Question

Six year old Rosie wants to write down all counting numbers up to one thousand. When she finished writing 12, she had 15 digits.
Rosie gave up after she had correctly written 2358 digits.
What was the last number she wrote?

Answer 1

9 1-digit numbers
90 2-digit numbers
so, there were (2358-99)/3 3-digit numbers

Answer 2

But you aren't trying to count how many numbers but many many digits (so 1-12 there would be 15 digits) so how many numbers is 2358 digits?

Answer 3

Umm, I guess that would be

(2358-99)/3

right?

Answer 4

Actually we can represent this with algebra:

Note there are three stages of digits:

Stage 1 - one digit numbers (1 to 9) there are 9 digits total

Stage 2 - two digit numbers (10 to 99) there are 89 x 2 = 178 digits total

Stage 3 - We don't no how far to go so we stop here

Rosie reached 2358 which gets into stage three of three digit numbers.

We would represent our situation with an equation:

2358 = 189 + 3x

now keep terms of x on one side, and the rest on the other side

2358 - 189 = 189-189 +3x

2169 = 3x

Now simple divide both sides by 3 to get X

723 = x