A positive integer is called enterprising if its digits sum to either 4 or 7. So both 4 and 7 are enterprising (since 4 = 4, and 7 = 7), and so is, for example, 355, because 3 + 5 + 5 = 13 and 1 + 3 = 4.

Find three examples of enterprising numbers which are between 10 and 30. 

Are the squares of these numbers also enterprising?  

If you square 355, is the answer also enterprising?

What happens if you replace 355 with a different enterprising number?

Does the same thing happen with any enterprising number? Explain your reasoning carefully.