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The number of non-overlapping segments formed by ( n ) collinear points is given by the formula ( \frac{n(n-1)}{2} ). This is because each pair of points can form a unique segment, and the total number of pairs of ( n ) points is calculated using combinations: ( \binom{n}{2} ). Thus, for ( n ) points, the maximum number of non-overlapping segments is ( \frac{n(n-1)}{2} ).

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