mathschallenge.net

Problem

A group of children stand holding hands in a large circle and a teacher walks around the circle giving each child in order a number 1, 2, 3, 4, ...

If number 12 is standing opposite number 30, how many children are there in the circle?

Solution

Let c be the number of children in the circle. Half the children, ^c/₂, will be in-between child 12 and child 30.

So 12 + ^c/₂ = 30.

Therefore ^c/₂ = 18.

That is, there are 36 children in the circle.