Game Of Squares
One day Ram and Shyam were playing a game in which they connect the dots(4 by 4, as shown below) with a line such that a square can be formed out of them, the one who completes a square (i.e. who draws the fourth side of the square, owns that square).
I have shown an incomplete part of the game in which black lines are drawn by Ram and the red line are drawn by Shyam. Its Ram's turn right now.
What is the maximum number of squares that Ram can form?
Details and Assumptions :
Ram begins the game. Each one of them draws the line alternately. When a player forms a square, he gets an additional chance to make a new line.Both of them play optimally.
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1 solution
There are 9 squares to be formed.
Ram concedes the square at the top left, forcing Shyam to open the next chain. Shyam's best option is to open the chain of 3 at the bottom left. Ram takes the square on the middle left and then double-crosses Shyam by drawing the final link on the bottom edge.
Shyam takes his two squares and has to open the final chain of 5 squares, which Ram takes. Total squares for Ram: 1 + 5 = 6