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How many integers from 100 to 999 can be written with no 7's?

 May 10, 2020
 #1
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999  -  100 +  1 = 900 numbers between 100 and 999 inclusive.

 

There are 252 numbers with at least one 7 in them between 100 and 999 inclusive.

 

There are: 900  - 252 = 648 numbers that have NO 7 in them between 100 and 999 inclusive.

 May 11, 2020
 #2
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Like Guest said, there are 999 - 100 + 1 = 900 numbers between 100 and 999 inclusive.

 

Now, think about it. The hundreds. Let's tackle 100. 107, 117, 127, 137, 147, 157, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 187, and 197. How many numbers is that? Counting, it is a list of 19 numbers. 19 x 9 = 171. Why is it times 9, not 10? Well, we gotta skip the 700s because there is a 7 in all of them. In 700 - 799, there are 100 numbers with a 7 in it. 100 + 171 = 271. Therefore, 900 - 271 = 629 numbers 100 - 999 which can be written without 7's.

 May 11, 2020
 #3
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Shadowfax 13: There are 271 numbers with at least one 7 in them between 1 and 999. But the question is between 100 and 999.So, you must subtract 19 numbers with at least one 7 in them between 1 and 99. Therefore, you only have: 271 - 19 =252 numbers with at least one seven in them beween 100 and 999.

So, 900 - 252 =648 numbers between 100 and 999 with NO seven in them.

 May 11, 2020
edited by Guest  May 11, 2020

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