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?

My answer is 6.

I made a chart:
Digits Range Number Count Cumulative
1       1to3      3           3        3
2       4to9      6           12      15
3      10to31    22         66      81
4      32to99    68        272    353
5      100to316 217      1085  1438
6 digits squares will take this over 2010
2010 - 1438 = 572 more digits
572/6 = 95 r 2
316 + 95 = 411
We need 2 digits into the next square
412^2 = 169744 the second digit of this is 6.

Posted by Jer on 2010-01-28 11:44:39