I MANAGED to solve your impossipuzzle about the twins with the other children being a year older and the sum of all the ages to be the square of the twins' age.
I wanted to let you know that using some algebra you can figure out that not only is there another whole number solution with 16 children there is also a solution for any amount of children you choose if you allow solutions where the ages of the children are in between years.
Thank you for the puzzle though, I am a teacher and will be using it as a brainteaser for students. 
DARREN STILLMAN
Swindon