From a strictly logical point of view, even if there is a set of twins who are older than the third daughter, one of the twins will be older than the other.

True of course, which is the reason I stipulated that the ages were reckoned in years. Indeed you don't even need to have twins to have two kids the same age; they could have been born eleven months apart...

The "hole-in-the-sphere" problem is nifty (whatever that means, but generally positive). If the diameter of the hole isn't given, and the problem is presented as having a unique solution, then the diameter must be irrelevant and you can choose any convenient figure you like. Including zero. But you do need the diameter of the original sphere!

The proof that the size of the hole is indeed irrelevant is left as an exercise for the reader...all you mathematicians out there listening?