Circle Children

Question

A number of children are
standing in a circle. They
are numbered in order and
there is an equal distance
between each child. The
6th child is directly opposite
the 16th child. How many
children are there in the
circle?

Answer 1

Draw and label of diagram!

Nine children are between the 6th and the 16th (7, 8, 9, 10, 11, 12, 13, 14, 15)

So nine children must be between the 16th and the 6th.

Five of the ten are children 1, 2, 3, 4, 5. So four children must be after the 16th (17, 18, 19, 20)

 

Twenty children are in the circle.

Answer 2

draw a circle and put the 6th child at the top and the 16th child at the bottom

on the right side...

between the 6th and the 16th are 9 numbers (16-6=10, 10-1=9)

from the 6th to the 16th inclusive there are 11 numbers but 6 and 16 are not included so 11-2=9 again

7,8,9,10,11,12,13,14,15 are the numbers

there must be 9 children on the left side as well

the numbers 1, 2, 3, 4, 5 must be on the left (or children 1, 2, 3, 4, 5 must be on the left)

that leaves 4 numbers (or children)

17, 18, 19, 20 are also on the left

there are 20 children in the circle

or simply speaking there are 9 numbers between 6 and 16 on the right so there has to be 9 numbers on the left

9+9+2=20 (6 and 16 were given )