Question

How many 1's are present from 149 to 389?

Answer 1

So , my lower and upper limits are 149 and 389. And I am to count number of 1s. 

I feel there is some loss of information, but for that I will divide the solutions in three phases.

Phase I
I am counting how many numbers have 1 as their last digit.
Starting with 151 and my final number is 381
Difference between two successive numbers is 10
So by Arithmetic progression,
a of n(Last term) = a (first term) + (n-1)*d(difference)
⇒381 = 151 + (n-1)10
⇒381-151 = (n-1)10
⇒230 = (n-1)10
⇒23=n-1
⇒n = 24 
No. of numbers with last digit 1 = 24

Phase II
Here I am finding numbers which have their Second digit as 1
So to start from , I have number 210,211,212....219
So between 200 to 300
there are 10 numbers 
and from 300 to 389
There are 10 numbers as well (310,311,312...319)
So total numbers observed = 20

Phase III
Here I am searching for numbers with their first digit as 1.
So I have to stay within 149 to 199
So i have around 51 numbers which have 1 as first digit...
And finally If you didn't get your answer in one of the three phases , probably you are searching for numbers with 1 as any of the digits
So , on adding the results of the above Phases, we get (24 + 20 + 51)= 95
Therefore there are 95 1's present from 149 to 389