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The Number 6174, Kaprekar's Operation

Topic closed. 13 replies. Last post 3 years ago by ALX.

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Zeta Reticuli Star System
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Member #30470
January 17, 2006
10351 Posts
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Posted: November 30, 2013, 7:35 pm - IP Logged

The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special.

Kaprekar's operation

In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar's operation. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

It is a simple operation, but Kaprekar discovered it led to a surprising result. Let's try it out, starting with the number 2005, the digits of last year. The maximum number we can make with these digits is 5200, and the minimum is 0025 or 25 (if one or more of the digits is zero, embed these in the left hand side of the minimum number). The subtractions are:

5200 - 0025 = 5175
7551 - 1557 = 5994
9954 - 4599 = 5355
5553 - 3555 = 1998
9981 - 1899 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174
7641 - 1467 = 6174

When we reach 6174 the operation repeats itself, returning 6174 every time. We call the number 6174 a kernel of this operation. So 6174 is a kernel for Kaprekar's operation, but is this as special as 6174 gets? Well not only is 6174 the only kernel for the operation, it also has one more surprise up its sleeve. Let's try again starting with a different number, say 1789.

9871 - 1789 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174

We reached 6174 again!

6174: a very mysterious number...

A very mysterious number...

When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. In fact, you reach 6174 for all four digit numbers that don't have all the digits the same. It's marvellous, isn't it? Kaprekar's operation is so simple but uncovers such an interesting result. And this will become even more intriguing when we think about the reason why all four digit numbers reach this mysterious number 6174.

More - a lot more: http://plus.maths.org/content/os/issue38/features/nishiyama/index

Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

Lep

There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

    increase's avatar - focus
    VA
    United States
    Member #54828
    August 31, 2007
    37880 Posts
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    Posted: November 30, 2013, 8:03 pm - IP Logged

    Very interesting.  I love that number!

    I was born in 1967 on the 14th.

    So, I play the 6174 combo often.

    Thanks for sharing!

    I am a millionaire!

      Coin Toss's avatar - shape barbed.jpg
      Zeta Reticuli Star System
      United States
      Member #30470
      January 17, 2006
      10351 Posts
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      Posted: November 30, 2013, 8:06 pm - IP Logged

      Thanks for replying, increase.

      This number fits you like a glove!

      Lep

      Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

      Lep

      There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

        lakerben's avatar - spherewall
        New Mexico
        United States
        Member #86099
        January 29, 2010
        11119 Posts
        Offline
        Posted: December 6, 2013, 6:07 pm - IP Logged

        The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special.

        Kaprekar's operation

        In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar's operation. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

        It is a simple operation, but Kaprekar discovered it led to a surprising result. Let's try it out, starting with the number 2005, the digits of last year. The maximum number we can make with these digits is 5200, and the minimum is 0025 or 25 (if one or more of the digits is zero, embed these in the left hand side of the minimum number). The subtractions are:

        5200 - 0025 = 5175
        7551 - 1557 = 5994
        9954 - 4599 = 5355
        5553 - 3555 = 1998
        9981 - 1899 = 8082
        8820 - 0288 = 8532
        8532 - 2358 = 6174
        7641 - 1467 = 6174

        When we reach 6174 the operation repeats itself, returning 6174 every time. We call the number 6174 a kernel of this operation. So 6174 is a kernel for Kaprekar's operation, but is this as special as 6174 gets? Well not only is 6174 the only kernel for the operation, it also has one more surprise up its sleeve. Let's try again starting with a different number, say 1789.

        9871 - 1789 = 8082
        8820 - 0288 = 8532
        8532 - 2358 = 6174

        We reached 6174 again!

        6174: a very mysterious number...

        A very mysterious number...

        When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. In fact, you reach 6174 for all four digit numbers that don't have all the digits the same. It's marvellous, isn't it? Kaprekar's operation is so simple but uncovers such an interesting result. And this will become even more intriguing when we think about the reason why all four digit numbers reach this mysterious number 6174.

        More - a lot more: http://plus.maths.org/content/os/issue38/features/nishiyama/index

        Thumbs Up

        How about them cowboys!

