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Can you find the numbers

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  • Mahesh
    Can you find the numbers asked here http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
    Message 1 of 18 , Jul 30, 2011
    • Jerry
      Mahesh, haven t found the numbers but I can tell you that both numbers are divisible by nine and therefore must be squares of numbers that are divisible by
      Message 2 of 18 , Aug 8, 2011
        Mahesh, haven't found the numbers but I can tell you that both numbers are divisible by nine and therefore must be squares of numbers that are divisible by three.

        I guess if I had my excel program I would print out the 7207 possible squares and scan for the answers. WIth a little tweaking, I could have Excel highlight all of the squares whose digits add up to 45 which must be the case here. The smallest possible square root is 10002 and the largest is 31620, neither of which work.

        Jerry Newport

        --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@...> wrote:
        >
        > Can you find the numbers asked here
        > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
        >
      • George Lane
        Hi folks.   It might also be worth noting that potential roots ending with 0 owuld not work either. They owuld have squares also ending in 0 (indeed
        Message 3 of 18 , Aug 10, 2011
          Hi folks.
           
          It might also be worth noting that potential roots ending with '0' owuld not work either. They owuld have squares also ending in '0' (indeed '00'), and so would not produce squares with the digits from 1 to 9 since two of the digits would be zeros. Just a thought.
           
          Best regards,
           
          George

          --- On Mon, 8/8/11, Jerry <wholphin48@...> wrote:


          From: Jerry <wholphin48@...>
          Subject: [Mental Calculation] Re: Can you find the numbers
          To: MentalCalculation@yahoogroups.com
          Date: Monday, 8 August, 2011, 21:31


           




          Mahesh, haven't found the numbers but I can tell you that both numbers are divisible by nine and therefore must be squares of numbers that are divisible by three.

          I guess if I had my excel program I would print out the 7207 possible squares and scan for the answers. WIth a little tweaking, I could have Excel highlight all of the squares whose digits add up to 45 which must be the case here. The smallest possible square root is 10002 and the largest is 31620, neither of which work.

          Jerry Newport

          --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@...> wrote:
          >
          > Can you find the numbers asked here
          > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
          >








          [Non-text portions of this message have been removed]
        • Jerry
          George, Thanks for adding that. It eliminates over 700 potential roots. You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc to the
          Message 4 of 18 , Aug 10, 2011
            George, Thanks for adding that. It eliminates over 700 potential roots. You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc to the left of the square as anything containing two of the same digit will be ruled out. For example, squares of 10491 through 11088 are out as the squares will start with 121 or 122.

            Jerry Newport



            --- In MentalCalculation@yahoogroups.com, George Lane <george972453@...> wrote:
            >
            > Hi folks.
            >  
            > It might also be worth noting that potential roots ending with '0' owuld not work either. They owuld have squares also ending in '0' (indeed '00'), and so would not produce squares with the digits from 1 to 9 since two of the digits would be zeros. Just a thought.
            >  
            > Best regards,
            >  
            > George
            >
            > --- On Mon, 8/8/11, Jerry <wholphin48@...> wrote:
            >
            >
            > From: Jerry <wholphin48@...>
            > Subject: [Mental Calculation] Re: Can you find the numbers
            > To: MentalCalculation@yahoogroups.com
            > Date: Monday, 8 August, 2011, 21:31
            >
            >
            >  
            >
            >
            >
            >
            > Mahesh, haven't found the numbers but I can tell you that both numbers are divisible by nine and therefore must be squares of numbers that are divisible by three.
            >
            > I guess if I had my excel program I would print out the 7207 possible squares and scan for the answers. WIth a little tweaking, I could have Excel highlight all of the squares whose digits add up to 45 which must be the case here. The smallest possible square root is 10002 and the largest is 31620, neither of which work.
            >
            > Jerry Newport
            >
            > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
            > >
            > > Can you find the numbers asked here
            > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
            > >
            >
            >
            >
            >
            >
            >
            >
            >
            > [Non-text portions of this message have been removed]
            >
          • Jerry
            In my last post, I meant to write that with squares of numbers from 10491 through 11088, they either start with 11 or 121 or 122. But you can also eliminate
            Message 5 of 18 , Aug 10, 2011
              In my last post, I meant to write that with squares of numbers from 10491 through 11088, they either start with 11 or 121 or 122. But you can also eliminate 10002 through 10488 since they all start with 100, 101, 102, etc through 109 and no zeros are allowed in the final square.

              Jerry Newport
            • gmanchali@yahoo.com
              Sir Can you please suggest an easy method to find the cube of a 3 digit number.pl reply. I will be waiting Gururaj Sent from BlackBerry® on Airtel ... From:
              Message 6 of 18 , Aug 11, 2011
                Sir
                Can you please suggest an easy method to find the cube of a 3 digit number.pl reply. I will be waiting
                Gururaj
                Sent from BlackBerry� on Airtel

                -----Original Message-----
                From: "Jerry" <wholphin48@...>
                Sender: MentalCalculation@yahoogroups.com
                Date: Wed, 10 Aug 2011 18:13:02
                To: <MentalCalculation@yahoogroups.com>
                Reply-To: MentalCalculation@yahoogroups.com
                Subject: [Mental Calculation] Re: Can you find the numbers


                George, Thanks for adding that. It eliminates over 700 potential roots. You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc to the left of the square as anything containing two of the same digit will be ruled out. For example, squares of 10491 through 11088 are out as the squares will start with 121 or 122.

