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Hardcore Maths Question

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  • R Raj Lal

    Ok lets me be the first to ask a maths question Find a number which 1. divided by 10 gives a remainder 9 2. divided by 9 gives remainder 8 --- --- so on till divided by 2 gives a remainder 1 Any one ?

    Omit Needless Words - Strunk, William, Jr.


    Online Project Management
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    L Offline
    L Offline
    leppie
    wrote on last edited by
    #4

    2701439 last 4 digits by deduction, rest trial and error guess with 3/9 rule. :)

    **

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    **

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    • R Raj Lal

      Ok lets me be the first to ask a maths question Find a number which 1. divided by 10 gives a remainder 9 2. divided by 9 gives remainder 8 --- --- so on till divided by 2 gives a remainder 1 Any one ?

      Omit Needless Words - Strunk, William, Jr.


      Online Project Management
      Universal DBA | Ajax Rating | ExplorerTree

      J Offline
      J Offline
      Judah Gabriel Himango
      wrote on last edited by
      #5

      Provided I've understood the question correctly, I think I've solved it. I kind of cheated though; I wrote a C# program that solves this:

              int start = 1;
              int divisor = 10;
              while (divisor >= 2)
              {
                  if (start % divisor == divisor - 1)
                  {
                      divisor--;
                  }
                  else
                  {
                      start++;
                      divisor = 10;
                  }
              }
      

      Soon as that loop exits, you've got your number, which happens to be 2519.

      L R U 3 Replies Last reply
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      • J Judah Gabriel Himango

        Provided I've understood the question correctly, I think I've solved it. I kind of cheated though; I wrote a C# program that solves this:

                int start = 1;
                int divisor = 10;
                while (divisor >= 2)
                {
                    if (start % divisor == divisor - 1)
                    {
                        divisor--;
                    }
                    else
                    {
                        start++;
                        divisor = 10;
                    }
                }
        

        Soon as that loop exits, you've got your number, which happens to be 2519.

        L Offline
        L Offline
        leppie
        wrote on last edited by
        #6

        Judah Himango wrote:

        I kind of cheated.

        He did say "find a number" :) So there are more than one of these. I wonder if its some kind of series...

        **

        xacc.ide-0.2.0.50 - now with partial MSBuild support!

        **

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        • L leppie

          Judah Himango wrote:

          I kind of cheated.

          He did say "find a number" :) So there are more than one of these. I wonder if its some kind of series...

          **

          xacc.ide-0.2.0.50 - now with partial MSBuild support!

          **

          J Offline
          J Offline
          Judah Gabriel Himango
          wrote on last edited by
          #7

          yeah yeah :) Hey, I worked for it at least. :) *edit* oooh, misunderstood you there leppie. I though you were chiding me for solving it with code rather than brain. :) Yes, there are other numbers, it appears every 2520 iteration matches the criteria.

          Tech, life, family, faith: Give me a visit. I'm currently blogging about: Messianic Instrumentals (with audio) The apostle Paul, modernly speaking: Epistles of Paul Judah Himango

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          • J Judah Gabriel Himango

            Provided I've understood the question correctly, I think I've solved it. I kind of cheated though; I wrote a C# program that solves this:

                    int start = 1;
                    int divisor = 10;
                    while (divisor >= 2)
                    {
                        if (start % divisor == divisor - 1)
                        {
                            divisor--;
                        }
                        else
                        {
                            start++;
                            divisor = 10;
                        }
                    }
            

            Soon as that loop exits, you've got your number, which happens to be 2519.

            R Offline
            R Offline
            Raj Lal
            wrote on last edited by
            #8

            Judah Himango wrote:

            I kind of cheated though

            well thats ok , and of course there are more numbers but the fun is when you deduce how to do it It's the journey, not the destination

            Omit Needless Words - Strunk, William, Jr.


            Online Project Management
            Universal DBA | Ajax Rating | ExplorerTree

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            • L leppie

              Judah Himango wrote:

              I kind of cheated.

              He did say "find a number" :) So there are more than one of these. I wonder if its some kind of series...

              **

              xacc.ide-0.2.0.50 - now with partial MSBuild support!

