ABSTRACT
Dots and Boxes is a fun pencil and paper game for two players. It was introduced by French mathematician Édouard Lucas in the 19th century. Dots and Boxes is a game played on a square lattice of size https://www.w3.org/1998/Math/MathML"> 3 × 3 , 4 × 4 , 5 × 5 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003268024/2a3a6f03-5de8-4860-ba0c-ddf4e8b4910a/content/C013_equ_0001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , etc. As the name indicates, each player plays alternatingly and connects any two adjacent vertices (that is, makes an edge) to make a square box. Each edge should be drawn one by one either horizontally or vertically. Even if your opponent draws three edges of a square, you can take the square if you draw the last edge. The last rule is most important. If you make a square in your turn, you have to draw another edge. If you make another square by drawing an edge, you can continue to draw an edge. The game is over when all the edges are drawn. A winner is a person with more boxes. If there is an equal number of boxes, the first player loses the game.
