Discussion Forum

Let $n\geq2$   be an integer .Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the numbers  of red  and blue line segments are equal, then the  value of n is 

Answer:

Explanation:

Plan Number of line segment joining pair of adjacent point =n

 Number of red k=line segment = $^{n}C_{2}-n$

 Number of blue line segments= n

   $\therefore$    $^{n}C_{2}-n=n$

$\Rightarrow$              $\frac{n(n-1)}{2}=2n$

$\Rightarrow$           n=5