Forums >Off the Beaten Path>mathematics Q

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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?

i find the sunshine beckons me to open up the gate and dream and dream ~~robbie williams

is this the correct expression?

37!*32!=x

i find the sunshine beckons me to open up the gate and dream and dream ~~robbie williams

maybe i don't need the factorial?

i find the sunshine beckons me to open up the gate and dream and dream ~~robbie williams

modified: 10/1/2012 at 10:03 AM

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?.

2015 Goals:

#1: Do what I can do. **<DOING>**

#2: sub 5:40 @ 1/2 Ironman (Benton Harbor, MI) **<DONE... 5:35:05>**

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.

i find the sunshine beckons me to open up the gate and dream and dream ~~robbie williams

modified: 10/1/2012 at 10:13 AM

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

modified: 10/1/2012 at 10:37 AM

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...

2015 Goals:

#1: Do what I can do. **<DOING>**

#2: sub 5:40 @ 1/2 Ironman (Benton Harbor, MI) **<DONE... 5:35:05>**

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

"You NEED to do this" - Shara

modified: 10/1/2012 at 10:48 AM

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.

modified: 10/1/2012 at 10:54 AM

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.

i find the sunshine beckons me to open up the gate and dream and dream ~~robbie williams

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?

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.

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.

i find the sunshine beckons me to open up the gate and dream and dream ~~robbie williams

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Forums >Off the Beaten Path>mathematics Q