If N is the sum of all digits used in writing all the numbers from 1 to 1000. Then the sum of digits in the number N is
 

We write all the numbers from 0 to 999 as 3-digit numbers
000, 001, 002, 003……..998,999 and writing these in reverse 999,998,997,996……..001,000
Adding all these we get 999,999,999,………999
 Now the sum of the digits of the 1000
 Numbers from 0 to 999 is $=\frac{27000}{2}=13500$ 
 Now delete 0 and add 1000 to the list of 1000 numbers then N=13501