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?

(In reply to Gazillionth.. by ed bottemiller)

From an article in Wikipedia in regards to the English numerals, the American usage of four-digit numbers with non-zero hundreds are often named using multiples of "hundred" instead of using "thousand". For example, for 1101 the usage would be "eleven hundred and one" rather than "one thousand one hundred one". But as the 20100th letter occurs prior to the first difference that this usage would create, the solutions to the present puzzle are unaffected.

The 2010th letter is the 'y' in "one hundred and sixty-four".
The 20100th letter is the 'f' in "one thousand eighty-five".

Posted by Dej Mar on 2010-08-24 19:49:32