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Use the formula (n2 - n)/2 where n is the given number of lines.

That gives:

(12 - 1)/2 = 0 for one line,

(22 - 2)/2 = 1 for two lines,

(32 - 3)/2 = 3 for three lines,

(42 - 4)/2 = 6 for four lines,

(52 - 5)/2 = 10 for five lines,

and so on.

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Q: How do you find the maximum number of intersections between a given number of lines?
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