I realize this may not be a particularly satisfying answer, but I think **you're overthinking this**. Remember this is a young child's homework problem. While it may not have been expressed particularly clearly, the goal is plainly not to find a single definitive answer, but to fill out the boxes using an identifiable consistent pattern. 

As you surmised, Child 1 made the rows into **addition problems**. Child 2 made each column have a **shared difference**. Child 3 made the **sum of the top row equal the sum of bottom row** (with an arbitrary sum!). This is intended to show the test-taker what kind of answer they are seeking --not a logically unique answer, but a *defensible* one.

Given the numbers chosen, I would surmise that they wanted to give the test-taker an easy possibility for another possible pattern --to make each row **a multiplication problem.**