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RE: [Mental Calculation] Can powers that end in powers be calculated?

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  • A.W.A.P. Bouman
    Good afternoon fellow calcualtors, The following number powered to 4 give 20736 at the end: 12, 12488, 12512, 24988, 25012, 37488, 37512, 49988, 50012, 62488,
    Message 1 of 9 , Jan 22, 2013
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      Good afternoon fellow calcualtors,



      The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
      24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
      87512, 99988.



      And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
      62816, 74684, 75316, 87184, 87816, 99684.



      Best regards,



      Willem Bouman







      Van: MentalCalculation@yahoogroups.com
      [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
      Verzonden: dinsdag 22 januari 2013 9:20
      Aan: MentalCalculation@yahoogroups.com
      Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
      calculated?





      Hello Daniel

      Great one- maybe some CPU power could help to find more curiosities like
      powers that end in squares or cubes? Can this be solved by mod arithmetics?

      Eg. which number powered can result in ...20736 at the end?

      --- In MentalCalculation@yahoogroups.com
      <mailto:MentalCalculation%40yahoogroups.com> , "dacastro93" wrote:
      >
      > Hi, Mr. Reto,
      >
      > He said in one of his videos that some number have these strange
      properties. One example is 18^12 that starts with 34^2 = 1156. I think that
      if we start looking deep into the numbers, we will find a lot of patterns,
      which would help us with the memorization process.
      >
      > Cheers,
      >
      > Daniel
      >
      > --- In MentalCalculation@yahoogroups.com
      <mailto:MentalCalculation%40yahoogroups.com> , "Retothejuggler" wrote:
      > >
      > > Hello Willem
      > >
      > > Thanks for your input. I guess there is another interesting fact, some
      numbers are coming up again and again but this only holds true for numbers
      ending in 5.
      > >
      > > The regular two digit endings do not come to regular left side
      begnnings, though :-).
      > >
      > > Kinders regards
      > >
      > > Reto
      > >
      > > --- In MentalCalculation@yahoogroups.com
      <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman" wrote:
      > > >
      > > > Good afternoon Reto,
      > > >
      > > >
      > > >
      > > > Although I am no clairvoyant, I have the feeling that the following is
      > > > meant, and who is concerned : there is a clear structure in the
      numbers when
      > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
      when
      > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
      41,
      > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
      some
      > > > experience one can feel what will come when powering and this can be
      very
      > > > helpful .
      > > >
      > > >
      > > >
      > > >
      > > >
      > > > Kindest regards,
      > > >
      > > >
      > > >
      > > >
      > > >
      > > > Willem Bouman
      > > >
      > > >
      > > >
      > > >
      > > >
      > > >
      > > >
      > > >
      > > >
      > > >
      > > >
      > > > Van: MentalCalculation@yahoogroups.com
      <mailto:MentalCalculation%40yahoogroups.com>
      > > > [mailto:MentalCalculation@yahoogroups.com
      <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
      > > > Verzonden: zaterdag 19 januari 2013 12:33
      > > > Aan: MentalCalculation@yahoogroups.com
      <mailto:MentalCalculation%40yahoogroups.com>
      > > > Onderwerp: [Mental Calculation] Relationships between powers?
      > > >
      > > >
      > > >
      > > >
      > > >
      > > > This one still puzzles me:
      > > >
      > > > "For example, knowing perfectly squares and cubes, he started to grasp
      the
      > > > relationships between powers and used this memorised knowledge to
      learn how
      > > > to raise numbers to new powers."
      > > >
      > > > What parts of numbers would you choose?
      > > >
      > > > Greetings from Switzerland
      > > >
      > > > Reto
      > > >
      > > >
      > > >
      > > >
      > > >
      > > > [Non-text portions of this message have been removed]
      > > >
      > >
      >





      [Non-text portions of this message have been removed]
    • dacastro93
      Hello, Mr. Bouman, These patterns keep showing...12512+12488=25000 How did you find these numbers? Does this work for any power? I also would like to know
      Message 2 of 9 , Jan 22, 2013
      • 0 Attachment
        Hello, Mr. Bouman,

        These patterns keep showing...12512+12488=25000

        How did you find these numbers? Does this work for any power?

        I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?

