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Your first algebra question

First of all we have to find my friends Alice and Bill, who live in two different houses on Algebra Avenue. Each of the houses on Algebra Avenue is numbered with a two-digit number from 10 to 99. I can't remember where Alice and Bill live, but I remember that their house numbers are the reverse of each other (in the sense that "21" is the reverse of "12".) I also remember that the sum of their two house numbers is a perfect square. The difference between their two house numbers is also a perfect square. Alice lives in the house with the smaller house number. What is the number of Bill's house?

This can be solved using Algebra. Guessing and checking is also a possibliltiy. Good luck. Leave the answer in the comment box.

Mr. H

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