Interpretation is that when a number k is called, the children are grouped into rows of size k, and “no one got out” means the children formed complete rows with no remainder. So: “No one got out” when 6 was called ⇒ the total number N is divisible by 6. “No one got out” when 9 was called ⇒ N is divisible by 9. “Some people got out” when 10 was called ⇒ N is not divisible by 10. If N is divisible by both 6 and 9, then it must be divisible by their LCM: LCM (6, 9) = 18. So N is a multiple of 18, but not a multiple of 10. Now check the options: (a) 72 = 18 × 4 – divisible by 18 and not by 10 → possible. (b) 90 = 18 × 5 – divisible by 18 but is divisible by 10 → not possible. (c) 45 – not divisible by 18 → not possible. (d) 3 – not divisible by 18 → not possible. (e) 36 = 18 × 2 – divisible by 18 and not by 10 → possible. So the numbers that could have been playing are 36 and 72.