How many of the natural numbers from 1 to 600, inclusive, contain the digit 5 at least once? (The numbers 152 and 553 are two natural numbers that contain the digit 5 at least once, but 430 is not.)

Logic
Oct 12, 2018

#1**+2 **

We have 60 decades from 1 to 600 ( 1st decade is 1,2,3,4,5,6,7,8,9,10) every one of this include 1 time the number 5 but from 500 to 599 include 100 times and for every decade with 5x exp. 150-159 include 10 times so from 1-100 include (5,15,25,35,45,65,75,85,95) 9+10 times so 19 times total,the same and from 100 to 499 so (19*5)+100= 195 total times include the number 5 from 1-600!

I hope I helped you!

Dimitristhym
Oct 12, 2018

#1**+2 **

Best Answer

We have 60 decades from 1 to 600 ( 1st decade is 1,2,3,4,5,6,7,8,9,10) every one of this include 1 time the number 5 but from 500 to 599 include 100 times and for every decade with 5x exp. 150-159 include 10 times so from 1-100 include (5,15,25,35,45,65,75,85,95) 9+10 times so 19 times total,the same and from 100 to 499 so (19*5)+100= 195 total times include the number 5 from 1-600!

I hope I helped you!

Dimitristhym
Oct 12, 2018

#2**+3 **

100 integers from 500 - 599 contain at least one 5

And in each of the 499 integers

_5, _15, _25, _35, _ 45, _55 , _65, _ 75, _ 85 , _ 95

In each hundred from 1 to 499 contain at least one 5

And there are 5 sets of these = 5 * 10 = 50

And in each hundred from 1 to 499 we have the integers

_5_ where the last digit is not a 5

And we have 9 of these in every hundred

So...we have 5 * 9 = 45 of these

So....100 + 50 + 45 = 195

Just as Dimitristhym found !!!

CPhill
Oct 13, 2018