SOLUTION: The sum of a two digit number and the number obtained by reversing its digits is a square number. How many such numbers are there?

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Question 1080520: The sum of a two digit number and the number obtained by reversing its digits is a square number. How many such numbers are there?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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Let a be the first digit, and let b be the second digit.
The value of the number is 10a%2Bb .
The value of the number obtained by reversing its digits is 10b%2Ba .
Their sum is
10a%2Bb%2B10b%2Ba=11a%2B11b=11%28a%2Bb%29 .
For that sum to be the square of an integer, it must be true that
a%2Bb=11 .
There are 4 possible pastors of digits adding to 11 :
2%2B9=11 ,
3%2B8=11 ,
4%2B7=11 , and
5%2B6=11 .s
Since we can make two 2-digit number out of each paiR
by changing the other of the digits,
there are 2%2A4=8 numbers that could be
the original 2-digit number in the problem.