Floors are numbered by skipping fours, Find actual number of floors.












2












$begingroup$


How do you find the number of floors,in a tetraphobic numbering system like 1,2,3,5,6,7,..,12,13,15..,39,50.



I am trying to find the pattern and the mathematical algorithm to solve for floor numbered n.



for eg
n = 3 : ans = 3
n = 8 : ans = 7
n = 22 : ans = 20



Note: This is not a HW problem , I read about it and tried to solve it as fun, I am stuck so I am asking here






combinatorics elementary-number-theory







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  • 1




    $begingroup$
    Why do you have 12 in there?
    $endgroup$
    – Mohammad Zuhair Khan
    Jan 26 at 7:46










  • $begingroup$
    @MohammadZuhairKhan I think the OP is leaving out all numbers in which the digit $4$ occurs. That's why he skips from $39$ to $50.$
    $endgroup$
    – saulspatz
    Jan 26 at 9:24


















2












$begingroup$


How do you find the number of floors,in a tetraphobic numbering system like 1,2,3,5,6,7,..,12,13,15..,39,50.



I am trying to find the pattern and the mathematical algorithm to solve for floor numbered n.



for eg
n = 3 : ans = 3
n = 8 : ans = 7
n = 22 : ans = 20



Note: This is not a HW problem , I read about it and tried to solve it as fun, I am stuck so I am asking here






combinatorics elementary-number-theory







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    Why do you have 12 in there?
    $endgroup$
    – Mohammad Zuhair Khan
    Jan 26 at 7:46










  • $begingroup$
    @MohammadZuhairKhan I think the OP is leaving out all numbers in which the digit $4$ occurs. That's why he skips from $39$ to $50.$
    $endgroup$
    – saulspatz
    Jan 26 at 9:24
















2












2








2





$begingroup$


How do you find the number of floors,in a tetraphobic numbering system like 1,2,3,5,6,7,..,12,13,15..,39,50.



I am trying to find the pattern and the mathematical algorithm to solve for floor numbered n.



for eg
n = 3 : ans = 3
n = 8 : ans = 7
n = 22 : ans = 20



Note: This is not a HW problem , I read about it and tried to solve it as fun, I am stuck so I am asking here






combinatorics elementary-number-theory







share|cite|improve this question









$endgroup$




How do you find the number of floors,in a tetraphobic numbering system like 1,2,3,5,6,7,..,12,13,15..,39,50.



I am trying to find the pattern and the mathematical algorithm to solve for floor numbered n.



for eg
n = 3 : ans = 3
n = 8 : ans = 7
n = 22 : ans = 20



Note: This is not a HW problem , I read about it and tried to solve it as fun, I am stuck so I am asking here






combinatorics elementary-number-theory




combinatorics elementary-number-theory






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 26 at 7:27









Ajinkya GawaliAjinkya Gawali

212




212








  • 1




    $begingroup$
    Why do you have 12 in there?
    $endgroup$
    – Mohammad Zuhair Khan
    Jan 26 at 7:46










  • $begingroup$
    @MohammadZuhairKhan I think the OP is leaving out all numbers in which the digit $4$ occurs. That's why he skips from $39$ to $50.$
    $endgroup$
    – saulspatz
    Jan 26 at 9:24
















  • 1




    $begingroup$
    Why do you have 12 in there?
    $endgroup$
    – Mohammad Zuhair Khan
    Jan 26 at 7:46










  • $begingroup$
    @MohammadZuhairKhan I think the OP is leaving out all numbers in which the digit $4$ occurs. That's why he skips from $39$ to $50.$
    $endgroup$
    – saulspatz
    Jan 26 at 9:24










1




1




$begingroup$
Why do you have 12 in there?
$endgroup$
– Mohammad Zuhair Khan
Jan 26 at 7:46




$begingroup$
Why do you have 12 in there?
$endgroup$
– Mohammad Zuhair Khan
Jan 26 at 7:46












$begingroup$
@MohammadZuhairKhan I think the OP is leaving out all numbers in which the digit $4$ occurs. That's why he skips from $39$ to $50.$
$endgroup$
– saulspatz
Jan 26 at 9:24






$begingroup$
@MohammadZuhairKhan I think the OP is leaving out all numbers in which the digit $4$ occurs. That's why he skips from $39$ to $50.$
$endgroup$
– saulspatz
Jan 26 at 9:24












2 Answers
2






active

oldest

votes


















1












$begingroup$

I'll do an example. You can elaborate it into an algorithm. Which floor has number $7619?$



The way to approach this is to count how many floors we skip. Call $10$ consecutive two-digit numbers where the first ends in $1$ and the last in $0$ a "decade." Similarly define a "century" and a "millennium." In a decade that starts with $4$ we skip $10$ numbers, and in a decade that doesn't start with $4$ we skip $1$ number, so in a century that doesn't start with $4$ we skip $19$ numbers and in a millennium that doesn't start with $4$ we skip $100+9cdot19=271$ numbers.



