Form the biggest squaring number

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You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:



  • Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)

  • Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)

  • You may apply this as many times as you want. ($(13)$ -> $169$ then $1(69)$->$14761$)


What is the biggest final number you can have?







mathematics logical-deduction







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  • 1




    Biggest final number? or biggest starting number?
    – SteveV
    50 mins ago










  • is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
    – elias
    12 mins ago










  • @elias "you may take the square the number itself too". written on the first rule. no restriction.
    – Oray
    11 mins ago














up vote
3
down vote

favorite












You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:



  • Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)

  • Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)

  • You may apply this as many times as you want. ($(13)$ -> $169$ then $1(69)$->$14761$)


What is the biggest final number you can have?







mathematics logical-deduction







share|improve this question



















  • 1




    Biggest final number? or biggest starting number?
    – SteveV
    50 mins ago










  • is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
    – elias
    12 mins ago










  • @elias "you may take the square the number itself too". written on the first rule. no restriction.
    – Oray
    11 mins ago












up vote
3
down vote

favorite









up vote
3
down vote

favorite











You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:



  • Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)

  • Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)

  • You may apply this as many times as you want. ($(13)$ -> $169$ then $1(69)$->$14761$)


What is the biggest final number you can have?







mathematics logical-deduction







share|improve this question















You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:



  • Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)

  • Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)

  • You may apply this as many times as you want. ($(13)$ -> $169$ then $1(69)$->$14761$)


What is the biggest final number you can have?







mathematics logical-deduction




mathematics logical-deduction






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 50 mins ago

























asked 1 hour ago









Oray

14.3k435140




14.3k435140







  • 1




    Biggest final number? or biggest starting number?
    – SteveV
    50 mins ago










  • is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
    – elias
    12 mins ago










  • @elias "you may take the square the number itself too". written on the first rule. no restriction.
    – Oray
    11 mins ago












  • 1




    Biggest final number? or biggest starting number?
    – SteveV
    50 mins ago










  • is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
    – elias
    12 mins ago










  • @elias "you may take the square the number itself too". written on the first rule. no restriction.
    – Oray
    11 mins ago







1




1




Biggest final number? or biggest starting number?
– SteveV
50 mins ago




Biggest final number? or biggest starting number?
– SteveV
50 mins ago












is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
12 mins ago




is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
12 mins ago












@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
11 mins ago




@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
11 mins ago










1 Answer
1






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up vote
4
down vote













Not proven to be maximal at all, but I managed to reach




10 digits with 4817093625




The steps are:




(705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625







share|improve this answer




















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    1 Answer
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    active

    oldest

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    4
    down vote













    Not proven to be maximal at all, but I managed to reach




    10 digits with 4817093625




    The steps are:




    (705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625







    share|improve this answer
























      up vote
      4
      down vote













      Not proven to be maximal at all, but I managed to reach




      10 digits with 4817093625




      The steps are:




      (705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625







      share|improve this answer






















        up vote
        4
        down vote










        up vote
        4
        down vote









        Not proven to be maximal at all, but I managed to reach




        10 digits with 4817093625




        The steps are:




        (705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625







        share|improve this answer












        Not proven to be maximal at all, but I managed to reach




        10 digits with 4817093625




        The steps are:




        (705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 27 mins ago









        elias

        7,63232051




        7,63232051



























             

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