Question 175459: In numbering the pages of a book, a printer uses 522 digits. How many numbered pages does the book have?
: So this is what i tried:
Ones: 9
Tens: 90
Hundreds: 900
I just don't know what to do, please, please help!
Found 3 solutions by stanbon, solver91311, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In numbering the pages of a book, a printer uses 522 digits. How many numbered pages does the book have?
: So this is what i tried:
Ones: Pages:9......Digits:9
Tens: Pages:99-9= 90....Digits: 2*90 = 180
Hundreds: Digits: 522-(189) = 333; Pages = 111
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Total Pages 9+99+111 = 219
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Cheers,
Stan H.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! The first nine pages are numbered with a single digit, so the first nine pages use 9 digits to number them.
Pages 10 through 99 are numbered with two digits, 99 minus 10 is 89 plus 1 is 90 pages that use two digits to number them.
So far, we are on the same track.
Here's where you need to go from where you were:
There are 90 pages that each use two digits, so that is 180 digits used.
So far we have used 9 plus 180 digits, or 189 digits of the 522 total used. 522 minus 189 is 333. Each of the pages subsequent to page 99 uses three digits, so if the number of digits used to number three digit pages is 333, there must be 333 divided by 3 = 111 three-digit pages.
That makes a total of 9 plus 180 plus 111 equals 210 pages.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! i second the motion:
HELP !!!!!
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how you interpret this is extremely important.
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assume that a digit is any number 0-9
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a 1 digit number has a maximum of 9 pages.
a 2 digit number has a maximum of 19 pages.
a 3 digit number has a maximum of 29 pages.
a 4 digit number has a maximum of 39 pages.
a 5 digit number has a maximum of 49 pages.
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is there a pattern?
can we form an equation from this?
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here's a pattern that i see.
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let n = number of digits.
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when n = 1, the maximum number of pages is 10^1 - 1 = 10 - 1 = 9
when n = 2, the maximum number of pages is 10^2 - 1 = 100 - 1 = 99
when n = 3, the maximum number of pages is 10^3 - 1 = 1000 - 1 = 999
.....
carry this out to n = 522, and the maximum number of pages would be:
10^522 - 1 = a very big number.
this number is so big my calculator won't handle it.
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your answer should be:
the maximum number of pages is 10^522 - 1.
you answer should also be:
the minimum number of pages is 10^522 - 10
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here's why i think the minimum number of pages is 10^522 - 10.
take n = 3.
the maximum number of pages is 10^3 - 1 = 1000 - 1 = 999
the smallest number would be 990 using all 3 digits.
990 is 10^3 - 10 = 1000 - 10 = 990.
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go two steps higher just to see if this holds:
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take n = 5
the maximum number of pages is 10^5 - 1 = 100,000 - 1 = 99,999
the minimum number of pages is 10^5 - 10 = 100,000 - 10 = 99,990
you can't go higher than 99,999 with 5 digits.
you can't go lower than 99,990 with 5 digits.
answer looks good.
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answer is:
maximum number of pages is 10^n - 1
minimum number of pages is 10^n - 10
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a caveat:
10^n works if n is > 1.
take n = 2
max = 100 - 1 = 99
min = 100 - 10 = 90
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take n = 1, however:
max = 10 - 1 = 9
min = 10 - 10 = 0
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since the numbering of pages starts at 1, you need to qualify your statement as follows:
if n = 1, the maximum number of pages is 9, and the minimum number of pages is 1.
if n > 1, the maximum number of pages is 10^n - 1, and the minimum number of pages is 10^n - 10.
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hope this helps.
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