Now back to $7619.$ There are $7$ millennia up to $7000$. In one of them we skip $1000$ number and in $6$ of them we skip $271$ giving $2626.$ Now we have to figure out how many are skipped from $7001$ to $7619.$ This is clearly the same number that are skip from $1$ to $619$. There are $6$ centuries up to $600$ and in one of them we skip $100$ numbers, and in the other $5$ we skip $19$, making $195,$ and a total of $2821$ so far. Now we have to count how many number are skipped from $601$ to $619$ which is the same as the number skipped from $1$ to $19$. We can apply the same idea and get $2,$ so that $2823$ numbers are skipped in all.



The final answer is $7619-2823=4796$






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    I found a better answer. The floor number are in basically in base-9 as it never uses one number (0-3 and 5-9) where as the number of floors is in base-10 (0-9) because it uses all decimal digits.



    We convert the floor number to proper base-9 number decrementing all digits that are greater than 4 by 1. Once you have a base-9 number , convert it to base-10.
    Eg. Floor-number : 56
    Base -9. : 45
    Base-10 (Ans): 41






    share|cite|improve this answer









    $endgroup$













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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      1












      $begingroup$

      I'll do an example. You can elaborate it into an algorithm. Which floor has number $7619?$



      The way to approach this is to count how many floors we skip. Call $10$ consecutive two-digit numbers where the first ends in $1$ and the last in $0$ a "decade." Similarly define a "century" and a "millennium." In a decade that starts with $4$ we skip $10$ numbers, and in a decade that doesn't start with $4$ we skip $1$ number, so in a century that doesn't start with $4$ we skip $19$ numbers and in a millennium that doesn't start with $4$ we skip $100+9cdot19=271$ numbers.



      Now back to $7619.$ There are $7$ millennia up to $7000$. In one of them we skip $1000$ number and in $6$ of them we skip $271$ giving $2626.$ Now we have to figure out how many are skipped from $7001$ to $7619.$ This is clearly the same number that are skip from $1$ to $619$. There are $6$ centuries up to $600$ and in one of them we skip $100$ numbers, and in the other $5$ we skip $19$, making $195,$ and a total of $2821$ so far. Now we have to count how many number are skipped from $601$ to $619$ which is the same as the number skipped from $1$ to $19$. We can apply the same idea and get $2,$ so that $2823$ numbers are skipped in all.



      The final answer is $7619-2823=4796$






      share|cite|improve this answer









      $endgroup$


















        1












        $begingroup$

        I'll do an example. You can elaborate it into an algorithm. Which floor has number $7619?$



        The way to approach this is to count how many floors we skip. Call $10$ consecutive two-digit numbers where the first ends in $1$ and the last in $0$ a "decade." Similarly define a "century" and a "millennium." In a decade that starts with $4$ we skip $10$ numbers, and in a decade that doesn't start with $4$ we skip $1$ number, so in a century that doesn't start with $4$ we skip $19$ numbers and in a millennium that doesn't start with $4$ we skip $100+9cdot19=271$ numbers.



        Now back to $7619.$ There are $7$ millennia up to $7000$. In one of them we skip $1000$ number and in $6$ of them we skip $271$ giving $2626.$ Now we have to figure out how many are skipped from $7001$ to $7619.$ This is clearly the same number that are skip from $1$ to $619$. There are $6$ centuries up to $600$ and in one of them we skip $100$ numbers, and in the other $5$ we skip $19$, making $195,$ and a total of $2821$ so far. Now we have to count how many number are skipped from $601$ to $619$ which is the same as the number skipped from $1$ to $19$. We can apply the same idea and get $2,$ so that $2823$ numbers are skipped in all.



