Good girls and bad boys (9)

Since the talking children said 3 different things, thus at most only one of them can be right, and if we add the silent sibling in, then at most the honest children can never be more than half of the total, so the youngest one must be the littlest brother.

Since the other 2 statements can be true in different situations, we have two possible combinations in all :
1) Brother, sister, brother, brother
OR
2) Sister, brother, sister, brother

Of the three younger children, exactly one of them must be a truth teller otherwise there will be a contradiction. In other words, among one of them is a girl. This means the other two must be boys. So in total, there are at least two boys out of four. This is already half the total number of children so it is impossible for there to be fewer boys than girls. So the youngest child must be a liar and hence a boy.

Suppose the second child is a girl. Then there are more boys than girls. The only possibility for this is 3 boys and 1 girl which makes her the only girl among the four. 2 boys and 2 girls would make it even whereas 4 boys is impossible because as mentioned, there must be one girl among the three youngest. Here we have boy, girl, boy, boy.

It is also possible for the third child to be a girl. Then the second and youngest would both be boys. As a girl, she must be telling the truth so there must be exactly two boys and two girls. This is possible if and only if the oldest is a girl too. Here we have girl, boy, girl, boy.

We have 2 possible combinations in all.