The seven points A, B, C, D, E, F, and G are located on a circle, as shown below. How many line segments having two of these points as endpoints can be drawn?

Question

The seven points A, B, C, D, E, F, and G are located on a circle, as shown below. How many line segments having two of these points as endpoints can be drawn?

Answer 1

2 points 1 line connecting them

3 points 3 lines 1+2

4 points 6 lines 3+3

5 points 10 lines 6+4

6 points 15 lines 10+5

7 points 21 lines 15+ 6

8 points 28 lines 21+7

9 points 36 lines 28+8

10 points 45 lines 36+9

n points 1+2+3+4+5+... +n-1 lines connecting n points

7 points = 1+2+3+4+5+6 = 21 lines connecting 7 points

by Gauss the sum of n integers = n(n+1)/2

sum of n-1 integers = (n-1)n/2

sum of 7 integers, one through seven = 6/7)/2 = 42/2 =21