        Cheers,

        Daniel

        --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" wrote:
        >
        > Good afternoon fellow calcualtors,
        >
        >
        >
        > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
        > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
        > 87512, 99988.
        >
        >
        >
        > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
        > 62816, 74684, 75316, 87184, 87816, 99684.
        >
        >
        >
        > Best regards,
        >
        >
        >
        > Willem Bouman
        >
        >
        >
        >
        >
        >
        >
        > Van: MentalCalculation@yahoogroups.com
        > [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
        > Verzonden: dinsdag 22 januari 2013 9:20
        > Aan: MentalCalculation@yahoogroups.com
        > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
        > calculated?
        >
        >
        >
        >
        >
        > Hello Daniel
        >
        > Great one- maybe some CPU power could help to find more curiosities like
        > powers that end in squares or cubes? Can this be solved by mod arithmetics?
        >
        > Eg. which number powered can result in ...20736 at the end?
        >
        > --- In MentalCalculation@yahoogroups.com
        > , "dacastro93" wrote:
        > >
        > > Hi, Mr. Reto,
        > >
        > > He said in one of his videos that some number have these strange
        > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
        > if we start looking deep into the numbers, we will find a lot of patterns,
        > which would help us with the memorization process.
        > >
        > > Cheers,
        > >
        > > Daniel
        > >
        > > --- In MentalCalculation@yahoogroups.com
        > , "Retothejuggler" wrote:
        > > >
        > > > Hello Willem
        > > >
        > > > Thanks for your input. I guess there is another interesting fact, some
        > numbers are coming up again and again but this only holds true for numbers
        > ending in 5.
        > > >
        > > > The regular two digit endings do not come to regular left side
        > begnnings, though :-).
        > > >
        > > > Kinders regards
        > > >
        > > > Reto
        > > >
        > > > --- In MentalCalculation@yahoogroups.com
        > , "A.W.A.P. Bouman" wrote:
        > > > >
        > > > > Good afternoon Reto,
        > > > >
        > > > >
        > > > >
        > > > > Although I am no clairvoyant, I have the feeling that the following is
        > > > > meant, and who is concerned : there is a clear structure in the
        > numbers when
        > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
        > when
        > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
        > 41,
        > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
        > some
        > > > > experience one can feel what will come when powering and this can be
        > very
        > > > > helpful .
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > Kindest regards,
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > Willem Bouman
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > Van: MentalCalculation@yahoogroups.com
        >
        > > > > [mailto:MentalCalculation@yahoogroups.com
        > ] Namens Retothejuggler
        > > > > Verzonden: zaterdag 19 januari 2013 12:33
        > > > > Aan: MentalCalculation@yahoogroups.com
        >
        > > > > Onderwerp: [Mental Calculation] Relationships between powers?
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > This one still puzzles me:
        > > > >
        > > > > "For example, knowing perfectly squares and cubes, he started to grasp
        > the
        > > > > relationships between powers and used this memorised knowledge to
        > learn how
        > > > > to raise numbers to new powers."
        > > > >
        > > > > What parts of numbers would you choose?
        > > > >
        > > > > Greetings from Switzerland
        > > > >
        > > > > Reto
        > > > >
        > > > >
        > > > >
        > > > >
        > > > >
        > > > > [Non-text portions of this message have been removed]
        > > > >
        > > >
        > >
        >
        >
        >
        >
        >
        > [Non-text portions of this message have been removed]
        >
      • A.W.A.P. Bouman
        Hi, Daniel, Well for 100^100 you do not need software, I suppose J. To be more serious: indeed there exists software for this kind of questions: academic
        Message 3 of 9 , Jan 22, 2013
        • 0 Attachment
          Hi, Daniel,



          Well for 100^100 you do not need software, I suppose J.



          To be more serious: indeed there exists software for this kind of questions: academic calculation programs, which will be very expensive and surely exceed the money you have in your purse, I have even heard of € 3.200!



          And indeed: you discovered the pattern. There is much, very much more to say about this. The world of the structure in the numbers is a magic world!! I am busy with describing my knowledge in my PC, momentally it concerns Modulo Calculation, very very interesting. Powering will certainly also be described, I have not yet a plan. After having finished the Modulo Calculation I could start with powering. The way I’ll publish this and when its all still in the stars.



          Best regards,



          Willem Bouman







          Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
          Verzonden: dinsdag 22 januari 2013 16:48
          Aan: MentalCalculation@yahoogroups.com
          Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?





