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.

The answer is 3869:

   10   for Sr0=1 to 99
   20     Sr1=Sr0+0.2012
   30     Sr2=Sr0+0.2013
   40     Sq1=Sr1*Sr1
   50     Sq2=Sr2*Sr2
   60     if int(Sq2)<>int(Sq1) then print Sq1,Sq2
   70   next
OK
run
 3868.989281439999999999         3869.0017216899999999979
OK
?sqrt(3869)
 62.2012861603359452591

Posted by Charlie on 2012-04-04 12:37:44