Counting the numbers on the kilometer markers Along a road, there exists marks for every passed kilometer after every kilometer, at the start where the mark shows 0. A hiker who starts walking at the roads start devote himself to count the numbers on the marks. How many kilometers has the hiker walked/passed at the mark showing the number 2013?
I have the solutions aswell but I don't understand the solution. However I will delay with posting the solution until later, perhaps somebody here can solve it anyway.
Regards!
 A: If the hiker sees mile 1, 2, 3, like normal, it is a simple formula - $\frac{x^2+x}{2}$
A: Solution: The single digit numbers add up to $10$ numbers and corresponds to $9$ passed kilometers. The $2$ digit numbers together holds a total of $180$ numbers (I don't get this part). When you pass the sign with the number $99$, which is the biggest two digit number, you have walked a total of $9+90=99$km. All the three digit numbers together contain $3\times 900>2013$ numbers. So, when one have passed the sign with the $2013$ number/digit one have walked at least a $3$ digit number of kilometers. We have the following:
$$2013 = 10 + 180 + 6 · (3 · 100) + 3 · 7 + 2$$ 
Which means that at the sign with the $2013$th digit, one passed 
$9 + 90 + 6 \times 100 + 7 + 1 = 707$ kilometers.
If somebody could explain this I would be greatful.
A: Each $2$ digit number is composed of $2$ digits, and there are $90$ of them. Therefore there are $2\times90=180$ digits in $2$ digit numbers.
With this you get the answer:$$2013=1(10)+2(90)+3(607)+2$$
$1,2,3$ are the amount of digits in a number.
Thus the total amount of numbers is $$10+90+607=707$$