              **

              R Offline
              R Offline
              Raj Lal
              wrote on last edited by
              #9

              yes thats true there are many , but if you think it might take a day to get the solution , without any computer help, but its worth

              Omit Needless Words - Strunk, William, Jr.


              Online Project Management
              Universal DBA | Ajax Rating | ExplorerTree

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              • J Judah Gabriel Himango

                yeah yeah :) Hey, I worked for it at least. :) *edit* oooh, misunderstood you there leppie. I though you were chiding me for solving it with code rather than brain. :) Yes, there are other numbers, it appears every 2520 iteration matches the criteria.

                Tech, life, family, faith: Give me a visit. I'm currently blogging about: Messianic Instrumentals (with audio) The apostle Paul, modernly speaking: Epistles of Paul Judah Himango

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                Paul Conrad
                wrote on last edited by
                #10

                There was a question of if there were more number, yes, there are. Here is a modification of your code that shows others :)

                #include using namespace std;

                int main()
                {
                int start = 1;
                int divisor = 10;
                while ( start <1000000 ) // Or whatevery you want in signed 32-bit range
                {
                while (divisor >= 2)
                {
                if (start % divisor == divisor - 1)
                {
                divisor--;
                }
                else
                {
                start++;
                divisor = 10;
                }
                }

                    cout<
                
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                • L leppie

                  Judah Himango wrote:

                  I kind of cheated.

                  He did say "find a number" :) So there are more than one of these. I wonder if its some kind of series...

                  **

                  xacc.ide-0.2.0.50 - now with partial MSBuild support!

                  **

                  J Offline
                  J Offline
                  Judah Gabriel Himango
                  wrote on last edited by
                  #11

                  leppie wrote:

                  I wonder if its some kind of series...

                  It appears to be every 2520.

                  Tech, life, family, faith: Give me a visit. I'm currently blogging about: Messianic Instrumentals (with audio) The apostle Paul, modernly speaking: Epistles of Paul Judah Himango

                  P U 2 Replies Last reply
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                  • L leppie

                    Judah Himango wrote:

                    I kind of cheated.

                    He did say "find a number" :) So there are more than one of these. I wonder if its some kind of series...

                    **

                    xacc.ide-0.2.0.50 - now with partial MSBuild support!

                    **

                    P Offline
                    P Offline
                    Paul Conrad
                    wrote on last edited by
                    #12

                    leppie wrote:

                    So there are more than one of these. I wonder if its some kind of series...

                    Take a look at the modification of Judah's code that I posted. Your number is one of the numbers that come up :)


                    I'd like to help but I am too lazy to Google it for you.

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                    • R Raj Lal

                      Judah Himango wrote:

                      I kind of cheated though

                      well thats ok , and of course there are more numbers but the fun is when you deduce how to do it It's the journey, not the destination

                      Omit Needless Words - Strunk, William, Jr.


                      Online Project Management
                      Universal DBA | Ajax Rating | ExplorerTree

                      J Offline
                      J Offline
                      Judah Gabriel Himango
                      wrote on last edited by
                      #13

                      Quartz... wrote:

                      It's the journey, not the destination

                      Very true. I actually had fun writing a little piece of code to solve it, though, so it was the journey even still. :) I added some more code that added each match to a list box on a Windows Form. Then, after seeing how it froze up the UI, I did it on a background thread. Still, the UI thread would get flooded with matches, almost preventing it from painting, so I further chagned the code to only update during app idle. Voila, cool little WinForms program that solves it. :cool:

                      Tech, life, family, faith: Give me a visit. I'm currently blogging about: Messianic Instrumentals (with audio) The apostle Paul, modernly speaking: Epistles of Paul Judah Himango

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                      • J Judah Gabriel Himango

                        leppie wrote:

                        I wonder if its some kind of series...

                        It appears to be every 2520.

                        Tech, life, family, faith: Give me a visit. I'm currently blogging about: Messianic Instrumentals (with audio) The apostle Paul, modernly speaking: Epistles of Paul Judah Himango

                        P Offline
                        P Offline
                        Paul Conrad
                        wrote on last edited by
                        #14

                        Judah Himango wrote:

                        It appears to be every 2520.