         

         

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          Slick Nick's avatar - Lottery-035.jpg
          Rochester
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          January 1, 2011
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          Posted: December 7, 2013, 7:44 am - IP Logged

          I might give it a try, hey ya never know!I Agree!

          Money is a terrible master, but a great servant...Smile

            ranman17's avatar - jzy6nr
            New York
            United States
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            November 27, 2009
            2132 Posts
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            Posted: December 7, 2013, 7:31 pm - IP Logged

            Two kernels in this rundown (started with 5303)

            Start
            530353303354995
            4995994545995346
            5346654334563087
            308778303787452
            7452754224575085
            508585505587992
            7992997227997173
            7173773113776354
            6354654334563087
            3087780330874716
            4716764114676174
            6174764114676174

            Be kind, because everyone you meet is fighting a great battle.

            An Unruly Evil

              rcbbuckeye's avatar - Lottery-043.jpg
              Texas
              United States
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              October 23, 2007
              5600 Posts
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              Posted: December 8, 2013, 11:59 am - IP Logged

              Pretty cool CoinToss.

              I played around with it a little to see if any winning numbers would have come up in Tx. Alas, not in the last few months.

              It's still amazing.

              CAN'T WIN IF YOU'RE NOT IN

              A DOLLAR AND A DREAM (OR $2)

                Avatar

                United States
                Member #65075
                September 16, 2008
                643 Posts
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                Posted: December 9, 2013, 11:26 pm - IP Logged

                The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special.

                Kaprekar's operation

                In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar's operation. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

                It is a simple operation, but Kaprekar discovered it led to a surprising result. Let's try it out, starting with the number 2005, the digits of last year. The maximum number we can make with these digits is 5200, and the minimum is 0025 or 25 (if one or more of the digits is zero, embed these in the left hand side of the minimum number). The subtractions are:

                5200 - 0025 = 5175
                7551 - 1557 = 5994
                9954 - 4599 = 5355
                5553 - 3555 = 1998
                9981 - 1899 = 8082
                8820 - 0288 = 8532
                8532 - 2358 = 6174
                7641 - 1467 = 6174

                When we reach 6174 the operation repeats itself, returning 6174 every time. We call the number 6174 a kernel of this operation. So 6174 is a kernel for Kaprekar's operation, but is this as special as 6174 gets? Well not only is 6174 the only kernel for the operation, it also has one more surprise up its sleeve. Let's try again starting with a different number, say 1789.

                9871 - 1789 = 8082
                8820 - 0288 = 8532
                8532 - 2358 = 6174

                We reached 6174 again!

                6174: a very mysterious number...

                A very mysterious number...

                When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. In fact, you reach 6174 for all four digit numbers that don't have all the digits the same. It's marvellous, isn't it? Kaprekar's operation is so simple but uncovers such an interesting result. And this will become even more intriguing when we think about the reason why all four digit numbers reach this mysterious number 6174.

                More - a lot more: http://plus.maths.org/content/os/issue38/features/nishiyama/index

                Very interesting.

                So I played around too for SC draws. Some of you won't follow this, but those of you familiar with some 999 Book of Numbers titles will follow along nicely with the concepts. I won't get into too much explanation.

                You'll see some number substitutions in this method. The rules for those are 3=6; 0=1; 7=9. So anytime I have one of those digits on the X line, I will have to make allowances for the fact that these digits often mask as twins.

                So here goes...

                First I took a draw, lets say 4145 on Nov 27 in SC, then I wrote it from low to high, i.e. 1445

                Next I took the "difference" between the rewritten combination and the constant 6174. When you are dealing with differences, you do not care which combination is on the top of the equation or the bottom because the answer will be the same. You are not adding or substracting, but finding the difference value of the digits.

                So:

                1445

                6174

                5330--5331--5333

                5X31

                5X61

                In this case, the difference was 5331.

                Next, I stretched out the third line by going one down on the left side, and two up on the right side.

                On the fourth line I decided where my X value would go based on my difference combo calculated on line 3 (5331). In this case I put it as a 2nd digit place holder. Anytime I deal with Pick 4, I am only trying to get three of the four digits because that narrows my plays down to just 10 combinations.

                I had to create a fifth line in the example above because there is a 3 on my X line, so I have to also have a 6 substitution there. I should also do the same for the 1 there which should be substituted for a 0, but for the purposes of this demonstration, I will leave it out. The third X equation if I did the 1=0 substitution would read 5X30 and 5X60, if I wanted to play 40 combinations instead of 20.

