How many 2 digit numbers when flipped and added together result in a perfect square?
details and assumptions
The two digit numbers are in the form of AB where it is 10A+B, not A B.
The sum is of the numbers AB and BA.
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A B = 1 0 A + B .
B A = 1 0 B + A .
A B + B A = 1 1 A + 1 1 B = 1 1 ( A + B ) .
Therefore A+B must me 11 for A B + B A to be a perfect square.
Possible combinations are (9,2), (8,3),(7,4),(6,5).
From each combination we can get two numbers like 92 and 29.
Total possible Numbers = 2x4= 8 .