The Natural Numbers are written successively as shown below:
12345678910111213141516..........., such that the 4th digit is '4' the 9th digit is '9' but the 11th digit is '0', the 15th digit '2', the 17th '3', and so on.
What is the 40,000th digit that appears in this list ?

The answer is 1, the reasoning is as follows:

There are 9 one-digit numbers, 90 two-digit numbers, 900 three-digit numbers,...., 9*(10^n) n-digit numbers.

This means that:

Digits 1-9 come from the 1-digit numbers
Digits 10-189 come from the 2-digit numbers
Digits 190-2889 come from the 3-digit numbers
Digits 2890-38889 come from the 4-digit numbers
Digits 38890-488889 come from the 5-digit numbers

So the 40000th digit must be the 1111th digit of the sequence of 5 digit numbers.

1111 = 222x5 + 1

So the 1111th digit is the first digit of the 223rd 5 digit number. 10222 is the 223rd 5 digit number, which means that 1 is the 40000th digit of the overall sequence.

Posted by fwaff on 2003-08-29 08:37:23