Question 175459
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
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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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