Question 1142356
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Here is an unorthodox solution method that is fast if you understand it....<br>
The house number is 14 less than one perfect square and 14 more than another, so it is halfway between two perfect squares whose difference is 28.<br>
Now use the fact that the difference between consecutive perfect squares n^2 and (n+1)^2 is 2n+1.  That difference is clearly always odd.  So the two perfect squares in this problem are not consecutive perfect squares.<br>
So what about squares of numbers that differ by 2?  28 = 13+15.  13 = 2(6)+1 is the difference between 6^2 and 7^2, and 15 = 2(7)+1 is the difference between 7^2 and 8^2.  And so 28 is the difference between 6^2 and 8^2.<br>
So the two perfect squares in the problem are 6^2=36 and 8^2 = 64; the house number is halfway between 36 and 64, so it is 50.