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How many times is the digit "3" written while

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Ravshonbek
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How many times is the digit "3" written while [#permalink] New post   21 Nov 2007, 11:08
How many times is the digit "3" written while numbering the pages of
a book from 1 to 1000?



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Re: How many times is the digit "3" written while [#permalink] New post   21 Nov 2007, 11:24
3 will be written 100 times in the hundreds digits
3 will be written 100 times in the tens digits
3 will be written 100 times in the units digits

Therefore, total 300 times.
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Re: How many times is the digit "3" written while [#permalink] New post   21 Nov 2007, 11:30
Ravshonbek wrote:
How many times is the digit "3" written while numbering the pages of
a book from 1 to 1000?


We have
3
13
23
43
53
63
73
83
93 9 for all doubles w/o the 30's

Same for triples w/o 300's
We have: 10, 100, 200, 400, 500, 600, 700, 800, 900
9*9=81 3's excluding the 30's and 300's.

Now for the 30's we have 31,32,33,34,35,36,37,38,39. We have 10 3's dont forget to count 33 twice.

So 10*9=90. 81+90=171.

Now we have to include the 300's yuck. exclude 330's 301,302,303,304,305,306,307,308,309 We have 10 3's again

0, 10, 20, 40, 50, 60, 70, 80, 90 So 10*90=90

171+90=261. Final one

331,332,333,334,335,336,337,338,339. 19 3's

261+19= 290.


I think everything is ok, but im not sure. Im not the best at these.
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Re: How many times is the digit "3" written while [#permalink] New post   21 Nov 2007, 11:35
eileen1017 wrote:
3 will be written 100 times in the hundreds digits
3 will be written 100 times in the tens digits
3 will be written 100 times in the units digits

Therefore, total 300 times.


Arghhh I knew it was 300, where am I missing the other 10 3's??? :twisted:
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Re: How many times is the digit "3" written while [#permalink] New post   21 Nov 2007, 14:06
Expert Reply
000
001
....
998
999

for the set one has the same frequency for every digit. So
N=3*1000/10=300



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Re: How many times is the digit "3" written while [#permalink]
21 Nov 2007, 14:06
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
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