How many times will the digit 7 be written when listing the integers from 1 to 1000?

Answer 1

Let us take a systematic approach to answer this (make a list):

For numbers (3 digit) when there is EXACTLY one 7  there are 9 possibilities (0,1,2,3,4,5,6,8,9) for each of the other 2 digits i.e 81. However the 7 could be in the units, tens or hundreds place so there is a total of 81 x 3 = 243 occurrences.

- - 7;  - 7 -; 7 - -.

 

For numbers (3 digit) when there are EXACTLY two 7's  there are 9 possibilities for the other digit. However the two 7's could be positioned in 3 ways so there is a total of 9 x 3 = 27 occurrences. 

- 7 7; 7 - 7; 7 7 -

 

There is exactly 1 number with all three sevens (777) .

 

So we have a total of 243 + 27 + 1 =271.

Note

ALL the BEST!

Pradip