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mathematics Q (Read 712 times)

R2E


"run" "to" "eat"

    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

    R2E


    "run" "to" "eat"

      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

      R2E


      "run" "to" "eat"

        maybe i don't need the factorial?

        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 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?.

          2014 Goals:

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

          #2: 365 Hours training <NOPE, INJURED>

           

          R2E


          "run" "to" "eat"

            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

              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...

                2014 Goals:

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

                #2: 365 Hours training <NOPE, INJURED>

                 

                  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

                    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.

                    2013 H1:  7 hours/week base.  Q3: Train for goal race.  Q4:  Goal Race.

                      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 = 

                       

                      sum_(n=1)^32 37^n = 156442372462157487686465364234921251964766516907360

                       

                      (calculator here: http://www.wolframalpha.com Wink

                       

                      so 1.6 x 10^50

                       

                      (MTA: of course, everybody posted at the same time, and Im slow)

                      R2E


                      "run" "to" "eat"

                        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


                        HobbyJogger & HobbyRacer

                          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.


                          I'm back!

                            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.

                              R2E


                              "run" "to" "eat"

                                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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