                Jerry Newport



                --- In MentalCalculation@yahoogroups.com, George Lane <george972453@...> wrote:
                >
                > Hi folks.
                > ��
                > It might also be worth noting that potential roots ending with '0' owuld not work either. They owuld have squares also ending in '0' (indeed '00'), and so would not produce squares with the digits from 1 to 9 since two of the digits would be zeros. Just a thought.
                > ��
                > Best regards,
                > ��
                > George
                >
                > --- On Mon, 8/8/11, Jerry <wholphin48@...> wrote:
                >
                >
                > From: Jerry <wholphin48@...>
                > Subject: [Mental Calculation] Re: Can you find the numbers
                > To: MentalCalculation@yahoogroups.com
                > Date: Monday, 8 August, 2011, 21:31
                >
                >
                > ��
                >
                >
                >
                >
                > Mahesh, haven't found the numbers but I can tell you that both numbers are divisible by nine and therefore must be squares of numbers that are divisible by three.
                >
                > I guess if I had my excel program I would print out the 7207 possible squares and scan for the answers. WIth a little tweaking, I could have Excel highlight all of the squares whose digits add up to 45 which must be the case here. The smallest possible square root is 10002 and the largest is 31620, neither of which work.
                >
                > Jerry Newport
                >
                > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                > >
                > > Can you find the numbers asked here
                > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                > >
                >
                >
                >
                >
                >
                >
                >
                >
                > [Non-text portions of this message have been removed]
                >





                [Non-text portions of this message have been removed]
              • Mahesh
                Hi, This is a very famous problem and to my knowledge I feel this can be found thro trial and error method ; Since a perfect square can end only with 1, 4,5,6
                Message 7 of 18 , Aug 11, 2011
                  Hi,

                  This is a very famous problem and to my knowledge I feel this can be found thro'
                  trial and error method ; Since a perfect square can end only with 1, 4,5,6 and 9
                  the rest options can be discarded for the last digit options. I feel there can
                  be even more possibilities for reducing search space. may b need computer
                  programing to find out.


                  I am also told that a famous mathematician before the time of computer had found
                  the result to this.. so may be there could be some methods.. I wonder what
                  though .. If someone has an idea to it .. plz share..

                  Regards
                  Mahesh
                   
                   
                  Great men don't do different things but does things differently
                  --------------------------Mahesh




                  ________________________________
                  From: George Lane <george972453@...>
                  To: MentalCalculation@yahoogroups.com
                  Sent: Wed, 10 August, 2011 6:05:34 AM
                  Subject: Re: [Mental Calculation] Re: Can you find the numbers

                   
                  Hi folks.
                   
                  It might also be worth noting that potential roots ending with '0' owuld not
                  work either. They owuld have squares also ending in '0' (indeed '00'), and so
                  would not produce squares with the digits from 1 to 9 since two of the digits
                  would be zeros. Just a thought.
                   
                  Best regards,
                   
                  George

                  --- On Mon, 8/8/11, Jerry <wholphin48@...> wrote:

                  From: Jerry <wholphin48@...>
                  Subject: [Mental Calculation] Re: Can you find the numbers
                  To: MentalCalculation@yahoogroups.com
                  Date: Monday, 8 August, 2011, 21:31

                   

                  Mahesh, haven't found the numbers but I can tell you that both numbers are
                  divisible by nine and therefore must be squares of numbers that are divisible by
                  three.


                  I guess if I had my excel program I would print out the 7207 possible squares
                  and scan for the answers. WIth a little tweaking, I could have Excel highlight
                  all of the squares whose digits add up to 45 which must be the case here. The
                  smallest possible square root is 10002 and the largest is 31620, neither of
                  which work.


                  Jerry Newport

                  --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@...> wrote:
                  >
                  > Can you find the numbers asked here
                  > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                  >

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




                  [Non-text portions of this message have been removed]
                • George Lane
                  Hi Gururaj,   As long as you don t mind finding (or perhaps remembering) the square of a two-digit number, along with a few likewise simple & straightforward
                  Message 8 of 18 , Aug 12, 2011
                    Hi Gururaj,
                     
                    As long as you don't mind finding (or perhaps remembering) the square of a two-digit number, along with a few likewise simple & straightforward elements, here's how I do it:
                     
                    A three-digit number can be treated as a two-digit number followed by a single digit. Take the square of the two-digit number, add a zero on the end, then add twice the two-digit number multiplied by the single digit, add another zero to the end, then finally add the square of the single digit.
                     
                    Example: Finding the square of 358.
                     
                    1. This number is split into 35 and 8.
                    2. 35 squared is 1225
                    3. Followed by a zero, this becomes 12250
                    4. 35x8=280, and 2x280=560. Adding this gives us 12810.
                    5. Placing another zero gives us 128100
                    6. The square of 8 is 64; adding this gives us our final answer of 128164.
                     
                    Please let me know if you would like me to simplify this further; however I have already given my method for finding the square of a two-digit number in a very recent post.
                     
                    Best regards,
                     
                    George


                    --- On Thu, 11/8/11, gmanchali@... <gmanchali@...> wrote:


                    From: gmanchali@... <gmanchali@...>
                    Subject: Re: [Mental Calculation] Re: Can you find the numbers
                    To: MentalCalculation@yahoogroups.com
                    Date: Thursday, 11 August, 2011, 14:17


                    Sir
                    Can you please suggest an easy method to find the cube of a 3 digit number.pl reply. I will be waiting
                    Gururaj
                    Sent from BlackBerry® on Airtel

                    -----Original Message-----
                    From: "Jerry" <wholphin48@...>
                    Sender: MentalCalculation@yahoogroups.com
                    Date: Wed, 10 Aug 2011 18:13:02
                    To: <MentalCalculation@yahoogroups.com>
                    Reply-To: MentalCalculation@yahoogroups.com
                    Subject: [Mental Calculation] Re: Can you find the numbers


                          George, Thanks for adding that. It eliminates over 700 potential roots. You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc to the left of the square as anything containing two of the same digit will be ruled out. For example, squares of 10491 through 11088 are out as the squares will start with 121 or 122.

                                                                  Jerry Newport



                    --- In MentalCalculation@yahoogroups.com, George Lane <george972453@...> wrote:
                    >
                    > Hi folks.
                    >  
                    > It might also be worth noting that potential roots ending with '0' owuld not work either. They owuld have squares also ending in '0' (indeed '00'), and so would not produce squares with the digits from 1 to 9 since two of the digits would be zeros. Just a thought.
                    >  
                    > Best regards,
                    >  
                    > George
                    >
                    > --- On Mon, 8/8/11, Jerry <wholphin48@...> wrote:
                    >
                    >
                    > From: Jerry <wholphin48@...>
                    > Subject: [Mental Calculation] Re: Can you find the numbers
                    > To: MentalCalculation@yahoogroups.com
                    > Date: Monday, 8 August, 2011, 21:31
                    >
                    >
                    >  
                    >
                    >
                    >
                    >
                    > Mahesh, haven't found the numbers but I can tell you that both numbers are divisible by nine and therefore must be squares of numbers that are divisible by three.
                    >
                    > I guess if I had my excel program I would print out the 7207 possible squares and scan for the answers. WIth a little tweaking, I could have Excel highlight all of the squares whose digits add up to 45 which must be the case here. The smallest possible square root is 10002 and the largest is 31620, neither of which work.
                    >
                    > Jerry Newport
                    >
                    > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                    > >
                    > > Can you find the numbers asked here
                    > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                    > >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    >
                    > [Non-text portions of this message have been removed]
                    >





