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The sum of a two digit number and the number represented with the aid of the same digits but in the reverse order is a perfect square. The number of such two digit numbers is ______
Correct Answer: 8
For the number $$10a + b$$, the sum is $$(10a + b) + (10b + a) = 11(a + b)$$. Since $$a + b \le 18$$, this is a perfect square only when $$a + b = 11$$. The numbers are 29, 38, 47, 56, 65, 74, 83 and 92, so there are 8 of them.
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