                        It is. Modifying the your code that I modified and posted, shows this to be true :)


                        I'd like to help but I am too lazy to Google it for you.

                        U 1 Reply Last reply
                        0
                        • J Judah Gabriel Himango

                          Quartz... wrote:

                          It's the journey, not the destination

                          Very true. I actually had fun writing a little piece of code to solve it, though, so it was the journey even still. :) I added some more code that added each match to a list box on a Windows Form. Then, after seeing how it froze up the UI, I did it on a background thread. Still, the UI thread would get flooded with matches, almost preventing it from painting, so I further chagned the code to only update during app idle. Voila, cool little WinForms program that solves it. :cool:

                          Tech, life, family, faith: Give me a visit. I'm currently blogging about: Messianic Instrumentals (with audio) The apostle Paul, modernly speaking: Epistles of Paul Judah Himango

                          P Offline
                          P Offline
                          Paul Conrad
                          wrote on last edited by
                          #15

                          Judah Himango wrote:

                          Voila, cool little WinForms program that solves it. :cool:

                          That's cool. Mine is just a plain boring console app :->


                          I'd like to help but I am too lazy to Google it for you.

                          U 1 Reply Last reply
                          0
                          • R Raj Lal

                            Ok lets me be the first to ask a maths question Find a number which 1. divided by 10 gives a remainder 9 2. divided by 9 gives remainder 8 --- --- so on till divided by 2 gives a remainder 1 Any one ?

                            Omit Needless Words - Strunk, William, Jr.


                            Online Project Management
                            Universal DBA | Ajax Rating | ExplorerTree

                            J Offline
                            J Offline
                            Jon Sagara
                            wrote on last edited by
                            #16

                            N(1) = 2519 N(2) = 2519 + 2520 = 5039 N(3) = 2519 + 2520 + 2520 = 7559 N(4) = 2519 + 2520 + 2520 + 2520 = 10079 ... N(n) = 2519 + (n - 1)*(2520) No idea what the heck it means, though. Care to enlighten us mathematically-challenged folks?

                            Jon Sagara When I grow up, I'm changing my name to Joe Kickass! My Site | My Blog | My Articles

                            L R U 4 Replies Last reply
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                            • J Jon Sagara

                              N(1) = 2519 N(2) = 2519 + 2520 = 5039 N(3) = 2519 + 2520 + 2520 = 7559 N(4) = 2519 + 2520 + 2520 + 2520 = 10079 ... N(n) = 2519 + (n - 1)*(2520) No idea what the heck it means, though. Care to enlighten us mathematically-challenged folks?

                              Jon Sagara When I grow up, I'm changing my name to Joe Kickass! My Site | My Blog | My Articles

                              L Offline
                              L Offline
                              leppie
                              wrote on last edited by
                              #17

                              Jon Sagara wrote:

                              N(n) = 2519 + (n - 1)*(2520)

                              N(n) = (n * 2520) - 1 = 2520n - 1

                              **

                              xacc.ide-0.2.0.50 - now with partial MSBuild support!

                              **

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                              • J Jon Sagara

                                N(1) = 2519 N(2) = 2519 + 2520 = 5039 N(3) = 2519 + 2520 + 2520 = 7559 N(4) = 2519 + 2520 + 2520 + 2520 = 10079 ... N(n) = 2519 + (n - 1)*(2520) No idea what the heck it means, though. Care to enlighten us mathematically-challenged folks?

                                Jon Sagara When I grow up, I'm changing my name to Joe Kickass! My Site | My Blog | My Articles

                                L Offline
                                L Offline
                                leppie
                                wrote on last edited by
                                #18

                                Some other interesting and useless observations:

                                1*2*3*4*5*6*7*8*9 is divisible by 2520 = 144
                                2520 is divisible by 2 * 3 * 5 * 7 = 12 (product of prime 1 - 9)
                                4 * 6 * 8 * 9 is divisible by 144 = 12 (product of 'non' prime 1 - 9)

                                :doh:

                                **

                                xacc.ide-0.2.0.50 - now with partial MSBuild support!