                What was the result?

                On December 4, 5-1-6-1 showed--That's a straight hit off the 5X61 line.

                Ex 2: Let's take the 6124 drawn on Nov 23

                Turn that draw combination into 1246 (from low to high), then find the difference between that and the constant "6174"

                1246

                6174

                5131--5132--5134

                5x32

                5x62

                On Nov 25, just three draws later, 5-7-3-2 showed--That's a straight hit off the5X32 line.

                Straight is good. I did a few more random samples that did not yield straights, ie 5521 (drawn on Nov 30) yielded 5121 as the difference line (line 3), turned that into 5x21 and 5x20, resulting in a 5x20 hit five draws later as 5002.

                Anyway, this method is just using a "constant" variable (i.e 6174 which seemingly has some special properties) to predict 3 of 4 digits in the Pick 4. Of course this method needs more testing to see how consistent it will be as a straight predictor, and also whether it works just in non-computerized drawing states or others as well.

                Final: Ex 3: 1123 drawing on Nov 29

                1123

                6174

                5051

                5x51--draw #2 showed as 5512

                5x50

                 

                Note: For anyone who might want to do more testing on this method, you should also keep in mind that when you have a "double" number on your X line, you will also want to consider the complement of that double, ie 5x51 is also 5X11 (551=511).

                5X11 showed on December 4 as 5161.

                 

                Thanks Coin Toss for sharing!

                "999 Book of Numbers  ... Because today is a great day to win!"

                  Coin Toss's avatar - shape barbed.jpg
                  Zeta Reticuli Star System
                  United States
                  Member #30470
                  January 17, 2006
                  10351 Posts
                  Offline
                  Posted: December 10, 2013, 2:46 am - IP Logged

                  rcbuckeye,

                  Thanks. I was wondering if this could lead to some Pick4 plays.

                  SBIP$999,

                  It looks like you certainly figured that out!

                  Wow, great job there!

                  Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

                  Lep

                  There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

                    lakerben's avatar - spherewall
                    New Mexico
                    United States
                    Member #86099
                    January 29, 2010
                    11119 Posts
                    Offline
                    Posted: January 7, 2014, 12:51 pm - IP Logged

                    Very interesting.

                    So I played around too for SC draws. Some of you won't follow this, but those of you familiar with some 999 Book of Numbers titles will follow along nicely with the concepts. I won't get into too much explanation.

                    You'll see some number substitutions in this method. The rules for those are 3=6; 0=1; 7=9. So anytime I have one of those digits on the X line, I will have to make allowances for the fact that these digits often mask as twins.

                    So here goes...

                    First I took a draw, lets say 4145 on Nov 27 in SC, then I wrote it from low to high, i.e. 1445

                    Next I took the "difference" between the rewritten combination and the constant 6174. When you are dealing with differences, you do not care which combination is on the top of the equation or the bottom because the answer will be the same. You are not adding or substracting, but finding the difference value of the digits.

                    So:

                    1445

                    6174

                    5330--5331--5333

                    5X31

                    5X61

                    In this case, the difference was 5331.

                    Next, I stretched out the third line by going one down on the left side, and two up on the right side.

                    On the fourth line I decided where my X value would go based on my difference combo calculated on line 3 (5331). In this case I put it as a 2nd digit place holder. Anytime I deal with Pick 4, I am only trying to get three of the four digits because that narrows my plays down to just 10 combinations.

                    I had to create a fifth line in the example above because there is a 3 on my X line, so I have to also have a 6 substitution there. I should also do the same for the 1 there which should be substituted for a 0, but for the purposes of this demonstration, I will leave it out. The third X equation if I did the 1=0 substitution would read 5X30 and 5X60, if I wanted to play 40 combinations instead of 20.

                    What was the result?

                    On December 4, 5-1-6-1 showed--That's a straight hit off the 5X61 line.

                    Ex 2: Let's take the 6124 drawn on Nov 23

                    Turn that draw combination into 1246 (from low to high), then find the difference between that and the constant "6174"

                    1246

                    6174

                    5131--5132--5134

                    5x32

                    5x62

                    On Nov 25, just three draws later, 5-7-3-2 showed--That's a straight hit off the5X32 line.