        The final answer is $7619-2823=4796$






        share|cite|improve this answer









        $endgroup$
















          1












          1








          1





          $begingroup$

          I'll do an example. You can elaborate it into an algorithm. Which floor has number $7619?$



          The way to approach this is to count how many floors we skip. Call $10$ consecutive two-digit numbers where the first ends in $1$ and the last in $0$ a "decade." Similarly define a "century" and a "millennium." In a decade that starts with $4$ we skip $10$ numbers, and in a decade that doesn't start with $4$ we skip $1$ number, so in a century that doesn't start with $4$ we skip $19$ numbers and in a millennium that doesn't start with $4$ we skip $100+9cdot19=271$ numbers.



          Now back to $7619.$ There are $7$ millennia up to $7000$. In one of them we skip $1000$ number and in $6$ of them we skip $271$ giving $2626.$ Now we have to figure out how many are skipped from $7001$ to $7619.$ This is clearly the same number that are skip from $1$ to $619$. There are $6$ centuries up to $600$ and in one of them we skip $100$ numbers, and in the other $5$ we skip $19$, making $195,$ and a total of $2821$ so far. Now we have to count how many number are skipped from $601$ to $619$ which is the same as the number skipped from $1$ to $19$. We can apply the same idea and get $2,$ so that $2823$ numbers are skipped in all.



          The final answer is $7619-2823=4796$






          share|cite|improve this answer









          $endgroup$



          I'll do an example. You can elaborate it into an algorithm. Which floor has number $7619?$



          The way to approach this is to count how many floors we skip. Call $10$ consecutive two-digit numbers where the first ends in $1$ and the last in $0$ a "decade." Similarly define a "century" and a "millennium." In a decade that starts with $4$ we skip $10$ numbers, and in a decade that doesn't start with $4$ we skip $1$ number, so in a century that doesn't start with $4$ we skip $19$ numbers and in a millennium that doesn't start with $4$ we skip $100+9cdot19=271$ numbers.



          Now back to $7619.$ There are $7$ millennia up to $7000$. In one of them we skip $1000$ number and in $6$ of them we skip $271$ giving $2626.$ Now we have to figure out how many are skipped from $7001$ to $7619.$ This is clearly the same number that are skip from $1$ to $619$. There are $6$ centuries up to $600$ and in one of them we skip $100$ numbers, and in the other $5$ we skip $19$, making $195,$ and a total of $2821$ so far. Now we have to count how many number are skipped from $601$ to $619$ which is the same as the number skipped from $1$ to $19$. We can apply the same idea and get $2,$ so that $2823$ numbers are skipped in all.



          The final answer is $7619-2823=4796$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 26 at 9:48









          saulspatzsaulspatz

          17k31435




          17k31435























              1












              $begingroup$

              I found a better answer. The floor number are in basically in base-9 as it never uses one number (0-3 and 5-9) where as the number of floors is in base-10 (0-9) because it uses all decimal digits.



              We convert the floor number to proper base-9 number decrementing all digits that are greater than 4 by 1. Once you have a base-9 number , convert it to base-10.
              Eg. Floor-number : 56
              Base -9. : 45
              Base-10 (Ans): 41






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                I found a better answer. The floor number are in basically in base-9 as it never uses one number (0-3 and 5-9) where as the number of floors is in base-10 (0-9) because it uses all decimal digits.



                We convert the floor number to proper base-9 number decrementing all digits that are greater than 4 by 1. Once you have a base-9 number , convert it to base-10.
                Eg. Floor-number : 56
                Base -9. : 45
                Base-10 (Ans): 41






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  I found a better answer. The floor number are in basically in base-9 as it never uses one number (0-3 and 5-9) where as the number of floors is in base-10 (0-9) because it uses all decimal digits.



                  We convert the floor number to proper base-9 number decrementing all digits that are greater than 4 by 1. Once you have a base-9 number , convert it to base-10.
                  Eg. Floor-number : 56
                  Base -9. : 45
                  Base-10 (Ans): 41






                  share|cite|improve this answer









                  $endgroup$



                  I found a better answer. The floor number are in basically in base-9 as it never uses one number (0-3 and 5-9) where as the number of floors is in base-10 (0-9) because it uses all decimal digits.



                  We convert the floor number to proper base-9 number decrementing all digits that are greater than 4 by 1. Once you have a base-9 number , convert it to base-10.
                  Eg. Floor-number : 56
                  Base -9. : 45
                  Base-10 (Ans): 41







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Jan 27 at 8:45









                  Ajinkya GawaliAjinkya Gawali

                  212




                  212






























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