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if you have available 37 characters (a-z [case insensitive], 0-9, and the underbar) and file names can range from 1 to 32 characters in length, how many unique file names can you create?
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is this the correct expression?
37!*32!=x
maybe i don't need the factorial?
is this the correct expression? 37!*32!=x
I don't think that's right, but that's a 2 minute review of your question, not knowing the solution yet.... The thought that the file name can either be 1, 2, ..., 32 characters has me thinking its more like: 37!+36!+35!+...2!+1!
But, it's been a LONG time since I've tried to think like this.
mta: nope, I'm definitely wrong after thinking more. Each characters still available to select. Your formula looks close... But, why the 2nd factorial? Wouldn't it be 37!*32?.
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#1: Do what I can do. <DOING>
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i was thinking 1-37 characters in combinations of 1-32 would mean both had to be factorials.
but that's why i am asking, because i don't know.
Not sure on the exact formula but ti would be something lik
(37^1)+(37^2)+(37^3)+....(37^32)
which equals
156,442,372,462,157,000,000,000,000,000,000,000,000,000,000,000,000.00
I'd recommend thinking about it in smaller terms.
For example, there are 2 characters (0 & 1), with a maximum length of 3.
Therefore, it could be:
000, 001, 010, 011, 100, 101, 110, 111
So, with the above example, you have 8 possible combinations, so, you back door into the math. 2!*3! = 12. Not right answer
2!*3 = 2*3=6. Not right answer
3!*2 = 6*2=12. Not right answer
dang it!
mta: disregard...
In the case of a file name with one character you would have 37 different possibilities
in the case of a file name with two characters you would have 37*37 (37^2) or 1369 different possibilities
so for a file name of 1 or 2 characters that could be any of 37 different characters you would have a possibility of 37 + 1369 = 1406
If you keep following this line of thought for a possible file size of 32 characters you would come up with the sum of:
37^1 + 37^2 + 37^3...37^32
This is roughly 1.564 x10^50 possibilities
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Not sure on the exact formula but ti would be something lik (37^1)+(37^2)+(37^3)+....(37^32) which equals 156,442,372,462,157,000,000,000,000,000,000,000,000,000,000,000,000.00
+1
No need for factorials because there are no rules about order, replacement, etc.
MTA: +1 for Hannibal too.
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I'll take a stab at it...it's a harder question than I originally thought....
37 possible characters, length 1: 37 possibilities
+
length 2: 37*37
length 3: 37*37*37
...
length 32: 37^32
=
37+37^2+37^3+...+37^32 = sum(n=1 to 32) 37^n =
(calculator here: http://www.wolframalpha.com
so 1.6 x 10^50
(MTA: of course, everybody posted at the same time, and Im slow)
In the case of a file name with one character you would have 37 different possibilities in the case of a file name with two characters you would have 37*37 (37^2) or 1369 different possibilities so for a file name of 1 or 2 characters that could be any of 37 different characters you would have a possibility of 37 + 1369 = 1406 If you keep following this line of thought for a possible file size of 32 characters you would come up with the sum of: 37^1 + 37^2 + 37^3...37^32 This is roughly 1.564 x10^50 possibilities
ah, super.
i need an answer for whiny systems users who are complaining about not having enough characters to create unique filenames because they cannot use symbols in their filenames.
1.564x10^50 combinations.
that should hold them for at least six months.
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But... this precludes the filename l'administrador és molt estúpid !!
It's a 5k. It hurt like hell...then I tried to pick it up. The end.
ah, super. i need an answer for whiny systems users who are complaining about not having enough characters to create unique filenames because they cannot use symbols in their filenames. 1.564x10^50 combinations. that should hold them for at least six months.
AKA 156 quindecillion, AKA 1.56 sqrt(googol).
More generally, for filenames of length 1 to n using p characters, the closed-form expression is
where B_p are the Bernoulli numbers, and B_p(n) the Bernoulli polynomials.
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bhearn, that looks like the type of formula my son (college junior) is studying to prepare for the first actuarial exam next month! I asked, "Is it a closed-book test??" He double-checked and it is. I think I'll stick to engineering.
okay, bhearn, that is some good stuff right there.
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