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



                    ------------------------------------


                    Yahoo! Groups Links





                    [Non-text portions of this message have been removed]
                  • Medha Singh
                    Let us find out square of 358 using (a+b)^2  (a+b)^2 = a^2 + 2ab + b^2 Consider 35 as a and 8 as b Start from the Right--- I have written the intermediate
                    Message 9 of 18 , Aug 12, 2011
                      Let us find out square of 358 using (a+b)^2 

                      (a+b)^2 = a^2 + 2ab + b^2

                      Consider 35 as "a" and 8 as "b"

                      Start from the Right--- I have written the intermediate step below


                      1225/560/64

                      You can write directly:
                      128164

                      Visit http://www.magicalmethods.com to get a lot more.


                      Medha



                      ________________________________
                      From: George Lane <george972453@...>
                      To: MentalCalculation@yahoogroups.com
                      Sent: Friday, August 12, 2011 2:48 PM
                      Subject: Re: [Mental Calculation] Re: Can you find the numbers


                       
                      Hi Gururaj,
                       
                      As long as you don't mind finding (or perhaps remembering) the square of a two-digit number, along with a few likewise simple & straightforward elements, here's how I do it:
                       
                      A three-digit number can be treated as a two-digit number followed by a single digit. Take the square of the two-digit number, add a zero on the end, then add twice the two-digit number multiplied by the single digit, add another zero to the end, then finally add the square of the single digit.
                       
                      Example: Finding the square of 358.
                       
                      1. This number is split into 35 and 8.
                      2. 35 squared is 1225
                      3. Followed by a zero, this becomes 12250
                      4. 35x8=280, and 2x280=560. Adding this gives us 12810.
                      5. Placing another zero gives us 128100
                      6. The square of 8 is 64; adding this gives us our final answer of 128164.
                       
                      Please let me know if you would like me to simplify this further; however I have already given my method for finding the square of a two-digit number in a very recent post.
                       
                      Best regards,
                       
                      George

                      --- On Thu, 11/8/11, gmanchali@... <gmanchali@...> wrote:

                      From: gmanchali@... <gmanchali@...>
                      Subject: Re: [Mental Calculation] Re: Can you find the numbers
                      To: MentalCalculation@yahoogroups.com
                      Date: Thursday, 11 August, 2011, 14:17

                      Sir
                      Can you please suggest an easy method to find the cube of a 3 digit number.pl reply. I will be waiting
                      Gururaj
                      Sent from BlackBerry® on Airtel

                      -----Original Message-----
                      From: "Jerry" <wholphin48@...>
                      Sender: MentalCalculation@yahoogroups.com
                      Date: Wed, 10 Aug 2011 18:13:02
                      To: <MentalCalculation@yahoogroups.com>
                      Reply-To: MentalCalculation@yahoogroups.com
                      Subject: [Mental Calculation] Re: Can you find the numbers

                            George, Thanks for adding that. It eliminates over 700 potential roots. You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc to the left of the square as anything containing two of the same digit will be ruled out. For example, squares of 10491 through 11088 are out as the squares will start with 121 or 122.

                                                                    Jerry Newport

                      --- In MentalCalculation@yahoogroups.com, George Lane <george972453@...> wrote:
                      >
                      > Hi folks.
                      >  
                      > It might also be worth noting that potential roots ending with '0' owuld not work either. They owuld have squares also ending in '0' (indeed '00'), and so would not produce squares with the digits from 1 to 9 since two of the digits would be zeros. Just a thought.
                      >  
                      > Best regards,
                      >  
                      > George
                      >
                      > --- On Mon, 8/8/11, Jerry <wholphin48@...> wrote:
                      >
                      >
                      > From: Jerry <wholphin48@...>
                      > Subject: [Mental Calculation] Re: Can you find the numbers
                      > To: MentalCalculation@yahoogroups.com
                      > Date: Monday, 8 August, 2011, 21:31
                      >
                      >
                      >  
                      >
                      >
                      >
                      >
                      > Mahesh, haven't found the numbers but I can tell you that both numbers are divisible by nine and therefore must be squares of numbers that are divisible by three.
                      >
                      > I guess if I had my excel program I would print out the 7207 possible squares and scan for the answers. WIth a little tweaking, I could have Excel highlight all of the squares whose digits add up to 45 which must be the case here. The smallest possible square root is 10002 and the largest is 31620, neither of which work.
                      >
                      > Jerry Newport
                      >
                      > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                      > >
                      > > Can you find the numbers asked here
                      > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                      > >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      >
                      > [Non-text portions of this message have been removed]
                      >

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

                      ------------------------------------

                      Yahoo! Groups Links

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




                      [Non-text portions of this message have been removed]
                    • Oleg Stepanov
                      MS Let us find out square of 358 using (a+b)^2  MS (a+b)^2 = a^2 + 2ab + b^2 MS Consider 35 as a and 8 as b MS Start from the Right--- I have written
                      Message 10 of 18 , Aug 12, 2011
                        MS> Let us find out square of 358 using (a+b)^2 
                        MS> (a+b)^2 = a^2 + 2ab + b^2
                        MS> Consider 35 as "a" and 8 as "b"
                        MS> Start from the Right--- I have written the intermediate step below
                        MS> 1225/560/64
                        MS> You can write directly:
                        MS> 128164

                        358x358 = (358+42)x(358-42)+42x42 = 400x316+1764 = 126400+1764 = 128164

                        Sincerely Yours, Oleg Stepanov.
                        http://stepanov.lk.net/
                      • Mahesh
                         Dear Gururaj, Try this method... http://maths-4-fun.blogspot.com/2011/08/cube-of-3-digit-number-ending-in-1.html Great men don t do different things but does
                        Message 11 of 18 , Aug 12, 2011
                           Dear Gururaj,

                          Try this method...
                          http://maths-4-fun.blogspot.com/2011/08/cube-of-3-digit-number-ending-in-1.html

                          Great men don't do different things but does things differently
                          --------------------------Mahesh




