Determine the number of different variable names












4














Let name of a variable be a string of between 1 and 65535, inclusive, where each character can be an uppercase or a lowercase letter , a dollar sign, an underscore or a digit, except that the first character must not be a digit. What is the number of different variable names possible ?
Solution




  1. Given that the first char must not be a digit, this first character can be chosen in 26(lowercase) + 26(uppercase) + 1(dollar sign) + 1(underscore) = 54 ways.

  2. All subsequent chars can be chosen in $64^{65534}$ ways. As each subsequent digit cab be chosen in (26(uppercase) + 26(lowercase) + 1(dollar sign) + 1(underscore) + 10(digits)) = 64. As there are 65534 digits left, to get the number of possible combination 64 is multiplied 65534 times = $64^{65534}$.


  3. Hence total number of possible names is:
    $$
    54 * 64^{65534}
    $$
    Can this be the correct answer or I'm missing something ?







combinatorics







share|cite|improve this question
























  • Could you explain, how you did get $64^{65536}-1$ ?
    – callculus
    Sep 19 '15 at 7:46












  • that is a mistake. corrected it to $64^{65535}$....
    – dmytro.poliarush
    Sep 19 '15 at 8:01












  • What happened to the $54$? How can the possibly not be relevant to your final answer? And why do you say there are $65535$ digits left? The string is anywhere from $1$ to $65535$ characters long, it certainly isn't $65536$. You are definitely missing something.
    – Erick Wong
    Sep 19 '15 at 8:03












  • This is wrong; see the Java language specification. A variable name is an identifier. The characters in an identifier are not limited to the ones you list; the specification states only that these are included, immediately going on to say that others are included, too. Also, according to the specification, there is no length limit; if you encountered a length limit, it may have been imposed by a non-compliant implementation.
    – joriki
    Sep 19 '15 at 8:10












  • It is not about JAVA (corrected that). Main goal - is to find number of possible combinations given the conditions.
    – dmytro.poliarush
    Sep 19 '15 at 8:16
















4














Let name of a variable be a string of between 1 and 65535, inclusive, where each character can be an uppercase or a lowercase letter , a dollar sign, an underscore or a digit, except that the first character must not be a digit. What is the number of different variable names possible ?
Solution




  1. Given that the first char must not be a digit, this first character can be chosen in 26(lowercase) + 26(uppercase) + 1(dollar sign) + 1(underscore) = 54 ways.

  2. All subsequent chars can be chosen in $64^{65534}$ ways. As each subsequent digit cab be chosen in (26(uppercase) + 26(lowercase) + 1(dollar sign) + 1(underscore) + 10(digits)) = 64. As there are 65534 digits left, to get the number of possible combination 64 is multiplied 65534 times = $64^{65534}$.


  3. Hence total number of possible names is:
    $$
    54 * 64^{65534}
    $$
    Can this be the correct answer or I'm missing something ?







combinatorics







share|cite|improve this question
























  • Could you explain, how you did get $64^{65536}-1$ ?
    – callculus
    Sep 19 '15 at 7:46












  • that is a mistake. corrected it to $64^{65535}$....
    – dmytro.poliarush
    Sep 19 '15 at 8:01












  • What happened to the $54$? How can the possibly not be relevant to your final answer? And why do you say there are $65535$ digits left? The string is anywhere from $1$ to $65535$ characters long, it certainly isn't $65536$. You are definitely missing something.
    – Erick Wong
    Sep 19 '15 at 8:03












  • This is wrong; see the Java language specification. A variable name is an identifier. The characters in an identifier are not limited to the ones you list; the specification states only that these are included, immediately going on to say that others are included, too. Also, according to the specification, there is no length limit; if you encountered a length limit, it may have been imposed by a non-compliant implementation.
    – joriki
    Sep 19 '15 at 8:10












  • It is not about JAVA (corrected that). Main goal - is to find number of possible combinations given the conditions.
    – dmytro.poliarush
    Sep 19 '15 at 8:16














4












4








4







Let name of a variable be a string of between 1 and 65535, inclusive, where each character can be an uppercase or a lowercase letter , a dollar sign, an underscore or a digit, except that the first character must not be a digit. What is the number of different variable names possible ?
Solution




  1. Given that the first char must not be a digit, this first character can be chosen in 26(lowercase) + 26(uppercase) + 1(dollar sign) + 1(underscore) = 54 ways.

