Question 1173934
<br>
You learn nothing, and your brain gets no exercise, from our doing this problem for you.<br>
So I will show you an organized way to do the counting and let you find the answer.<br>
Note there is no magic formula that will find this answer for you.<br>
You could write a computer program to find the answer; and writing that program would be an excellent exercise.  But that is not what they want you to do.<br>
But other than that, the way to find the answer is to find an organized way to count the numbers so that you count each one once and only once.<br>
Numbers that are multiples of 5 have units digit either 5 or 0.  Split the process of counting the numbers you are looking for into those two cases.<br>
(1) Numbers 1 ... 2019 with units digit 5: 5, 15, 25, ..., 2015.  Count them.<br>
(2) Numbers 1 ... 2019 with units digit 0 and some digit 5....<br>
(2a) Numbers with 5 in the tens place and 0 in the units place: count them
(2b) Numbers with 5 in the hundreds place and 0 in the units place: count them
(2c) Numbers with 5 in BOTH the tens place and hundreds place: count them<br>
The numbers with 0 in the units place and 5 in both the tens and hundreds places were counted twice in steps (2a) and (2b).  So those numbers, counted in step (2c), must be subtracted from the total.<br>
The answer to the problem is then the numbers from<br>
(1) + ((2a)+(2b)) - (2c)<br>