Question

I write out all the whole numbers, starting from 1. If I wrote 1994 digits altogether, what was the last complete number I wrote down?

Answer 1

You wrote the numbers from 1 to 9: 9 digits.

You wrote the numbers from 10 to 99: 90*2 = 180 digits.

You have written 189 digits.

Then you wrote another 1994 - 189 = 1805

All the numbers from 100 to 999 have 3 digits

So you wrote 1805/3 = 601 2/3

This means 601 full numbers and 2 digits from the 602. number.

So 100 + 601 - 1 = 700 was the last number you wrote.

Do you agree?