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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, 04:56
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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, 12:16
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, 12:33
Expert's post
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, 08:04
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
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Re: How many times will the digit 7 be written? [#permalink] New post 08 Jul 2013, 00:10
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Re: How many times will the digit 7 be written? [#permalink] New post 14 Jul 2014, 16:54
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Alternate solution:

Using probability of occurrence = desired outcomes / total outcomes, desired outcomes = probability x total outcomes.

total outcomes = 1000.

probability of occurrence - to simplify this, the question statement could be interpreted as "what is the probability that the digit 7 is picked at least once when 3 digits are chosen at random?"

probability of at least one 7 = 7 in first digit OR 7 in second digit OR 7 in third digit = 1/10 + 1/10 + 1/10 = 3/10

desired outcomes = probability x total outcomes = 3/10 x 1000 = 300.
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Re: How many times will the digit 7 be written? [#permalink] New post 17 Jul 2014, 21:23
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The first time I did the question, my answer was C : 271 since I thought the question is "how many numbers from 0 - 1000, that contain the 7 digit". So I counted 77, 707,717,....,777,...797, 771, 772, 773,..., or 779 as one.
That may be the reason why 23% of people who answered the question decided to pick answer C.
That is really interesting question :)
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Re: How many times will the digit 7 be written? [#permalink] New post 18 Jul 2014, 00:08
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It is very interesting question, thanks for the all the suggestion but Banuel is relly a rock-star..
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Re: How many times will the digit 7 be written? [#permalink] New post 18 Jul 2014, 13:23
vad3tha wrote:
The first time I did the question, my answer was C : 271 since I thought the question is "how many numbers from 0 - 1000, that contain the 7 digit". So I counted 77, 707,717,....,777,...797, 771, 772, 773,..., or 779 as one.
That may be the reason why 23% of people who answered the question decided to pick answer C.
That is really interesting question :)


Yes, I made the same mistake.
Re: How many times will the digit 7 be written?   [#permalink] 18 Jul 2014, 13:23
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