                          ________________________________
                          From: "gmanchali@..." <gmanchali@...>
                          To: MentalCalculation@yahoogroups.com
                          Sent: Thu, 11 August, 2011 6:17:39 AM
                          Subject: Re: [Mental Calculation] Re: Can you find the numbers

                          Sir
                          Can you please suggest an easy method to find the cube of a 3 digit number.pl
                          reply. I will be waiting
                          Gururaj
                          Sent from BlackBerry® on Airtel

                          -----Original Message-----
                          From: "Jerry" <wholphin48@...>
                          Sender: MentalCalculation@yahoogroups.com
                          Date: Wed, 10 Aug 2011 18:13:02
                          To: <MentalCalculation@yahoogroups.com>
                          Reply-To: MentalCalculation@yahoogroups.com
                          Subject: [Mental Calculation] Re: Can you find the numbers


                                George, Thanks for adding that. It eliminates over 700 potential roots.
                          You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc
                          to the left of the square as anything containing two of the same digit will be
                          ruled out. For example, squares of 10491 through 11088 are out as the squares
                          will start with 121 or 122.


                                                                        Jerry Newport



                          --- In MentalCalculation@yahoogroups.com, George Lane <george972453@...> wrote:
                          >
                          > Hi folks.
                          >  
                          > It might also be worth noting that potential roots ending with '0' owuld not
                          >work either. They owuld have squares also ending in '0' (indeed '00'), and so
                          >would not produce squares with the digits from 1 to 9 since two of the digits
                          >would be zeros. Just a thought.
                          >  
                          > Best regards,
                          >  
                          > George
                          >
                          > --- On Mon, 8/8/11, Jerry <wholphin48@...> wrote:
                          >
                          >
                          > From: Jerry <wholphin48@...>
                          > Subject: [Mental Calculation] Re: Can you find the numbers
                          > To: MentalCalculation@yahoogroups.com
                          > Date: Monday, 8 August, 2011, 21:31
                          >
                          >
                          >  
                          >
                          >
                          >
                          >
                          > Mahesh, haven't found the numbers but I can tell you that both numbers are
                          >divisible by nine and therefore must be squares of numbers that are divisible by
                          >three.
                          >
                          >
                          > I guess if I had my excel program I would print out the 7207 possible squares
                          >and scan for the answers. WIth a little tweaking, I could have Excel highlight
                          >all of the squares whose digits add up to 45 which must be the case here. The
                          >smallest possible square root is 10002 and the largest is 31620, neither of
                          >which work.
                          >
                          >
                          > Jerry Newport
                          >
                          > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                          > >
                          > > Can you find the numbers asked here
                          > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                          > >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          > [Non-text portions of this message have been removed]
                          >





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



                          ------------------------------------


                          Yahoo! Groups Links



                          [Non-text portions of this message have been removed]
                        • Jerry
                          The square of 11826 is 139854276 The square of 12363 is 152843769 each square uses 1-9 only one time. However, I forget if zero is also supposed to
                          Message 12 of 18 , Aug 13, 2011
                            The square of 11826 is 139854276 The square of 12363 is 152843769 each square uses 1-9 only one time. However, I forget if zero is also supposed to appear.

                            If that is so, it still seems that along the journey to a solution one can find some interesting almost-solutions.

                            BTW, the most trivial situation is for squaring a one digit number: One squared is equal to one which appears only once. However, for 2,3,4,5 and six there will not be any squares which use only one of any of those number of digits whether zero is also included or not.

                            Jerry Newport

                            --- In MentalCalculation@yahoogroups.com, Mahesh <maheshluvsu@...> wrote:
                            >
                            >
                            >  Dear Gururaj,
                            >
                            > Try this method...
                            > http://maths-4-fun.blogspot.com/2011/08/cube-of-3-digit-number-ending-in-1.html
                            >
                            > Great men don't do different things but does things differently
                            > --------------------------Mahesh
                            >
                            >
                            >
                            >
                            > ________________________________
                            > From: "gmanchali@..." <gmanchali@...>
                            > To: MentalCalculation@yahoogroups.com
                            > Sent: Thu, 11 August, 2011 6:17:39 AM
                            > Subject: Re: [Mental Calculation] Re: Can you find the numbers
                            >
                            > Sir
                            > Can you please suggest an easy method to find the cube of a 3 digit number.pl
                            > reply. I will be waiting
                            > Gururaj
                            > Sent from BlackBerry® on Airtel
                            >
                            > -----Original Message-----
                            > From: "Jerry" <wholphin48@...>
                            > Sender: MentalCalculation@yahoogroups.com
                            > Date: Wed, 10 Aug 2011 18:13:02
                            > To: <MentalCalculation@yahoogroups.com>
                            > Reply-To: MentalCalculation@yahoogroups.com
                            > Subject: [Mental Calculation] Re: Can you find the numbers
                            >
                            >
                            >       George, Thanks for adding that. It eliminates over 700 potential roots.
                            > You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc
                            > to the left of the square as anything containing two of the same digit will be
                            > ruled out. For example, squares of 10491 through 11088 are out as the squares
                            > will start with 121 or 122.
                            >
                            >
                            >                                               Jerry Newport
                            >
                            >
                            >
                            > --- In MentalCalculation@yahoogroups.com, George Lane <george972453@> wrote:
                            > >
                            > > Hi folks.
                            > >  
                            > > It might also be worth noting that potential roots ending with '0' owuld not
                            > >work either. They owuld have squares also ending in '0' (indeed '00'), and so
                            > >would not produce squares with the digits from 1 to 9 since two of the digits
                            > >would be zeros. Just a thought.
                            > >  
                            > > Best regards,
                            > >  
                            > > George
                            > >
                            > > --- On Mon, 8/8/11, Jerry <wholphin48@> wrote:
                            > >
                            > >
                            > > From: Jerry <wholphin48@>
                            > > Subject: [Mental Calculation] Re: Can you find the numbers
                            > > To: MentalCalculation@yahoogroups.com
                            > > Date: Monday, 8 August, 2011, 21:31
                            > >
                            > >
                            > >  
                            > >
                            > >
                            > >
                            > >
                            > > Mahesh, haven't found the numbers but I can tell you that both numbers are
                            > >divisible by nine and therefore must be squares of numbers that are divisible by
                            > >three.
                            > >
                            > >
                            > > I guess if I had my excel program I would print out the 7207 possible squares
                            > >and scan for the answers. WIth a little tweaking, I could have Excel highlight
                            > >all of the squares whose digits add up to 45 which must be the case here. The
                            > >smallest possible square root is 10002 and the largest is 31620, neither of
                            > >which work.
                            > >
                            > >
                            > > Jerry Newport
                            > >
                            > > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                            > > >
                            > > > Can you find the numbers asked here
                            > > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                            > > >
                            > >
                            > >
                            > >
                            > >
                            > >
                            > >
                            > >
                            > >
                            > > [Non-text portions of this message have been removed]
                            > >
                            >
                            >
                            >
                            >
                            >
                            > [Non-text portions of this message have been removed]
                            >
                            >
                            >
                            > ------------------------------------
                            >
                            >
                            > Yahoo! Groups Links
                            >
                            >
                            >
                            > [Non-text portions of this message have been removed]
                            >
                          • Mahesh
                            zero is not included.. In 11826, I think you got the lowest.. Great men don t do different things but does things differently ...
                            Message 13 of 18 , Aug 14, 2011
                              zero is not included.. In 11826, I think you got the lowest..



