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Consider an integer n ≥ 2. Place n unique points on the circumference of a circle and connect every pair of points with a straight line. Color the lines connecting consecutive points blue, and all other lines red. If the count of red and blue lines is the same, what is the value of n?
- 2
- 3
- 4
- 5
Correct answer: 5
Solution
The correct answer is 5 because when the count of red and blue lines is the same, we can set up an equation based on the total number of line segments and solve for n, which represents the number of unique points on the circumference of the circle.
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