|Spoiler Inside: Solution to Puzzle||SelectShow>|
The second sibling is identified as another sibling. This means that there are at least two siblings. They can not be of the same sex, or their two statements would conflict.
Let m be the number of male siblings and f be the number of female siblings. I am doing it like this to keep it clear. (If you have two sisters and are male, there are two female siblings in your family, but if you are female, there are three female siblings in your family.)
Assume that the first speaker is male. Then, the second speaker is female. Their statements give m – 1 = 3f and f – 1 = m. The first equation can be modified to m = 3f + 1. The right-hand side is equal to m as is the left-hand side of the second equation. Combining gives 3f + 1 = f – 1 which has the solution f = -1. This is not possible.
Assume that the first speaker is female. Then, the second speaker is male. Their statements give m = 3(f – 1) and m – 1 = f. The second equation can be modified to m = f + 1. The right-hand side of each equation is equal to m. Combining gives 3(f – 1) = f + 1 which has a solution of f = 2. The first speaker has one sister and three times as many brothers (so three).
There are three male siblings and two female siblings. The first speaker is female, and the second speaker is male.