                              Great men don't do different things but does things differently
                              --------------------------Mahesh




                              ________________________________
                              From: Jerry <wholphin48@...>
                              To: MentalCalculation@yahoogroups.com
                              Sent: Sun, 14 August, 2011 1:11:16 AM
                              Subject: [Mental Calculation] Re: Can you find the numbers




                              The square of 11826 is 139854276 The square of 12363 is 152843769 each
                              square uses 1-9 only one time. However, I forget if zero is also supposed to
                              appear.

                              If that is so, it still seems that along the journey to a solution one can find
                              some interesting almost-solutions.

                              BTW, the most trivial situation is for squaring a one digit number: One squared
                              is equal to one which appears only once. However, for 2,3,4,5 and six there will
                              not be any squares which use only one of any of those number of digits whether
                              zero is also included or not.


                              Jerry Newport

                              --- In MentalCalculation@yahoogroups.com, Mahesh <maheshluvsu@...> wrote:
                              >
                              >
                              > Dear Gururaj,
                              >
                              > Try this method...
                              >
                              http://maths-4-fun.blogspot.com/2011/08/cube-of-3-digit-number-ending-in-1.html
                              >
                              > Great men don't do different things but does things differently
                              > --------------------------Mahesh
                              >
                              >
                              >
                              >
                              > ________________________________
                              > From: "gmanchali@..." <gmanchali@...>
                              > To: MentalCalculation@yahoogroups.com
                              > Sent: Thu, 11 August, 2011 6:17:39 AM
                              > Subject: Re: [Mental Calculation] Re: Can you find the numbers
                              >
                              > Sir
                              > Can you please suggest an easy method to find the cube of a 3 digit number.pl
                              > reply. I will be waiting
                              > Gururaj
                              > Sent from BlackBerry® on Airtel
                              >
                              > -----Original Message-----
                              > From: "Jerry" <wholphin48@...>
                              > Sender: MentalCalculation@yahoogroups.com
                              > Date: Wed, 10 Aug 2011 18:13:02
                              > To: <MentalCalculation@yahoogroups.com>
                              > Reply-To: MentalCalculation@yahoogroups.com
                              > Subject: [Mental Calculation] Re: Can you find the numbers
                              >
                              >
                              > George, Thanks for adding that. It eliminates over 700 potential roots.
                              > You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc
                              >
                              > to the left of the square as anything containing two of the same digit will be

                              > ruled out. For example, squares of 10491 through 11088 are out as the squares
                              > will start with 121 or 122.
                              >
                              >
                              > Jerry Newport
                              >
                              >
                              >
                              > --- In MentalCalculation@yahoogroups.com, George Lane <george972453@> wrote:
                              > >
                              > > Hi folks.
                              > > Â
                              > > It might also be worth noting that potential roots ending with '0' owuld not

                              > >work either. They owuld have squares also ending in '0' (indeed '00'), and so

                              > >would not produce squares with the digits from 1 to 9 since two of the digits

                              > >would be zeros. Just a thought.
                              > > Â
                              > > Best regards,
                              > > Â
                              > > George
                              > >
                              > > --- On Mon, 8/8/11, Jerry <wholphin48@> wrote:
                              > >
                              > >
                              > > From: Jerry <wholphin48@>
                              > > Subject: [Mental Calculation] Re: Can you find the numbers
                              > > To: MentalCalculation@yahoogroups.com
                              > > Date: Monday, 8 August, 2011, 21:31
                              > >
                              > >
                              > > Â
                              > >
                              > >
                              > >
                              > >
                              > > Mahesh, haven't found the numbers but I can tell you that both numbers are
                              > >divisible by nine and therefore must be squares of numbers that are divisible
                              >by
                              >
                              > >three.
                              > >
                              > >
                              > > I guess if I had my excel program I would print out the 7207 possible squares
                              >
                              > >and scan for the answers. WIth a little tweaking, I could have Excel highlight
                              >
                              > >all of the squares whose digits add up to 45 which must be the case here. The

                              > >smallest possible square root is 10002 and the largest is 31620, neither of
                              > >which work.
                              > >
                              > >
                              > > Jerry Newport
                              > >
                              > > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                              > > >
                              > > > Can you find the numbers asked here
                              > > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                              > > >
                              > >
                              > >
                              > >
                              > >
                              > >
                              > >
                              > >
                              > >
                              > > [Non-text portions of this message have been removed]
                              > >
                              >
                              >
                              >
                              >
                              >
                              > [Non-text portions of this message have been removed]
                              >
                              >
                              >
                              > ------------------------------------
                              >
                              >
                              > Yahoo! Groups Links
                              >
                              >
                              >
                              > [Non-text portions of this message have been removed]
                              >




                              [Non-text portions of this message have been removed]
                            • Jerry
                              Mahesh, Thanks for the clarification. As far as squares that only use 1-8 once, I have found four squares, 3678 5904 8559 and 9024 all produce squares that
                              Message 14 of 18 , Aug 14, 2011
                                Mahesh,

                                Thanks for the clarification. As far as squares that only use 1-8 once, I have found four squares, 3678 5904 8559 and 9024 all produce squares that use 1-8 only once.
                                The squares are 13527684 34857216 73356481 and 81432576

                                I have not found any squares that include only 1-7 one time each. For 1-6 and 1-5 there can be no solutions as the square has to be a multiple of three but not a multiple of nine. That is impossible since any integer which is a square and a multiple of three must also be a multiple of nine. For 1-4 or 1-3 it is easily shown that no squares exist either.