          Hello, Mr. Bouman,

          These patterns keep showing...12512+12488=25000

          How did you find these numbers? Does this work for any power?

          I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?

          Cheers,

          Daniel

          --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman" wrote:
          >
          > Good afternoon fellow calcualtors,
          >
          >
          >
          > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
          > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
          > 87512, 99988.
          >
          >
          >
          > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
          > 62816, 74684, 75316, 87184, 87816, 99684.
          >
          >
          >
          > Best regards,
          >
          >
          >
          > Willem Bouman
          >
          >
          >
          >
          >
          >
          >
          > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
          > Verzonden: dinsdag 22 januari 2013 9:20
          > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
          > calculated?
          >
          >
          >
          >
          >
          > Hello Daniel
          >
          > Great one- maybe some CPU power could help to find more curiosities like
          > powers that end in squares or cubes? Can this be solved by mod arithmetics?
          >
          > Eg. which number powered can result in ...20736 at the end?
          >
          > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          > , "dacastro93" wrote:
          > >
          > > Hi, Mr. Reto,
          > >
          > > He said in one of his videos that some number have these strange
          > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
          > if we start looking deep into the numbers, we will find a lot of patterns,
          > which would help us with the memorization process.
          > >
          > > Cheers,
          > >
          > > Daniel
          > >
          > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          > , "Retothejuggler" wrote:
          > > >
          > > > Hello Willem
          > > >
          > > > Thanks for your input. I guess there is another interesting fact, some
          > numbers are coming up again and again but this only holds true for numbers
          > ending in 5.
          > > >
          > > > The regular two digit endings do not come to regular left side
          > begnnings, though :-).
          > > >
          > > > Kinders regards
          > > >
          > > > Reto
          > > >
          > > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          > , "A.W.A.P. Bouman" wrote:
          > > > >
          > > > > Good afternoon Reto,
          > > > >
          > > > >
          > > > >
          > > > > Although I am no clairvoyant, I have the feeling that the following is
          > > > > meant, and who is concerned : there is a clear structure in the
          > numbers when
          > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
          > when
          > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
          > 41,
          > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
          > some
          > > > > experience one can feel what will come when powering and this can be
          > very
          > > > > helpful .
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > > Kindest regards,
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > > Willem Bouman
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          >
          > > > > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          > ] Namens Retothejuggler
          > > > > Verzonden: zaterdag 19 januari 2013 12:33
          > > > > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
          >
          > > > > Onderwerp: [Mental Calculation] Relationships between powers?
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > > This one still puzzles me:
          > > > >
          > > > > "For example, knowing perfectly squares and cubes, he started to grasp
          > the
          > > > > relationships between powers and used this memorised knowledge to
          > learn how
          > > > > to raise numbers to new powers."
          > > > >
          > > > > What parts of numbers would you choose?
          > > > >
          > > > > Greetings from Switzerland
          > > > >
          > > > > Reto
          > > > >
          > > > >
          > > > >
          > > > >
          > > > >
          > > > > [Non-text portions of this message have been removed]
          > > > >
          > > >
          > >
          >
          >
          >
          >
          >
          > [Non-text portions of this message have been removed]
          >





          [Non-text portions of this message have been removed]
        • dacastro93
          Do you plan to publish in english? Cheers, Daniel
          Message 4 of 9 , Jan 22, 2013
          • 0 Attachment
            Do you plan to publish in english?

