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Director  Joined: 16 Jul 2009
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How many times will the digit 7 be written when listing the integers f  [#permalink]

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11 00:00

Difficulty:   95% (hard)

Question Stats: 45% (01:00) correct 55% (01:04) wrong based on 316 sessions

### HideShow timer Statistics How many times will the digit 7 be written when listing the integers from 1 to 1000?

A. 110
B. 111
C. 271
D. 300
E. 304

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-many-times-will-the-digit-7-be-written-99914.html

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Originally posted by noboru on 31 Jul 2009, 09:35.
Last edited by Bunuel on 29 Oct 2014, 08:43, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Manager  Joined: 17 Dec 2007
Posts: 94
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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noboru wrote:
How many times will the digit 7 be written when listing the integers from 1 to 1000?

110
111
271
300
304

from 1- 100 , 7 occurs 20 times, similary for all other 100s except 701 - 800 & number 700.

on calculating it, it comes to 300 times, please post if there is anyother easy way to calculate this
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Joined: 30 Jul 2009
Posts: 23
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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[EDIT - REMOVED BY USER]

Originally posted by nplaneta on 31 Jul 2009, 12:58.
Last edited by nplaneta on 17 Jun 2012, 17:39, edited 1 time in total.
Senior Manager  Joined: 08 Jan 2009
Posts: 274
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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10
8
Take all the number as 3 digits ( 001 to 999)
i fill the units place with 7 , i can fill the ten and hundreds place in 10 ways
10 * 10 * 1 = 100

Same way for hundreds = 10 * 1 * 10 = 100
thousands = 1* 10* 10 = 100

So totally 300 ways
Intern  Joined: 14 Apr 2008
Posts: 46
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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can it be 270
if v do in how mny digits 7 will not be used it will be 9*9*9 =729
so 1000-729 =271
wot im missing help??? Intern  Joined: 14 Apr 2008
Posts: 46
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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can it be 270
if v do in how mny digits 7 will not be used it will be 9*9*9 =729
so 1000-729 =271
wot im missing help??? Manager  Joined: 20 Oct 2009
Posts: 89
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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300,
777 is counted three times when it should be only once. However, 777 has three 7's so it offsets its reappearance.

Here is how I did it:
Single digit: 1 (7);
2 Digits: 9+10=19;
3 Digits:

7 as the unit digit: 9*10=90
7 as the middle digit: 9*10=90
7 as the leading digit: 19*10 ( no restriction on 0 since it is not leading the number)

- 2 because 777 is counted in all three scenarios.
+2 because 777 has three 7's.

Awesome question though.
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Manager  Joined: 14 Apr 2010
Posts: 170
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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how did you get 9*10 for 3 digits??
Manager  Joined: 25 Aug 2008
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Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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1
1

From 1 to 100, total 7 digits will be 10 + 1 +9 = 20
From 1 to 1000 to 20 * 10 = 200 and 100 7 digits for 700 to 799
Total = 200 + 100 = 300
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Intern  Affiliations: CPA
Joined: 09 May 2011
Posts: 41
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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2
My method is not as simple, but I think it is easier to understand than the previous methods.

First off for single and double digit numbers, lets assume everyone can figure out that there are 20 7's.

Once we get into the hundreds, we know that the 700s will be tricky, but for all the other hundreds, we should be seeing 20 7's in each set of hundred. Other than the 700s, there are only 8 other sets of hundreds (100s, 200s, 300s, etc.). So we multiply 20 * 8 = 160...bringing the total to 180.

So far we have accounted for all the 7's for single and double digit numbers and all hundreds not including the 700s.

For the 700s, we already know that there is at least one 7 from the numbers 700-799. So there's 100 right there. At this point the only remaining numbers with 7 are the same ones we identified for single and double digit numbers. (20 of em)

So in the end we have...
20+160+100+20 = 300

compared to the above methods, this is a very crude way of doing this problem
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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6
4
noboru wrote:
How many times will the digit 7 be written when listing the integers from 1 to 1000?

A. 110
B. 111
C. 271
D. 300
E. 304

Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999

We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 7) 3000/10=300 times.

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-many-times-will-the-digit-7-be-written-99914.html
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Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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2
3
Bunuel wrote:
noboru wrote:
How many times will the digit 7 be written when listing the integers from 1 to 1000?

A. 110
B. 111
C. 271
D. 300
E. 304

Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999

We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 7) 3000/10=300 times.

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-many-times-will-the-digit-7-be-written-99914.html

Another approach:

In the range 0-100:
7 as units digit - 10 times (7, 17, 27, ..., 97);
7 as tens digit - 10 time (71, 72, 73, ..., 79);
So in first one hundred numbers 7 is written 10+10=20 times.

In 10 hundreds 7 as units or tens digit will be written 10*20=200 times. Plus 100 times when 7 is written as hundreds digit (700, 701, 702, ..., 799).

Total 200+100=300.

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Re: How many times will the digit 7 be written when listing the integers f  [#permalink]

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_________________ Re: How many times will the digit 7 be written when listing the integers f   [#permalink] 09 Sep 2018, 01:42
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