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How many times will the digit 7 be written?

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Re: How many times will the digit 7 be written? [#permalink] New post 10 Oct 2012, 05:56
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MOST EFFICIENT METHOD USING COMBINATORIX

As Bunuel said, think of each number as XXX ie 001 to 999

Numbers with one 7.

Either 7XX, X7X or XX7, so 3 x 1C9 x 1C9 = 3x9x9 = 243

Numbers with two 7's (nb question asks how many sevens are displayed, so this answer must be doubled)

Either 77X, 7X7 or X77, so 3x 1C9 = 27 (or 54 once you double it)

Numbers with three 7's

Only 1 (777). Triple it as there are three 7,s = 3

Add all together: 243+54+3 = 300

Answer => D
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Re: counting [#permalink] New post 29 Oct 2012, 13:16
tt11234 wrote:
How many times will the digit 7 be written when listing the integers from 1 to 1000?

110
111
271
300
304

any easy way to do this question?
here is how i did it...
let xyz be a 3-digit#, first, let Z=7, we have 10 options ( 0-9)for x and 10 options for y, then we get 10 x 10 =100, same logic is applied when y =7 and x = 7, we get 300 times.
is it correct?


started using the same method, but got stuck in the middle of the road.

Bunuel, could you please clarify if slot method can be applied to this problem. Thanks in advance.
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Re: counting [#permalink] New post 29 Oct 2012, 13:33
EV wrote:
tt11234 wrote:
How many times will the digit 7 be written when listing the integers from 1 to 1000?

110
111
271
300
304

any easy way to do this question?
here is how i did it...
let xyz be a 3-digit#, first, let Z=7, we have 10 options ( 0-9)for x and 10 options for y, then we get 10 x 10 =100, same logic is applied when y =7 and x = 7, we get 300 times.
is it correct?


started using the same method, but got stuck in the middle of the road.

Bunuel, could you please clarify if slot method can be applied to this problem. Thanks in advance.


Check here: how-many-times-will-the-digit-7-be-written-99914.html#p781456

Another approach: how-many-times-will-the-digit-7-be-written-99914.html#p770507
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Re: How many times will the digit 7 be written? [#permalink] New post 26 Jan 2013, 09:04
seekmba 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


i think using combinatorics is better on this type of a problem
Re: How many times will the digit 7 be written?   [#permalink] 26 Jan 2013, 09:04
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