# Q. 40 children are standing in a circle and one of 5 them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again?

(a) 14

(b) 15

(c) 16

(d) 17

Correct Answer: (b) 15

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## Sequence of Passing the Ring

The ring is passed in the following sequence: 1, 2, 4, 7, 11, 16, 22, 29, 37, 6, 16, 27, 39, 12, 26, 1.

This sequence is formed by adding 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 to the position of the child respectively and taking modulo 40 (since there are 40 children in the circle).

For example, the ring is initially with child-1. We add 1 to it and get 2. So, the ring is passed to child-2. Then we add 2 to 2 and get 4. So, the ring is passed to child-4. And so on.

When we add 15 to 26, we get 41. But since there are only 40 children, we take modulo 40 to get 1. So, the ring is passed back to child-1.

Therefore, the ring is back with child-1 after 15 changes. Hence, the correct answer is (b) 15.