  2. All subsequent chars can be chosen in $64^{65534}$ ways. As each subsequent digit cab be chosen in (26(uppercase) + 26(lowercase) + 1(dollar sign) + 1(underscore) + 10(digits)) = 64. As there are 65534 digits left, to get the number of possible combination 64 is multiplied 65534 times = $64^{65534}$.


  3. Hence total number of possible names is:
    $$
    54 * 64^{65534}
    $$
    Can this be the correct answer or I'm missing something ?







combinatorics







share|cite|improve this question















Let name of a variable be a string of between 1 and 65535, inclusive, where each character can be an uppercase or a lowercase letter , a dollar sign, an underscore or a digit, except that the first character must not be a digit. What is the number of different variable names possible ?
Solution




  1. Given that the first char must not be a digit, this first character can be chosen in 26(lowercase) + 26(uppercase) + 1(dollar sign) + 1(underscore) = 54 ways.

  2. All subsequent chars can be chosen in $64^{65534}$ ways. As each subsequent digit cab be chosen in (26(uppercase) + 26(lowercase) + 1(dollar sign) + 1(underscore) + 10(digits)) = 64. As there are 65534 digits left, to get the number of possible combination 64 is multiplied 65534 times = $64^{65534}$.


  3. Hence total number of possible names is:
    $$
    54 * 64^{65534}
    $$
    Can this be the correct answer or I'm missing something ?







combinatorics




combinatorics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 19 '15 at 8:10

























asked Sep 19 '15 at 7:37









dmytro.poliarush

564




564












  • Could you explain, how you did get $64^{65536}-1$ ?
    – callculus
    Sep 19 '15 at 7:46












  • that is a mistake. corrected it to $64^{65535}$....
    – dmytro.poliarush
    Sep 19 '15 at 8:01












  • What happened to the $54$? How can the possibly not be relevant to your final answer? And why do you say there are $65535$ digits left? The string is anywhere from $1$ to $65535$ characters long, it certainly isn't $65536$. You are definitely missing something.
    – Erick Wong
    Sep 19 '15 at 8:03












  • This is wrong; see the Java language specification. A variable name is an identifier. The characters in an identifier are not limited to the ones you list; the specification states only that these are included, immediately going on to say that others are included, too. Also, according to the specification, there is no length limit; if you encountered a length limit, it may have been imposed by a non-compliant implementation.
    – joriki
    Sep 19 '15 at 8:10












  • It is not about JAVA (corrected that). Main goal - is to find number of possible combinations given the conditions.
    – dmytro.poliarush
    Sep 19 '15 at 8:16


















  • Could you explain, how you did get $64^{65536}-1$ ?
    – callculus
    Sep 19 '15 at 7:46












  • that is a mistake. corrected it to $64^{65535}$....
    – dmytro.poliarush
    Sep 19 '15 at 8:01












  • What happened to the $54$? How can the possibly not be relevant to your final answer? And why do you say there are $65535$ digits left? The string is anywhere from $1$ to $65535$ characters long, it certainly isn't $65536$. You are definitely missing something.
    – Erick Wong
    Sep 19 '15 at 8:03












  • This is wrong; see the Java language specification. A variable name is an identifier. The characters in an identifier are not limited to the ones you list; the specification states only that these are included, immediately going on to say that others are included, too. Also, according to the specification, there is no length limit; if you encountered a length limit, it may have been imposed by a non-compliant implementation.
    – joriki
    Sep 19 '15 at 8:10












  • It is not about JAVA (corrected that). Main goal - is to find number of possible combinations given the conditions.
    – dmytro.poliarush
    Sep 19 '15 at 8:16
















Could you explain, how you did get $64^{65536}-1$ ?
– callculus
Sep 19 '15 at 7:46






Could you explain, how you did get $64^{65536}-1$ ?
– callculus
Sep 19 '15 at 7:46














that is a mistake. corrected it to $64^{65535}$....
– dmytro.poliarush
Sep 19 '15 at 8:01






that is a mistake. corrected it to $64^{65535}$....
– dmytro.poliarush
Sep 19 '15 at 8:01














