Question 119
There are 30 children, $a_1, a_2, \dots, a_{30}$, seated clockwise in a circle on the floor. The teacher walks behind the children in the clockwise direction with a box of 1000 candies. She drops a candy behind the first child $a_1$. She then skips one child and drops a candy behind the third child, $a_3$. Now she skips two children and drops a candy behind the next child, $a_6$. She continues this way, at each stage skipping one child more than at the preceding stage before dropping a candy behind the next child. How many children will never receive a candy? Justify your answer.