A two digit number is 18 less than the square of the sum of its digits. How many such numbers are there? Choose the correct option:  A) 22,33  B) 22,22  C) 221,1  D) 63,82  E) 23,17
Option 2   Take N = 10a+b.   Given that, (10a+b)+18 = K2 = (a+b)2   Given number = K2 - 18 = (10a+b)   That means, when we add 18 to the given number it should be a perfect square. So K2 takes the following values. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ....   1 to 16 are ruled out as if we subtract 18 from them, the resulting number is a single digit number.   Now  25 - 18= 
<gadget id="calculator"> 25 - 18</gadget>
<output>7</output>
7   36 - 18= 
<gadget id="calculator">36 - 18</gadget>
<output>18</output>
18   49 - 18= 
<gadget id="calculator">49 - 18</gadget>
<output>31</output>
31   64 - 18= 
<gadget id="calculator">64 - 18</gadget>
<output>46</output>
46   81 - 18= 
<gadget id="calculator">81 - 18</gadget>
<output>63</output>
63   100 - 18= 
<gadget id="calculator">100 - 18</gadget>
<output>82</output>
82   121 - 18= 
<gadget id="calculator">121 - 18</gadget>
<output>103</output>
103   Now 63, 82 satisfies.   Answer:63,82
<result>D</result>
A two digit number is 18 less than the square of the sum of its digits. How many such numbers are there?