                    Straight is good. I did a few more random samples that did not yield straights, ie 5521 (drawn on Nov 30) yielded 5121 as the difference line (line 3), turned that into 5x21 and 5x20, resulting in a 5x20 hit five draws later as 5002.

                    Anyway, this method is just using a "constant" variable (i.e 6174 which seemingly has some special properties) to predict 3 of 4 digits in the Pick 4. Of course this method needs more testing to see how consistent it will be as a straight predictor, and also whether it works just in non-computerized drawing states or others as well.

                    Final: Ex 3: 1123 drawing on Nov 29

                    1123

                    6174

                    5051

                    5x51--draw #2 showed as 5512

                    5x50

                     

                    Note: For anyone who might want to do more testing on this method, you should also keep in mind that when you have a "double" number on your X line, you will also want to consider the complement of that double, ie 5x51 is also 5X11 (551=511).

                    5X11 showed on December 4 as 5161.

                     

                    Thanks Coin Toss for sharing!

                    Thumbs Up

                    How about them cowboys!

                     

                     

                    US Flag

                      lucky 4moola's avatar - F2
                      New Member
                      Austin
                      United States
                      Member #151153
                      January 8, 2014
                      11 Posts
                      Offline
                      Posted: January 9, 2014, 8:04 pm - IP Logged

                      The funny number 6174 had to be a multiple of the magic 9 and it sure is (6+1+7+4=18=multiple of 9). And I've got news for those that try to find some meaning* that could be used in some lottery system: the number contains the Jackpot symbol 777:

                      6174 = 2X9X7X7X7

                      *like in at least being related to some well-known gambling-related lucky charm/symbol. 

                        sully16's avatar - sharan
                        Ringleader
                        Michigan
                        United States
                        Member #81740
                        October 28, 2009
                        40456 Posts
                        Online
                        Posted: January 19, 2014, 9:40 am - IP Logged

                        The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special.

                        Kaprekar's operation

                        In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar's operation. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

                        It is a simple operation, but Kaprekar discovered it led to a surprising result. Let's try it out, starting with the number 2005, the digits of last year. The maximum number we can make with these digits is 5200, and the minimum is 0025 or 25 (if one or more of the digits is zero, embed these in the left hand side of the minimum number). The subtractions are:

                        5200 - 0025 = 5175
                        7551 - 1557 = 5994
                        9954 - 4599 = 5355
                        5553 - 3555 = 1998
                        9981 - 1899 = 8082
                        8820 - 0288 = 8532
                        8532 - 2358 = 6174
                        7641 - 1467 = 6174

                        When we reach 6174 the operation repeats itself, returning 6174 every time. We call the number 6174 a kernel of this operation. So 6174 is a kernel for Kaprekar's operation, but is this as special as 6174 gets? Well not only is 6174 the only kernel for the operation, it also has one more surprise up its sleeve. Let's try again starting with a different number, say 1789.

                        9871 - 1789 = 8082
                        8820 - 0288 = 8532
                        8532 - 2358 = 6174

                        We reached 6174 again!

                        6174: a very mysterious number...

                        A very mysterious number...

                        When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. In fact, you reach 6174 for all four digit numbers that don't have all the digits the same. It's marvellous, isn't it? Kaprekar's operation is so simple but uncovers such an interesting result. And this will become even more intriguing when we think about the reason why all four digit numbers reach this mysterious number 6174.

                        More - a lot more: http://plus.maths.org/content/os/issue38/features/nishiyama/index

                        This is really cool, Going to get some paper and pencils and start playing around.

                        Did you exchange a walk on part in the war ?

                        For a lead role in a cage?

                         

                                                                    From Pink Floyd's " Wish you were here"

                          Avatar
                          Maine
                          United States
                          Member #99
                          January 27, 2002
                          1013 Posts
                          Offline
                          Posted: February 6, 2014, 12:58 pm - IP Logged

                          Very interesting.

                          So I played around too for SC draws. Some of you won't follow this, but those of you familiar with some 999 Book of Numbers titles will follow along nicely with the concepts. I won't get into too much explanation.