            Cheers,

            Daniel

            --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" wrote:
            >
            > Hi, Daniel,
            >
            >
            >
            > Well for 100^100 you do not need software, I suppose J.
            >
            >
            >
            > To be more serious: indeed there exists software for this kind of questions: academic calculation programs, which will be very expensive and surely exceed the money you have in your purse, I have even heard of € 3.200!
            >
            >
            >
            > And indeed: you discovered the pattern. There is much, very much more to say about this. The world of the structure in the numbers is a magic world!! I am busy with describing my knowledge in my PC, momentally it concerns Modulo Calculation, very very interesting. Powering will certainly also be described, I have not yet a plan. After having finished the Modulo Calculation I could start with powering. The way I’ll publish this and when its all still in the stars.
            >
            >
            >
            > Best regards,
            >
            >
            >
            > Willem Bouman
            >
            >
            >
            >
            >
            >
            >
            > Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
            > Verzonden: dinsdag 22 januari 2013 16:48
            > Aan: MentalCalculation@yahoogroups.com
            > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?
            >
            >
            >
            >
            >
            > Hello, Mr. Bouman,
            >
            > These patterns keep showing...12512+12488=25000
            >
            > How did you find these numbers? Does this work for any power?
            >
            > I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?
            >
            > Cheers,
            >
            > Daniel
            >
            > --- In MentalCalculation@yahoogroups.com , "A.W.A.P. Bouman" wrote:
            > >
            > > Good afternoon fellow calcualtors,
            > >
            > >
            > >
            > > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
            > > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
            > > 87512, 99988.
            > >
            > >
            > >
            > > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
            > > 62816, 74684, 75316, 87184, 87816, 99684.
            > >
            > >
            > >
            > > Best regards,
            > >
            > >
            > >
            > > Willem Bouman
            > >
            > >
            > >
            > >
            > >
            > >
            > >
            > > Van: MentalCalculation@yahoogroups.com
            > > [mailto:MentalCalculation@yahoogroups.com ] Namens Retothejuggler
            > > Verzonden: dinsdag 22 januari 2013 9:20
            > > Aan: MentalCalculation@yahoogroups.com
            > > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
            > > calculated?
            > >
            > >
            > >
            > >
            > >
            > > Hello Daniel
            > >
            > > Great one- maybe some CPU power could help to find more curiosities like
            > > powers that end in squares or cubes? Can this be solved by mod arithmetics?
            > >
            > > Eg. which number powered can result in ...20736 at the end?
            > >
            > > --- In MentalCalculation@yahoogroups.com
            > > , "dacastro93" wrote:
            > > >
            > > > Hi, Mr. Reto,
            > > >
            > > > He said in one of his videos that some number have these strange
            > > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
            > > if we start looking deep into the numbers, we will find a lot of patterns,
            > > which would help us with the memorization process.
            > > >
            > > > Cheers,
            > > >
            > > > Daniel
            > > >
            > > > --- In MentalCalculation@yahoogroups.com
            > > , "Retothejuggler" wrote:
            > > > >
            > > > > Hello Willem
            > > > >
            > > > > Thanks for your input. I guess there is another interesting fact, some
            > > numbers are coming up again and again but this only holds true for numbers
            > > ending in 5.
            > > > >
            > > > > The regular two digit endings do not come to regular left side
            > > begnnings, though :-).
            > > > >
            > > > > Kinders regards
            > > > >
            > > > > Reto
            > > > >
            > > > > --- In MentalCalculation@yahoogroups.com
            > > , "A.W.A.P. Bouman" wrote:
            > > > > >
            > > > > > Good afternoon Reto,
            > > > > >
            > > > > >
            > > > > >
            > > > > > Although I am no clairvoyant, I have the feeling that the following is
            > > > > > meant, and who is concerned : there is a clear structure in the
            > > numbers when
            > > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
            > > when
            > > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
            > > 41,
            > > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
            > > some
            > > > > > experience one can feel what will come when powering and this can be
            > > very
            > > > > > helpful .
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > Kindest regards,
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > Willem Bouman
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > Van: MentalCalculation@yahoogroups.com
            > >
            > > > > > [mailto:MentalCalculation@yahoogroups.com
            > > ] Namens Retothejuggler
            > > > > > Verzonden: zaterdag 19 januari 2013 12:33
            > > > > > Aan: MentalCalculation@yahoogroups.com
            > >
            > > > > > Onderwerp: [Mental Calculation] Relationships between powers?
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > This one still puzzles me:
            > > > > >
            > > > > > "For example, knowing perfectly squares and cubes, he started to grasp
            > > the
            > > > > > relationships between powers and used this memorised knowledge to
            > > learn how
            > > > > > to raise numbers to new powers."
            > > > > >
            > > > > > What parts of numbers would you choose?
            > > > > >
            > > > > > Greetings from Switzerland
            > > > > >
            > > > > > Reto
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > >
            > > > > > [Non-text portions of this message have been removed]
            > > > > >
            > > > >
            > > >
            > >
            > >
            > >
            > >
            > >
            > > [Non-text portions of this message have been removed]
            > >
            >
            >
            >
            >
            >
            > [Non-text portions of this message have been removed]
            >
          • A.W.A.P. Bouman
            Hi Daniel, Yes English, form y Chinese is not so good. Willem Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens
            Message 5 of 9 , Jan 22, 2013
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              Hi Daniel,



              Yes English, form y Chinese is not so good.



