Problem of the Day
Thirteen distinct points lie in a plane with exactly 
of the points lying on the same line and the other 
points non-collinear. If 276 unique triangles can be drawn using these points as vertices, what is the value of ?
A. 2
B. 3
C. 4
D. 5
E. 7
Reveal Answer
Solution
[latexpage]
If all of the points were non-collinear, there would be $_{13}C_3=286$ unique triangles. However, any group of three points chosen that are collinear will fail to make a triangle. $286-{_{n}}C_{3}=276$. Solving this equation gives $n=5$.
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