                                Thanks for a fun problem!!

                                Jerry Newport

                                --- In MentalCalculation@yahoogroups.com, Mahesh <maheshluvsu@...> wrote:
                                >
                                > zero is not included.. In 11826, I think you got the lowest..
                                >
                                >
                                >
                                > Great men don't do different things but does things differently
                                > --------------------------Mahesh
                                >
                                >
                                >
                                >
                                > ________________________________
                                > From: Jerry <wholphin48@...>
                                > To: MentalCalculation@yahoogroups.com
                                > Sent: Sun, 14 August, 2011 1:11:16 AM
                                > Subject: [Mental Calculation] Re: Can you find the numbers
                                >
                                >
                                >
                                >
                                > The square of 11826 is 139854276 The square of 12363 is 152843769 each
                                > square uses 1-9 only one time. However, I forget if zero is also supposed to
                                > appear.
                                >
                                > If that is so, it still seems that along the journey to a solution one can find
                                > some interesting almost-solutions.
                                >
                                > BTW, the most trivial situation is for squaring a one digit number: One squared
                                > is equal to one which appears only once. However, for 2,3,4,5 and six there will
                                > not be any squares which use only one of any of those number of digits whether
                                > zero is also included or not.
                                >
                                >
                                > Jerry Newport
                                >
                                > --- In MentalCalculation@yahoogroups.com, Mahesh <maheshluvsu@> wrote:
                                > >
                                > >
                                > > Dear Gururaj,
                                > >
                                > > Try this method...
                                > >
                                > http://maths-4-fun.blogspot.com/2011/08/cube-of-3-digit-number-ending-in-1.html
                                > >
                                > > Great men don't do different things but does things differently
                                > > --------------------------Mahesh
                                > >
                                > >
                                > >
                                > >
                                > > ________________________________
                                > > From: "gmanchali@" <gmanchali@>
                                > > To: MentalCalculation@yahoogroups.com
                                > > Sent: Thu, 11 August, 2011 6:17:39 AM
                                > > Subject: Re: [Mental Calculation] Re: Can you find the numbers
                                > >
                                > > Sir
                                > > Can you please suggest an easy method to find the cube of a 3 digit number.pl
                                > > reply. I will be waiting
                                > > Gururaj
                                > > Sent from BlackBerry® on Airtel
                                > >
                                > > -----Original Message-----
                                > > From: "Jerry" <wholphin48@>
                                > > Sender: MentalCalculation@yahoogroups.com
                                > > Date: Wed, 10 Aug 2011 18:13:02
                                > > To: <MentalCalculation@yahoogroups.com>
                                > > Reply-To: MentalCalculation@yahoogroups.com
                                > > Subject: [Mental Calculation] Re: Can you find the numbers
                                > >
                                > >
                                > > George, Thanks for adding that. It eliminates over 700 potential roots.
                                > > You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc
                                > >
                                > > to the left of the square as anything containing two of the same digit will be
                                >
                                > > ruled out. For example, squares of 10491 through 11088 are out as the squares
                                > > will start with 121 or 122.
                                > >
                                > >
                                > > Jerry Newport
                                > >
                                > >
                                > >
                                > > --- In MentalCalculation@yahoogroups.com, George Lane <george972453@> wrote:
                                > > >
                                > > > Hi folks.
                                > > > Â
                                > > > It might also be worth noting that potential roots ending with '0' owuld not
                                >
                                > > >work either. They owuld have squares also ending in '0' (indeed '00'), and so
                                >
                                > > >would not produce squares with the digits from 1 to 9 since two of the digits
                                >
                                > > >would be zeros. Just a thought.
                                > > > Â
                                > > > Best regards,
                                > > > Â
                                > > > George
                                > > >
                                > > > --- On Mon, 8/8/11, Jerry <wholphin48@> wrote:
                                > > >
                                > > >
                                > > > From: Jerry <wholphin48@>
                                > > > Subject: [Mental Calculation] Re: Can you find the numbers
                                > > > To: MentalCalculation@yahoogroups.com
                                > > > Date: Monday, 8 August, 2011, 21:31
                                > > >
                                > > >
                                > > > Â
                                > > >
                                > > >
                                > > >
                                > > >
                                > > > Mahesh, haven't found the numbers but I can tell you that both numbers are
                                > > >divisible by nine and therefore must be squares of numbers that are divisible
                                > >by
                                > >
                                > > >three.
                                > > >
                                > > >
                                > > > I guess if I had my excel program I would print out the 7207 possible squares
                                > >
                                > > >and scan for the answers. WIth a little tweaking, I could have Excel highlight
                                > >
                                > > >all of the squares whose digits add up to 45 which must be the case here. The
                                >
                                > > >smallest possible square root is 10002 and the largest is 31620, neither of
                                > > >which work.
                                > > >
                                > > >
                                > > > Jerry Newport
                                > > >
                                > > > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                                > > > >
                                > > > > Can you find the numbers asked here
                                > > > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                                > > > >
                                > > >
                                > > >
                                > > >
                                > > >
                                > > >
                                > > >
                                > > >
                                > > >
                                > > > [Non-text portions of this message have been removed]
                                > > >
                                > >
                                > >
                                > >
                                > >
                                > >
                                > > [Non-text portions of this message have been removed]
                                > >
                                > >
                                > >
                                > > ------------------------------------
                                > >
                                > >
                                > > Yahoo! Groups Links
                                > >
                                > >
                                > >
                                > > [Non-text portions of this message have been removed]
                                > >
                                >
                                >
                                >
                                >
                                > [Non-text portions of this message have been removed]
                                >
                              • Jerry
                                I meant to type 73256481 as the square of 8559. Sorry. Jerry Newport
                                Message 15 of 18 , Aug 14, 2011
                                  I meant to type 73256481 as the square of 8559. Sorry.

