To solve the problem, we must find the total number of children standing in a circle such that the 6th child is diametrically opposite the 16th child. When two points are diametrically opposite in a circle, they are separated by half the total number of points (children) in the circle. This means if the circumference of the circle in terms of children's positions is n, half of this would be n/2.
Given:
- The 6th child is opposite the 16th child.
Therefore, the number of children between the 6th child and the 16th child in a circular arrangement must be half the total number of children.
Calculating the distance between the 6th and 16th child:
16 - 6 = 10.
The distance calculated (10) is half the number of children since they are diametrically opposite, hence:
n/2 = 10.
Therefore, n = 10 × 2 = 20.
Thus, the total number of children standing in a circle is 20.
