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A two-digit number N has the following property: If you reverse the digits of N, you get M.  Then M + N is a perfect square.

 

How many possible values of N are there?

 

Can anyone help on this?  I don't know how to start.

 Jul 14, 2020
 #1
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Let the first digit be f and the second be s.

 

Then N = 10f + s  and M = 10s + f, so M+N = 11(f+s)

 

For this to be a perfect square we must have f + s = 11, so find all the digits, f and s that sum to 11.

 Jul 14, 2020

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