                                  Jerry Newport

                                  --- In MentalCalculation@yahoogroups.com, "Jerry" <wholphin48@...> wrote:
                                  >
                                  > Mahesh,
                                  >
                                  > Thanks for the clarification. As far as squares that only use 1-8 once, I have found four squares, 3678 5904 8559 and 9024 all produce squares that use 1-8 only once.
                                  > The squares are 13527684 34857216 73356481 and 81432576
                                  >
                                  > I have not found any squares that include only 1-7 one time each. For 1-6 and 1-5 there can be no solutions as the square has to be a multiple of three but not a multiple of nine. That is impossible since any integer which is a square and a multiple of three must also be a multiple of nine. For 1-4 or 1-3 it is easily shown that no squares exist either.
                                  >
                                  > Thanks for a fun problem!!
                                  >
                                  > Jerry Newport
                                  >
                                  > --- In MentalCalculation@yahoogroups.com, Mahesh <maheshluvsu@> wrote:
                                  > >
                                  > > zero is not included.. In 11826, I think you got the lowest..
                                  > >
                                  > >
                                  > >
                                  > > Great men don't do different things but does things differently
                                  > > --------------------------Mahesh
                                  > >
                                  > >
                                  > >
                                  > >
                                  > > ________________________________
                                  > > From: Jerry <wholphin48@>
                                  > > To: MentalCalculation@yahoogroups.com
                                  > > Sent: Sun, 14 August, 2011 1:11:16 AM
                                  > > Subject: [Mental Calculation] Re: Can you find the numbers
                                  > >
                                  > >
                                  > >
                                  > >
                                  > > The square of 11826 is 139854276 The square of 12363 is 152843769 each
                                  > > square uses 1-9 only one time. However, I forget if zero is also supposed to
                                  > > appear.
                                  > >
                                  > > If that is so, it still seems that along the journey to a solution one can find
                                  > > some interesting almost-solutions.
                                  > >
                                  > > BTW, the most trivial situation is for squaring a one digit number: One squared
                                  > > is equal to one which appears only once. However, for 2,3,4,5 and six there will
                                  > > not be any squares which use only one of any of those number of digits whether
                                  > > zero is also included or not.
                                  > >
                                  > >
                                  > > Jerry Newport
                                  > >
                                  > > --- In MentalCalculation@yahoogroups.com, Mahesh <maheshluvsu@> wrote:
                                  > > >
                                  > > >
                                  > > > Dear Gururaj,
                                  > > >
                                  > > > Try this method...
                                  > > >
                                  > > http://maths-4-fun.blogspot.com/2011/08/cube-of-3-digit-number-ending-in-1.html
                                  > > >
                                  > > > Great men don't do different things but does things differently
                                  > > > --------------------------Mahesh
                                  > > >
                                  > > >
                                  > > >
                                  > > >
                                  > > > ________________________________
                                  > > > From: "gmanchali@" <gmanchali@>
                                  > > > To: MentalCalculation@yahoogroups.com
                                  > > > Sent: Thu, 11 August, 2011 6:17:39 AM
                                  > > > Subject: Re: [Mental Calculation] Re: Can you find the numbers
                                  > > >
                                  > > > Sir
                                  > > > Can you please suggest an easy method to find the cube of a 3 digit number.pl
                                  > > > reply. I will be waiting
                                  > > > Gururaj
                                  > > > Sent from BlackBerry® on Airtel
                                  > > >
                                  > > > -----Original Message-----
                                  > > > From: "Jerry" <wholphin48@>
                                  > > > Sender: MentalCalculation@yahoogroups.com
                                  > > > Date: Wed, 10 Aug 2011 18:13:02
                                  > > > To: <MentalCalculation@yahoogroups.com>
                                  > > > Reply-To: MentalCalculation@yahoogroups.com
                                  > > > Subject: [Mental Calculation] Re: Can you find the numbers
                                  > > >
                                  > > >
                                  > > > George, Thanks for adding that. It eliminates over 700 potential roots.
                                  > > > You can also eliminate blocks of roots that produce numbers like 11,22, 101 etc
                                  > > >
                                  > > > to the left of the square as anything containing two of the same digit will be
                                  > >
                                  > > > ruled out. For example, squares of 10491 through 11088 are out as the squares
                                  > > > will start with 121 or 122.
                                  > > >
                                  > > >
                                  > > > Jerry Newport
                                  > > >
                                  > > >
                                  > > >
                                  > > > --- In MentalCalculation@yahoogroups.com, George Lane <george972453@> wrote:
                                  > > > >
                                  > > > > Hi folks.
                                  > > > > Â
                                  > > > > It might also be worth noting that potential roots ending with '0' owuld not
                                  > >
                                  > > > >work either. They owuld have squares also ending in '0' (indeed '00'), and so
                                  > >
                                  > > > >would not produce squares with the digits from 1 to 9 since two of the digits
                                  > >
                                  > > > >would be zeros. Just a thought.
                                  > > > > Â
                                  > > > > Best regards,
                                  > > > > Â
                                  > > > > George
                                  > > > >
                                  > > > > --- On Mon, 8/8/11, Jerry <wholphin48@> wrote:
                                  > > > >
                                  > > > >
                                  > > > > From: Jerry <wholphin48@>
                                  > > > > Subject: [Mental Calculation] Re: Can you find the numbers
                                  > > > > To: MentalCalculation@yahoogroups.com
                                  > > > > Date: Monday, 8 August, 2011, 21:31
                                  > > > >
                                  > > > >
                                  > > > > Â
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > > Mahesh, haven't found the numbers but I can tell you that both numbers are
                                  > > > >divisible by nine and therefore must be squares of numbers that are divisible
                                  > > >by
                                  > > >
                                  > > > >three.
                                  > > > >
                                  > > > >
                                  > > > > I guess if I had my excel program I would print out the 7207 possible squares
                                  > > >
                                  > > > >and scan for the answers. WIth a little tweaking, I could have Excel highlight
                                  > > >
                                  > > > >all of the squares whose digits add up to 45 which must be the case here. The
                                  > >
                                  > > > >smallest possible square root is 10002 and the largest is 31620, neither of
                                  > > > >which work.
                                  > > > >
                                  > > > >
                                  > > > > Jerry Newport
                                  > > > >
                                  > > > > --- In MentalCalculation@yahoogroups.com, "Mahesh" <maheshluvsu@> wrote:
                                  > > > > >
                                  > > > > > Can you find the numbers asked here
                                  > > > > > http://maths-4-fun.blogspot.com/2011/07/find-numbers.html
                                  > > > > >
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > >
                                  > > > > [Non-text portions of this message have been removed]
                                  > > > >
                                  > > >
                                  > > >
                                  > > >
                                  > > >
                                  > > >
                                  > > > [Non-text portions of this message have been removed]
                                  > > >
                                  > > >
                                  > > >
                                  > > > ------------------------------------
                                  > > >
                                  > > >
                                  > > > Yahoo! Groups Links
                                  > > >
                                  > > >
                                  > > >
                                  > > > [Non-text portions of this message have been removed]
                                  > > >
                                  > >
                                  > >
                                  > >
                                  > >
                                  > > [Non-text portions of this message have been removed]
                                  > >
                                  >
                                • Jerry
                                  If the three-digit number being squared is close to one ending in five or zero, I will mentally rewrite the number and square it as in these three
                                  Message 16 of 18 , Aug 14, 2011
                                    If the three-digit number being squared is close to one ending in five or zero, I will mentally rewrite the number and square it as in these three examples.....

