All the positive integers starting with 1 are considered in ascending order of magnitude – and spelled out in conformity with the American system, but disregarding hyphens, spaces, commas and, the word "and" - resulting in this infinite string:

onetwothreefourfivesixseveneightnineteneleventwelve
thirteenfourteenfifteensixteenseventeeneighteennineteen
twentytwentyonetwentytwotwentythreetwentyfour...........

Determine the 2010th letter in the above pattern. What is the 20100th letter in the above pattern?

I am not aware of any uniform "American system" which would specify a unique wording of all numbers.  For example, 1234 could equally well be "twelve hundred thirty four" and "one thousand two hundred thirty four." Individuals or institutions might have local conventions for their usage, but this is hardly a national "system."  Does UK require a unique wording? Of course the 2010th letter would in any case appear well before the thousandth number. 

Posted by ed bottemiller on 2010-08-24 11:31:10