Each child in a family has at least 5 brothers and 3 sisters What is the smallest number of children the family might have?

8

The answer is 9. If you are a boy, it would be 6 boys and 3 girls, but it you were a girl it would be 5 boys and 4 girls because you cannot be your own brother or sister.

10, the combination of 6 brothers and 4 sisters. Then each is guaranteed to have 5 brothers, 3 sisters. In the examples for 9 total, the girls in 6-3 would only have 2 sisters, and vice versa for the boys in 5-4.

It seems 9 is the correct answer for the way the question is worded. If the question were worded "What is the least number of of children that would guarantee that each child has five brothers and three sisters ?" then 10 would be correct.