              Willem



              Van: MentalCalculation@yahoogroups.com [mailto:MentalCalculation@yahoogroups.com] Namens dacastro93
              Verzonden: dinsdag 22 januari 2013 20:23
              Aan: MentalCalculation@yahoogroups.com
              Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?





              Do you plan to publish in english?

              Cheers,

              Daniel

              --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman" wrote:
              >
              > Hi, Daniel,
              >
              >
              >
              > Well for 100^100 you do not need software, I suppose J.
              >
              >
              >
              > To be more serious: indeed there exists software for this kind of questions: academic calculation programs, which will be very expensive and surely exceed the money you have in your purse, I have even heard of € 3.200!
              >
              >
              >
              > And indeed: you discovered the pattern. There is much, very much more to say about this. The world of the structure in the numbers is a magic world!! I am busy with describing my knowledge in my PC, momentally it concerns Modulo Calculation, very very interesting. Powering will certainly also be described, I have not yet a plan. After having finished the Modulo Calculation I could start with powering. The way I’ll publish this and when its all still in the stars.
              >
              >
              >
              > Best regards,
              >
              >
              >
              > Willem Bouman
              >
              >
              >
              >
              >
              >
              >
              > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> ] Namens dacastro93
              > Verzonden: dinsdag 22 januari 2013 16:48
              > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be calculated?
              >
              >
              >
              >
              >
              > Hello, Mr. Bouman,
              >
              > These patterns keep showing...12512+12488=25000
              >
              > How did you find these numbers? Does this work for any power?
              >
              > I also would like to know where can I find a software able to compute higher numbers like 100^100. Does somebody know?
              >
              > Cheers,
              >
              > Daniel
              >
              > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> , "A.W.A.P. Bouman" wrote:
              > >
              > > Good afternoon fellow calcualtors,
              > >
              > >
              > >
              > > The following number powered to 4 give 20736 at the end: 12, 12488, 12512,
              > > 24988, 25012, 37488, 37512, 49988, 50012, 62488, 62512, 74988, 75012, 87488,
              > > 87512, 99988.
              > >
              > >
              > >
              > > And: 316, 12184, 12816, 24684, 25316, 37184, 37816, 49684, 50316, 62184,
              > > 62816, 74684, 75316, 87184, 87816, 99684.
              > >
              > >
              > >
              > > Best regards,
              > >
              > >
              > >
              > > Willem Bouman
              > >
              > >
              > >
              > >
              > >
              > >
              > >
              > > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com> ] Namens Retothejuggler
              > > Verzonden: dinsdag 22 januari 2013 9:20
              > > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > > Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
              > > calculated?
              > >
              > >
              > >
              > >
              > >
              > > Hello Daniel
              > >
              > > Great one- maybe some CPU power could help to find more curiosities like
              > > powers that end in squares or cubes? Can this be solved by mod arithmetics?
              > >
              > > Eg. which number powered can result in ...20736 at the end?
              > >
              > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > > , "dacastro93" wrote:
              > > >
              > > > Hi, Mr. Reto,
              > > >
              > > > He said in one of his videos that some number have these strange
              > > properties. One example is 18^12 that starts with 34^2 = 1156. I think that
              > > if we start looking deep into the numbers, we will find a lot of patterns,
              > > which would help us with the memorization process.
              > > >
              > > > Cheers,
              > > >
              > > > Daniel
              > > >
              > > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > > , "Retothejuggler" wrote:
              > > > >
              > > > > Hello Willem
              > > > >
              > > > > Thanks for your input. I guess there is another interesting fact, some
              > > numbers are coming up again and again but this only holds true for numbers
              > > ending in 5.
              > > > >
              > > > > The regular two digit endings do not come to regular left side
              > > begnnings, though :-).
              > > > >
              > > > > Kinders regards
              > > > >
              > > > > Reto
              > > > >
              > > > > --- In MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > > , "A.W.A.P. Bouman" wrote:
              > > > > >
              > > > > > Good afternoon Reto,
              > > > > >
              > > > > >
              > > > > >
              > > > > > Although I am no clairvoyant, I have the feeling that the following is
              > > > > > meant, and who is concerned : there is a clear structure in the
              > > numbers when
              > > > > > powering. Let's take 3 and restrict ourselves to the 2 last digits
              > > when
              > > > > > powering. Then we get: 01, 03, 09, 27 81, 43, 29, 87, 61, 83, 49, 47,
              > > 41,
              > > > > > 23, 69, 07, 21, 63, 89, 67 and again: 01, 03. So afer having built up
              > > some
              > > > > > experience one can feel what will come when powering and this can be
              > > very
              > > > > > helpful .
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > > Kindest regards,
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > > Willem Bouman
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > > Van: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > >
              > > > > > [mailto:MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > > ] Namens Retothejuggler
              > > > > > Verzonden: zaterdag 19 januari 2013 12:33
              > > > > > Aan: MentalCalculation@yahoogroups.com <mailto:MentalCalculation%40yahoogroups.com>
              > >
              > > > > > Onderwerp: [Mental Calculation] Relationships between powers?
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > > This one still puzzles me:
              > > > > >
              > > > > > "For example, knowing perfectly squares and cubes, he started to grasp
              > > the
              > > > > > relationships between powers and used this memorised knowledge to
              > > learn how
              > > > > > to raise numbers to new powers."
              > > > > >
              > > > > > What parts of numbers would you choose?
              > > > > >
              > > > > > Greetings from Switzerland
              > > > > >
              > > > > > Reto
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > >
              > > > > > [Non-text portions of this message have been removed]
              > > > > >
              > > > >
              > > >
              > >
              > >
              > >
              > >
              > >
              > > [Non-text portions of this message have been removed]
              > >
              >
              >
              >
              >
              >
              > [Non-text portions of this message have been removed]
              >





