1-999; How many times is the digit 8 written?

Question

A person writes down all the numbers from 1 to 999 inclusive. How many times was the digit 8 written?

Answer 1

271 values with 300 digit 8's.

 

Start with the 800's:  From 800-899 there are 100 numbers with 8 in hundreds place.

 

Then all the 80's:  There are 10 sets of x80-x89 (10 values) --    100 numbers with 8 in tens place.

 

Finally, from 008 to 998, there 100 appearances of 8 in ones place (because 00-99 is 100 values).

 

The digit 8 appears 300 times in 271 values.

 

For fun:  how would you determine that there are 271 values (because of multiple 8's in a value)?