Determine the minimum value of a positive integer N such that the four digits immediately following the decimal point in the base ten expansion of √N is 2012.

*** For an extra challenge, solve this puzzle without using a computer program.

(In reply to re(2): computer solution by Charlie)

The difference of 5 can be explained.

(a+.20125^2) ≈ N

[(a+.20125)+5]^2 = (a+.20125)^2 +2*5*(a+.20125) + 5^2
= N + 10a + 27.0125

The key is the 27.0125 which is a near integer.

A much more persistent arithmetic sequence will be seen with a difference of 400 since my approximation .20125 = 161/800

Posted by Jer on 2012-04-05 13:35:48