                                **

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                                • R Raj Lal

                                  Ok lets me be the first to ask a maths question Find a number which 1. divided by 10 gives a remainder 9 2. divided by 9 gives remainder 8 --- --- so on till divided by 2 gives a remainder 1 Any one ?

                                  Omit Needless Words - Strunk, William, Jr.


                                  Online Project Management
                                  Universal DBA | Ajax Rating | ExplorerTree

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                                  J Offline
                                  JenovaProject
                                  wrote on last edited by
                                  #19

                                  10! - 1 = 3628799. Its 1 less than a multiple of 1, 2, 3 ... 10.

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                                  • J JenovaProject

                                    10! - 1 = 3628799. Its 1 less than a multiple of 1, 2, 3 ... 10.

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                                    Ingo
                                    wrote on last edited by
                                    #20

                                    ((3628799 + 1) / 10) / (2 * 3 * 4 * 6) + (9 - 7 + 8 - 10) + 1 = 2519. ;)

                                    ------------------------------ PROST Roleplaying Game War doesn't determine who's right. War determines who's left.

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                                    • R Raj Lal

                                      Ok lets me be the first to ask a maths question Find a number which 1. divided by 10 gives a remainder 9 2. divided by 9 gives remainder 8 --- --- so on till divided by 2 gives a remainder 1 Any one ?

                                      Omit Needless Words - Strunk, William, Jr.


                                      Online Project Management
                                      Universal DBA | Ajax Rating | ExplorerTree

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                                      Bassam Abdul Baki
                                      wrote on last edited by
                                      #21

                                      x = (i - 1) (mod i), 2 ≤ i ≤ 10. Thus, x = LCM(2, 3, 4, 5, 6, 7, 8, 9, 10) * k + LCM(2, 3, 4, 5, 6, 7, 8, 9, 10) - 1 LCM(2, 3, 4, 5, 6, 7, 8, 9, 10) = LCM(5, 7, 8, 9) = 23.32.5.7 = 2520. Thus, x = 2520k + 2519. min(x) = 2519. I had to redo it since I did it backwards.


                                      "People who want to share their religious views with you almost never want you to share yours with them." - Anonymous Web - Blog - RSS - Math - LinkedIn

                                      Last modified: Thursday, July 27, 2006 12:08:26 PM --

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                                      • R Raj Lal

                                        Ok lets me be the first to ask a maths question Find a number which 1. divided by 10 gives a remainder 9 2. divided by 9 gives remainder 8 --- --- so on till divided by 2 gives a remainder 1 Any one ?

                                        Omit Needless Words - Strunk, William, Jr.


                                        Online Project Management
                                        Universal DBA | Ajax Rating | ExplorerTree

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                                        K Offline
                                        Kacee Giger
                                        wrote on last edited by
                                        #22

                                        I know I'm a little late (and a valid solution has already been given), but no real explanation has been made. You first need to find a number that is a multiple of all these multiples (10 * 9, 9 * 8, etc), then one less than that will give the proper remainders. So, to find the least common multiple, first break these into primes: 10 * 9 = 2 * 3 * 3 * 5, 9 * 8 = 2 * 2 * 2 * 3 * 3, 8 * 7 = 2 * 2 * 2 * 7, etc. Take out what is unique for each to get 2 * 2 * 2 * 3 * 3 * 5 * 7 = 2520. So, one answer (though you already know) to the original problem is 2519.

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                                        • J Jon Sagara

                                          N(1) = 2519 N(2) = 2519 + 2520 = 5039 N(3) = 2519 + 2520 + 2520 = 7559 N(4) = 2519 + 2520 + 2520 + 2520 = 10079 ... N(n) = 2519 + (n - 1)*(2520) No idea what the heck it means, though. Care to enlighten us mathematically-challenged folks?

                                          Jon Sagara When I grow up, I'm changing my name to Joe Kickass! My Site | My Blog | My Articles

                                          R Offline
                                          R Offline
                                          Raj Lal
                                          wrote on last edited by
                                          #23

                                          its the LCM of all the numbers (2520) - 1

                                          Omit Needless Words - Strunk, William, Jr.


                                          Online Project Management
                                          Universal DBA | Ajax Rating | ExplorerTree

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