DOTS AND BOXES GAME
Dots and Boxes is a pencil-and-paper game for two players . It was first published in the 19th century by French mathematician Édouard Lucas.
The full game starts with an empty grid of dots ( 10;x 10 grid).The 2 players play with 2 different color pencils. The players take turns adding a single horizontal or vertical line between two unjoined adjacent dots. A player who completes the fourth side of a 1×1 box earns one point and takes another turn. (A point is typically recorded by placing a mark that identifies the player in the box, such as an initial.) The game ends when no more lines can be placed. The winner is the player with the most points.The board may be of any size grid.
DOTS and BOXES
The diagram on the left shows a game being played on a 2×2 board (3×3 dots). The second player ("B") plays a rotated mirror image of the first player's moves, hoping to divide the board into two pieces and tie the game. But the first player ("A") makes a sacrifice at move 7 and B accepts the sacrifice, getting one box. However, B must now add another line, and so B connects the center dot to the center-right dot, causing the remaining unscored boxes to be joined together in a chain (shown at the end of move 8). With A's next move, A gets all three of them and ends the game, winning 3–1.
SPROUTS
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2. The first player draws a line that join CD two of the spots, and makes a new spot in the middle of the line. (You can make a line joining one spot to itself also.)
In the following sample game with two spots Blue has the first move, and Red wins after 4 moves because Blue has no move:
We have this starting with 5 spots
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Sprouts was invented by the mathematicians M. S. Paterson and John H. Conway in 1967. It is a 2 person strategic game played by 2 and all you need is paper and 2 colored pens to distinguish between the 2 players. The actions are:
1. Draw two or three dots on the paper, spaced out a bit. They can really be anywhere you want.
2. The first player draws a line that join CD two of the spots, and makes a new spot in the middle of the line. (You can make a line joining one spot to itself also.)
The second player does the same.
3. Restrictions are
- There can Only be three lines per spot, coming to or from it
- Lines cannot cross one another.
4. The winner is the last person to draw a spot
The game is remarkably complicated, and even starting with two spots leads to an interesting game.
In the following sample game with two spots Blue has the first move, and Red wins after 4 moves because Blue has no move:
Start with 4 spots
We have this starting with 5 spots
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