RIDDLE A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

4 daughters and 3 sons

Explanation:

each brother has only half as many brothers as sisters

From the reference frame of one of the sisters, there are n sisters and n brothers.

However, from the reference frame of a parent, we see the sister did not include herself in the counting.

This means that there are n boys and n+1 girls.

From the reference frame of one of the brothers, there are n-1 brothers (since he wouldn’t count himself), and n+1 sisters. Also, each brother sees k brothers and 2k sisters.

As a result, we can combine these deductions to create the equation 2(n-1) = n+1. Solving, we find n=3.

Final There are 3 brothers and 4 sisters.