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May 22nd, 2016, 03:43 AM  #1 
Senior Member Joined: Dec 2013 Posts: 1,101 Thanks: 40  Optimal strategy?
Game name : "Fill the board" Goal of the game : the last player to place a piece on the board win. Material : Board : grid 14*14 squares 2 scissors 2 Bristol boards in form of grids 10*10 squares : two different colors (red and blue) Technicalities : all the squares have to be of the same size. At the setup the board 14*14 squares is empty and placed between the 2 players How is the game working? Step 1 : In the fist step each of the 2 players have to cut SECRETLY its grid 10*10 squares in 12 polyminoes of any form or size : look here for polyminoes: Polyomino  from Wolfram MathWorld Polyminoes with holes are allowed. Each player must start the game with exactly 12 pieces (polyminoes) and the sum of squares of 12 pieces must be equal to 100 squares. During this step no player knows how his opponents has cut its grid. Step 2: After this step then the 2 players put simultaneously each one its 12 pieces on the table near his side such as the 24 pieces could be known to the players. Step 3 : The criterion to determine who lay fist is the piece area. Each piece have an area of squares.The area of a pentomino is equal to 5 for example, monomino = 1, domino =2 etc... The player who owns a unique piece with less area start the game with this piece. Example : Player red has a piece with area = 1 and the player blue has a piece with less area = 2 then player red start placing this piece any where on the board 14*14. Player red has a with area = 1 and the player has 2 pieces with less area = 1 then player blue start the game placing this piece. We compare the pieces area. This step is very important. The minimal area must be UNIQUE. Only the player who owns it could start the game. Step 4 : Players take their turns alternatively. Turn player is finished when he places one of his piece. Rules of placement :  All the pieces must be placed inside the board.  No piece is allowed to be removed outside the board  Players on their turn are free to manipulate any piece yet (opponent or friendly) placed on the board in the way they could place their own piece  No overlapping is allowed. The game finishes when one of the 2 players can not place his piece. The winner is the last one who placed a piece. Question : Is there an optimal strategy to cut the 12 pieces no matter what your opponent`s cut? Thank you. 
May 24th, 2016, 09:22 AM  #2 
Senior Member Joined: Dec 2013 Posts: 1,101 Thanks: 40  

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