## Children In A Circle

#### 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.

Problem ID: 30 (Jan 2001) Difficulty: 1 Star