Question

A computer is programmed to scan the digits of the counting numbers. For example, if it scans 

1 2 3 4 5 6 7 8 9 10 11 12 13 
then it scanned 17 digits altogether. If the computer begins it's task and scans the first 1392 digits starting with 1, what is the last counting number scanned?

Answer 1

Number of 1-digit numbers scanned (i.e. 1 - 9) = 9 digits

Number of 2-digits numbers scanned (i.e. 10 - 99) = 2 x 90 = 180 digits

Let the number of 3-digits numbers scanned be x (i.e. 100 - y), then 3 x (y - 99) = (1392 - 180 - 9)
3y - 297 = 1203
3y = 1203 + 297 = 1500
y = 1500 / 3 = 500

Therefore, the last counting number scanned is 500.