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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

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