                                    361^2 = (360 +1)^2 = 129600 + 720 +1 = 130321

                                    344^2 = (345 - 1)^2 = 119025 -690 + 1 = 118336

                                    812^2 = (810 +2)^2 = 656100 + 3240 + 4 = 659344

                                    Jerry Newport




                                    --- In MentalCalculation@yahoogroups.com, Oleg Stepanov <olegstepanov@...> wrote:
                                    >
                                    > MS> Let us find out square of 358 using (a+b)^2 
                                    > MS> (a+b)^2 = a^2 + 2ab + b^2
                                    > MS> Consider 35 as "a" and 8 as "b"
                                    > MS> Start from the Right--- I have written the intermediate step below
                                    > MS> 1225/560/64
                                    > MS> You can write directly:
                                    > MS> 128164
                                    >
                                    > 358x358 = (358+42)x(358-42)+42x42 = 400x316+1764 = 126400+1764 = 128164
                                    >
                                    > Sincerely Yours, Oleg Stepanov.
                                    > http://stepanov.lk.net/
                                    >
                                  • A.W.A.P. Bouman
                                    Well Jerry, There is a dutch saying: There are always more roads which lead to Rome . Regards, Willem ... Van: Jerry Aan: MentalCalculation@yahoogroups.com
                                    Message 17 of 18 , Aug 15, 2011
                                      Well Jerry,

                                      There is a dutch saying: "There are always more roads which lead to Rome".
                                      Regards,

                                      Willem


                                      ----- Oorspronkelijk bericht -----
                                      Van: Jerry
                                      Aan: MentalCalculation@yahoogroups.com
                                      Verzonden: zondag 14 augustus 2011 21:56
                                      Onderwerp: [Mental Calculation] Re: Can you find the numbers





                                      If the three-digit number being squared is close to one ending in five or zero, I will mentally rewrite the number and square it as in these three examples.....

                                      361^2 = (360 +1)^2 = 129600 + 720 +1 = 130321

                                      344^2 = (345 - 1)^2 = 119025 -690 + 1 = 118336

                                      812^2 = (810 +2)^2 = 656100 + 3240 + 4 = 659344

                                      Jerry Newport


                                      --- In MentalCalculation@yahoogroups.com, Oleg Stepanov <olegstepanov@...> wrote:
                                      >
                                      > MS> Let us find out square of 358 using (a+b)^2
                                      > MS> (a+b)^2 = a^2 + 2ab + b^2
                                      > MS> Consider 35 as "a" and 8 as "b"
                                      > MS> Start from the Right--- I have written the intermediate step below
                                      > MS> 1225/560/64
                                      > MS> You can write directly:
                                      > MS> 128164
                                      >
                                      > 358x358 = (358+42)x(358-42)+42x42 = 400x316+1764 = 126400+1764 = 128164
                                      >
                                      > Sincerely Yours, Oleg Stepanov.
                                      > http://stepanov.lk.net/
                                      >





                                      [Non-text portions of this message have been removed]
                                    • Jerry
                                      WIllem, Good saying!! I was able to rule out some of the smaller cases by using modular arithmetic and reading your posts has made me more aware of the
                                      Message 18 of 18 , Aug 15, 2011
                                        WIllem, Good saying!! I was able to rule out some of the smaller cases by using modular arithmetic and reading your posts has made me more aware of the utility of that area.

                                        Jerry



                                        --- In MentalCalculation@yahoogroups.com, "A.W.A.P. Bouman" <awap.bouman@...> wrote:
                                        >
                                        > Well Jerry,
                                        >
                                        > There is a dutch saying: "There are always more roads which lead to Rome".
                                        > Regards,
                                        >
                                        > Willem
                                        >
                                        >
                                        > ----- Oorspronkelijk bericht -----
                                        > Van: Jerry
                                        > Aan: MentalCalculation@yahoogroups.com
                                        > Verzonden: zondag 14 augustus 2011 21:56
                                        > Onderwerp: [Mental Calculation] Re: Can you find the numbers
                                        >
                                        >
                                        >
                                        >
                                        >
                                        > If the three-digit number being squared is close to one ending in five or zero, I will mentally rewrite the number and square it as in these three examples.....
                                        >
                                        > 361^2 = (360 +1)^2 = 129600 + 720 +1 = 130321
                                        >
                                        > 344^2 = (345 - 1)^2 = 119025 -690 + 1 = 118336
                                        >
                                        > 812^2 = (810 +2)^2 = 656100 + 3240 + 4 = 659344
                                        >
                                        > Jerry Newport
                                        >
                                        >
                                        > --- In MentalCalculation@yahoogroups.com, Oleg Stepanov <olegstepanov@> wrote:
                                        > >
                                        > > MS> Let us find out square of 358 using (a+b)^2
                                        > > MS> (a+b)^2 = a^2 + 2ab + b^2
                                        > > MS> Consider 35 as "a" and 8 as "b"
                                        > > MS> Start from the Right--- I have written the intermediate step below
                                        > > MS> 1225/560/64
                                        > > MS> You can write directly:
                                        > > MS> 128164
                                        > >
                                        > > 358x358 = (358+42)x(358-42)+42x42 = 400x316+1764 = 126400+1764 = 128164
                                        > >
                                        > > Sincerely Yours, Oleg Stepanov.
                                        > > http://stepanov.lk.net/
                                        > >
                                        >
                                        >
                                        >
                                        >
                                        >
                                        > [Non-text portions of this message have been removed]
                                        >
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