All the positive perfect squares 1, 4, 9, 16, 25.... are written in strictly ascending order of magnitude and without the commas and spaces, resulting in the following infinite string:

149162536496481100121144......

Reading left to right, what is the 2010^th digit in the above pattern?

In my spreadsheet I squared consecutive numbers, recorded the number of digits in each square and then compile progressive totals of digits.  At N=411, the 2008th digit is a 'zero' while for N=412 the 2014th digit is a 'four'.  Counting 2 on from the 2008th I find an "6" for the 2010th.


      N      N^2      digits      Prog.
                                    Dig. Tot.
      1          1         1            1
      2          4         1            2
      3          9         1            3
      4        16         2            5
      5        25         2            7
….
    32     1024         4          85
    33     1089         4          89
…..
  100    10000        5         358
  101    10201        5         363
...
  411   168100       6        2008
  412   169744       6        2014

Edited on January 28, 2010, 8:36 pm

Posted by brianjn on 2010-01-28 20:19:18