                          You'll see some number substitutions in this method. The rules for those are 3=6; 0=1; 7=9. So anytime I have one of those digits on the X line, I will have to make allowances for the fact that these digits often mask as twins.

                          So here goes...

                          First I took a draw, lets say 4145 on Nov 27 in SC, then I wrote it from low to high, i.e. 1445

                          Next I took the "difference" between the rewritten combination and the constant 6174. When you are dealing with differences, you do not care which combination is on the top of the equation or the bottom because the answer will be the same. You are not adding or substracting, but finding the difference value of the digits.

                          So:

                          1445

                          6174

                          5330--5331--5333

                          5X31

                          5X61

                          In this case, the difference was 5331.

                          Next, I stretched out the third line by going one down on the left side, and two up on the right side.

                          On the fourth line I decided where my X value would go based on my difference combo calculated on line 3 (5331). In this case I put it as a 2nd digit place holder. Anytime I deal with Pick 4, I am only trying to get three of the four digits because that narrows my plays down to just 10 combinations.

                          I had to create a fifth line in the example above because there is a 3 on my X line, so I have to also have a 6 substitution there. I should also do the same for the 1 there which should be substituted for a 0, but for the purposes of this demonstration, I will leave it out. The third X equation if I did the 1=0 substitution would read 5X30 and 5X60, if I wanted to play 40 combinations instead of 20.

                          What was the result?

                          On December 4, 5-1-6-1 showed--That's a straight hit off the 5X61 line.

                          Ex 2: Let's take the 6124 drawn on Nov 23

                          Turn that draw combination into 1246 (from low to high), then find the difference between that and the constant "6174"

                          1246

                          6174

                          5131--5132--5134

                          5x32

                          5x62

                          On Nov 25, just three draws later, 5-7-3-2 showed--That's a straight hit off the5X32 line.

                          Straight is good. I did a few more random samples that did not yield straights, ie 5521 (drawn on Nov 30) yielded 5121 as the difference line (line 3), turned that into 5x21 and 5x20, resulting in a 5x20 hit five draws later as 5002.

                          Anyway, this method is just using a "constant" variable (i.e 6174 which seemingly has some special properties) to predict 3 of 4 digits in the Pick 4. Of course this method needs more testing to see how consistent it will be as a straight predictor, and also whether it works just in non-computerized drawing states or others as well.

                          Final: Ex 3: 1123 drawing on Nov 29

                          1123

                          6174

                          5051

                          5x51--draw #2 showed as 5512

                          5x50

                           

                          Note: For anyone who might want to do more testing on this method, you should also keep in mind that when you have a "double" number on your X line, you will also want to consider the complement of that double, ie 5x51 is also 5X11 (551=511).

                          5X11 showed on December 4 as 5161.

                           

                          Thanks Coin Toss for sharing!

                          I've been playing around with this in Maryland Pick4 a little and have noticed some interesting things. In the last 60 games there are only six games that do not have  a  6 or a 1 or a 7 or a 4 in the winning combo. Also when there is no 6-1-7-or 4 present.....the next game will have a double 6-1-7 or 4 present. I also found that the number you get when subtracting the winning number from 6 1 7 4 often has three of the winning numbers for the next two to three games if you use the mirror numbers of the subtracted result and combine them. Of course that is eight numbers so it's no big surprise ....but ofen the three are in the mirror numbers only. There is also some kind of relationship between every 12th winning combo that I don't quite get yet. Quite an interesting number 6174.

                          If it wasn't impossible I wouldn't even consider it!

                            Avatar
                            Maine
                            United States
                            Member #99
                            January 27, 2002
                            1013 Posts
                            Offline
                            Posted: February 6, 2014, 2:01 pm - IP Logged

                            This is what happened today after my last post. Maryland pick 4 day was 4746!! The 6174 minus 2545 (eve winner) = 3629, mirror # 8174 (using real math), then 6174 minus 2545 = 4431, mirror # 9986 (using lottery math). 3269 and 8174 there's the 746.....4431 and 9986 there's the 446! How you pick out the correct triads is a mystery but maybe with a little practice and history it will be easier. Also the winning number twelve games ago was 5767...there's the 67...so maybe that's a clue? Just saying............

                            If it wasn't impossible I wouldn't even consider it!