Good girls and bad boys (11)

Look at the statements made by the two oldest ones. One must be true, the other false. So one of the must be a boy, the other a girl. Similarly, considering the statements made by the middle and youngest child, one must also be true, the other false as a prime number is never a perfect square. Similarly, a perfect square is never a prime. So we have another pair of a boy and a girl.

Now we have at least two boys and at least two girls. This means the number of boys is either two or three. Whichever way, it is true that the number of boys is prime since two and three are both primes. Hence the middle child must be a truth teller and hence a girl. A prime number of boys is definitely not composite or a perfect square so the two youngest are both liars and hence boys.

So we have the middle child a girl with her two younger brothers. Her two elder siblings must consist of an elder brother and an elder sister. Whichever way we know we will end up with three boys so the oldest one is telling the truth (and hence a girl) while the second one is lying (and hence a boy).

We have girl, boy, girl, boy, boy. Our desired answer is 2+4+5=11.

Odd and even numbers are mutually exclusive, as are prime and composite numbers. So this means that we have a pair of boy-girl siblings with not just the oldest two but also the second duo pair (between the third and fourth siblings).

Anyway, in some configuration the oldest four is comprised of 2 boys and 2 girls, and therefore, the possibility for the 5 siblings are reduced to 3-2 or 2-3 for boys vs girls. Since neither 2 nor 3 is a perfect square, then the youngest must be a liar and a boy by default (or definition).

With the above-mentioned finding, we now have a total of 3 brothers and 2 sisters. 3 as an odd prime put the oldest and the middlemost children as the truthful sisters, so our answer should be 2 + 4 + 5 = 11.