Lateral Thinking Puzzles

Let B be the number of boys and G the number of girls in the family.

For any boy: number of sisters = G, number of brothers = B−1, so

G = B−1. (1)

For any girl: number of sisters = G−1, number of brothers = B, and she has only half as many sisters as brothers, so

G−1 = B/2. (2)

From (1), B = G+1. Substitute into (2):

G−1 = (G+1)/2 ⟹ 2G−2 = G+1 ⟹ G = 3 ⟹ B = 4.

Therefore, there are 4 boys and 3 girls in the family.