless.The rules are very simple. Each person takes turns to remove either 1, 2 or 3 matches. You win if your opponent is left with the last match.

## An Example Game

- || 15 || You remove 2 || 13 ||
- || 13 || Opponent removes 3 || 10 ||
- || 10 || You remove 1 || 9 ||
- || 9 || Opponent removes 2 || 7 ||
- || 7 || You remove 2 || 5 ||
- || 5 || Opponent removes 1 || 4 ||
- || 4 || You remove 3 || 1 Opponent looses! ||

How Does it Work?When you start,

you first remove 2 matches.You are then guaranteed to win.From then on, each time your opponent plays you make the count removed by you and your opponent up to 4. If they take 1 you take 3 if they take 2 you take 2 etc. This means your opponent is always left with the last match.

The key to this game is

TARGET NUMBERS. You arrange it so you leave your opponent with:## 13, 9, 5 and finally 1 match.

Once you've removed the first 2 matches, you keep making up the total removed in that round to 4.Can you win if your opponent starts?Yes you can unless they understand how to win and begin with 2.If they start with 1: you take away another1bringing you to yourtarget number of 13 left.If they start with 3, you remove another 3 making thetarget number 9.Source and more info: http://hubpages.com/hub/Matchsticks-Maths-Fun-is-Child-Play## Games Theory

Asimple gamelike this is an example of what mathematicians call anImpartial, two-persongamewithComplete Information.Impartialmeans that rules for moving apply equally to both players (unlike Chess, for example, which not impartial, because the white player can only move white pieces, and black can only move black pieces).Complete informationmeans that both players know the complete state of the game, in contrast to, for example, card games such as poker where one player does not know the cards held by the other player(s).## What if They Start and Remove 2?

Then you play randomly and try to reach a target number.For Example:START: 15 MatchesOpponent removes 2 matches (leaving 13)You remove 2 (leaving 11)Opponent removes 1 (leaving 10)You can then remove 1 (leaving 9 - target number). You can now win.Unless your opponent understands the trick they are almost certainly going to make a mistake and allow you to reach a target number before the end of the game.

Now you've mastered the game, try it out on your friends and your children. But remember, don't use your new found skills to cheat strangers in bars or pubs to buy you drinks. This could be illegal where you live and besides, you might make some powerful enemies!