What happened to the $54$? How can the possibly not be relevant to your final answer? And why do you say there are $65535$ digits left? The string is anywhere from $1$ to $65535$ characters long, it certainly isn't $65536$. You are definitely missing something.
– Erick Wong
Sep 19 '15 at 8:03






What happened to the $54$? How can the possibly not be relevant to your final answer? And why do you say there are $65535$ digits left? The string is anywhere from $1$ to $65535$ characters long, it certainly isn't $65536$. You are definitely missing something.
– Erick Wong
Sep 19 '15 at 8:03














This is wrong; see the Java language specification. A variable name is an identifier. The characters in an identifier are not limited to the ones you list; the specification states only that these are included, immediately going on to say that others are included, too. Also, according to the specification, there is no length limit; if you encountered a length limit, it may have been imposed by a non-compliant implementation.
– joriki
Sep 19 '15 at 8:10






This is wrong; see the Java language specification. A variable name is an identifier. The characters in an identifier are not limited to the ones you list; the specification states only that these are included, immediately going on to say that others are included, too. Also, according to the specification, there is no length limit; if you encountered a length limit, it may have been imposed by a non-compliant implementation.
– joriki
Sep 19 '15 at 8:10














It is not about JAVA (corrected that). Main goal - is to find number of possible combinations given the conditions.
– dmytro.poliarush
Sep 19 '15 at 8:16




It is not about JAVA (corrected that). Main goal - is to find number of possible combinations given the conditions.
– dmytro.poliarush
Sep 19 '15 at 8:16










1 Answer
1






active

oldest

votes


















1














The correct answer is:



$$54(65^0)+54(64^1)+54(64^2)+...+54(64^{65534})$$



Apply the formula of sum of geometry series:



$$sum_{i=0}^n ar^j = frac{ar^{n+1}-a}{r-1}, if r neq 1$$



The nicer answer is:



$$frac{54(64^{65535} - 1)}{63}$$



You have to take variable length into account. Your solution is only for variables of max length.






share|cite|improve this answer























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    1 Answer
    1






    active

    oldest

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1














    The correct answer is:



    $$54(65^0)+54(64^1)+54(64^2)+...+54(64^{65534})$$



    Apply the formula of sum of geometry series:



    $$sum_{i=0}^n ar^j = frac{ar^{n+1}-a}{r-1}, if r neq 1$$



    The nicer answer is:



    $$frac{54(64^{65535} - 1)}{63}$$



    You have to take variable length into account. Your solution is only for variables of max length.






    share|cite|improve this answer




























      1














      The correct answer is:



      $$54(65^0)+54(64^1)+54(64^2)+...+54(64^{65534})$$



      Apply the formula of sum of geometry series:



      $$sum_{i=0}^n ar^j = frac{ar^{n+1}-a}{r-1}, if r neq 1$$



      The nicer answer is:



      $$frac{54(64^{65535} - 1)}{63}$$



      You have to take variable length into account. Your solution is only for variables of max length.






      share|cite|improve this answer


























        1












        1








        1






        The correct answer is:



        $$54(65^0)+54(64^1)+54(64^2)+...+54(64^{65534})$$



        Apply the formula of sum of geometry series:



        $$sum_{i=0}^n ar^j = frac{ar^{n+1}-a}{r-1}, if r neq 1$$



        The nicer answer is:



        $$frac{54(64^{65535} - 1)}{63}$$



        You have to take variable length into account. Your solution is only for variables of max length.






        share|cite|improve this answer














        The correct answer is:



        $$54(65^0)+54(64^1)+54(64^2)+...+54(64^{65534})$$



        Apply the formula of sum of geometry series:



        $$sum_{i=0}^n ar^j = frac{ar^{n+1}-a}{r-1}, if r neq 1$$



        The nicer answer is:



        $$frac{54(64^{65535} - 1)}{63}$$



        You have to take variable length into account. Your solution is only for variables of max length.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Nov 26 '18 at 7:06

























        answered Nov 26 '18 at 6:27









        Alexander Crescent

        113




        113






























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