## Task 4 - 130614

Jörg and Claudia are arguing about whether there are more natural numbers from 0 to 1000 whose decimal representation contains (at least) one 5, or whether there are more that do not contain a 5.

Determine the correct answer to this question!
For the numbers between 0 and 100 that contain at least one digit 5, the following applies to individual subranges: between 0 and 49 there are 5 such numbers, between 50 and 59 there are 10 such numbers, and between 60 and 100 there are 4 such numbers.

Thus, between 0 and 99 there are 19 such numbers. Analogously, the ranges 100 to 199, 200 to 299, etc., can also be examined, with the exception of 500 to 599. This results in a total of $9 \cdot 19=171$ such numbers. Additionally, there are the numbers from 500 to 599.

Therefore, there are 271 numbers between 0 and 1000 that contain at least one digit 5. 1001 $271=730$ numbers do not contain the digit 5. Thus, there are fewer numbers with a 5 than numbers in this range without the digit 5.