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 ?

I did it with a spreadsheet ...

Range #digits Count of Range digxcount Remaining to 40000
1 to 9 1 9 9 9 39991
10 to 99 2 90 180 189 39811
100 to 999 3 900 2700 2889 37111
1000 to 9999 4 9000 36000 38889 1111
10000 to 10221 5 222 1110 39999 1

When you get to 9999 there are only 1111 spots left to go. The next numbers are five digits each. So divide 1111 by 5 and come up with 222.2. Since .2 = 1/5 it is the first number after the 222 digit. Well that's clearly a 1.

In the end of the spreadsheet clip above, you are 1 away from 40000, so the next number is a 1 -- the first digit of 10222.

Posted by Lawrence on 2003-08-30 00:39:45