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(C) The given lines are $y=x+r$ and $y=-x+r$ for $r \in \{0, 1, 2, 3, 4, 5, 6\}$.These lines form a grid of squares.Two lines $y=x+r_1$ and $y=x+r_2$

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$25$

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(C) The given lines are $y=x+r$ and $y=-x+r$ for $r \in \{0, 1, 2, 3, 4, 5, 6\}$.These lines form a grid of squares.Two lines $y=x+r_1$ and $y=x+r_2$ are parallel,and the distance between them is $\frac{|r_1-r_2|}{\sqrt{1^2+(-1)^2}} = \frac{|r_1-r_2|}{\sqrt{2}}$.For the side length of the square to be $\sqrt{2}$,we require $\frac{|r_1-r_2|}{\sqrt{2}} = \sqrt{2}$,which implies $|r_1-r_2| = 2$.For the set $r \in \{0, 1, 2, 3, 4, 5, 6\}$,the pairs $(r_1, r_2)$ with a difference of $2$ are $(0, 2), (1, 3), (2, 4), (3, 5), (4, 6)$. There are $5$ such pairs.Similarly,for the lines $y=-x+r$,the distance between $y=-x+r_3$ and $y=-x+r_4$ is $\frac{|r_3-r_4|}{\sqrt{1^2+1^2}} = \frac{|r_3-r_4|}{\sqrt{2}}$.Setting this to $\sqrt{2}$ gives $|r_3-r_4| = 2$,which also yields $5$ pairs.The total number of squares formed is the product of the number of intervals of length $2$ in each direction,which is $5 	imes 5 = 25$.

Consider the fourteen lines in the plane given by $y=x+r$ and $y=-x+r$,where $r \in \{0, 1, 2, 3, 4, 5, 6\}$. The number of squares formed by these lines,whose sides are of length $\sqrt{2}$,is:

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