              [Non-text portions of this message have been removed]
            • Gerald Newport
              Willem,   Please publish what you know and remember, neither of us is getting any younger.                     You have spent a lifetime adding to
              Message 6 of 9 , Jan 22, 2013
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                Willem,   Please publish what you know and remember, neither of us is getting any younger.                 

                   You have spent a lifetime adding to your natural talent. You will leave the world a great gift with a book of

                your knowledge about calculating.

                                                                                   Jerry Newport
              • Retothejuggler
                Dear Willem Thanks for your input. Can this be used for any power? Interesting... I`ll support a book and I`m sure other here as well. Respectful Reto
                Message 7 of 9 , Jan 23, 2013
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                  Dear Willem

                  Thanks for your input. Can this be used for any power? Interesting...

                  I`ll support a book and I`m sure other here as well.

                  Respectful

                  Reto

                  --- In MentalCalculation@yahoogroups.com, Gerald Newport wrote:
                  >
                  > Willem,   Please publish what you know and remember, neither of us is getting any younger.                 
                  >
                  >    You have spent a lifetime adding to your natural talent. You will leave the world a great gift with a book of
                  >
                  > your knowledge about calculating.
                  >
                  >                                                                    Jerry Newport
                  >
                • A.W.A.P. Bouman
                  Dear Gerald and Reto, Thank you for your encouraging words. I realise that I am getting older, to be precise: every day one piece. Describing what is going on
                  Message 8 of 9 , Jan 23, 2013
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                    Dear Gerald and Reto,



                    Thank you for your encouraging words. I realise that I am getting older, to
                    be precise: every day one piece. Describing what is going on in my curly
                    head will take a lot of time. I hope it will be granted to me by the Lord
                    Almighty.



                    Best regards,



                    Willem



                    Van: MentalCalculation@yahoogroups.com
                    [mailto:MentalCalculation@yahoogroups.com] Namens Retothejuggler
                    Verzonden: woensdag 23 januari 2013 10:13
                    Aan: MentalCalculation@yahoogroups.com
                    Onderwerp: Re: [Mental Calculation] Can powers that end in powers be
                    calculated?





                    Dear Willem

                    Thanks for your input. Can this be used for any power? Interesting...

                    I`ll support a book and I`m sure other here as well.

                    Respectful

                    Reto

                    --- In MentalCalculation@yahoogroups.com
                    <mailto:MentalCalculation%40yahoogroups.com> , Gerald Newport wrote:
                    >
                    > Willem, Please publish what you know and remember, neither of us is
                    getting any younger.
                    >
                    > You have spent a lifetime adding to your natural talent. You will leave
                    the world a great gift with a book of
                    >
                    > your knowledge about calculating.
                    >
                    > Jerry
                    Newport
                    >





                    [Non-text portions of this message have been removed]
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