MHB 1000 th Digit in a Given number N

[juantheron]

If all the multiples of 6 are written side-by-side, then a large integer $N$ is generated as follows:

$N=61218243036\ldots$ ,Then the question is to find the $1000$th digit of $N$.

 

[kaliprasad]

If all the multiples of 6 are written side-by-side, then a large integer $N$ is generated as follows:

$N=61218243036\ldots$ ,Then the question is to find the $1000$th digit of $N$.

Spoiler

we need to take n digit numbers starting from 1 = 1 on wards

there is 1 one digit number multiple of 6
so remaining digits = 999
then there are 15 ( 6 * 2 to 6 * 16) 2 digit numbers which is 30

so remaining number of digits = 969

there are 150 (6 * 17 to 6 * 166) 3 digit numbers and they take 450 digit and so remaining digits = 519

now there are much more 4 digit numbers multiple of 6 and for 516 digits we require 130 numbers and as 520 = 130 * 4 = 519 + 3 so it is tens digit digit.

now 1st 4 digit number = 1002 and so 130th 4 digit number = 1002 + 129 * 6 = 1002 + 774
= 1776
required digit is 7