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There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben.
Tom is $2$ years older than Ben.
The combined ages of the two boys is equal to the combined ages of the two girls.
Kate is twice as old as Sally.
A year ago Tom was twice as old as Sally was then.
How old are the children?
When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...