One attempt at proof is to determine all the possible numbers that converge to 6174 after a single iteration, and then attempt to reason that each too can be reached by the convergence of even more numbers in such a way that if i continue this reasoning i. Al nicholson, nick jefferson, mike westergaard, david jackson, bill jefferson, dorie jackson. Manick srinivasan and ramkumar ramamoorthy sent me more computer results. The fixed point, 6174, is sometimes called kaprekars constant. In addition, some results relating to the properties of the kaprekar numbers are also presented. Preserve footnotes with mail merge i have a two page document that i am merging.
I was thinking i could do this by creating the reports and then doing. So for any 4digit number the karpekar process ends with 6174 and in no more than 7 steps. Searching for kaprekars constants rims, kyoto university. Discover the mystery behind the 6174 loop by using any four digit number. The kaprekar method is very easy to use and is the following.
The number 6174 is the only unchanged mysterious number discovered by kaprekar s operation. If you allow numbers with noughts at the beginning like 0342 or 0045, then the kaprekar number fits for any four digit number except for 1111. The mail merge main document must be of the letter type, though that does not mean that the output cannot be sent as an email message. Preserve footnotes with mail merge microsoft community. This algorithm is credited to the indian mathematician d. On 2adic kaprekar constants and 2digit kaprekar distances. Albums include fate outsmarts desire, depth of field, and p52. Kaprekar from devlali, india, devised a process now known as kaprekar s operation. Naranan sixty years after its discovery and twenty years after kaprekars death, kaprekar constant 6174 continues to fascinate amateur mathematicians, mathematics teachers and devotees of recreational and experimental mathematics. Continuing with this process of forming and subtracting, we will always arrive at the number 6174. Kaprekar s constant of 6174 is notable for the following property 1 take any fourdigit number with at least two digits different. If you are as amazed as i am and want some additional information about the mathematics involved in the algorithm, then you can click on one of the links below.
Therefore the number 6174 is the only number unchanged by kaprekar s operation our mysterious number is unique. The number 6174 is the only unchanged mysterious number discovered by kaprekars operation. Pdf the decimal nkaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10n 1. In yesterdays post, we chose a three digit positive integer and we arranged the digits in ascending and descending order forming the largest and the smallest integer that can be formed using the three digits. Sep 30, 20 it should be generalized to an arbitrary length and an arbitrary base, then if it is true that there are a finite number of fixed points, the conjecture that it holds for an arbitrary base give two kaprekar functions of the base and length less th. Series for 4digit numbers there is one kaprekar constant for 4digit numbers 6174. The mystery and music of kaprekar constant 6174 renaissance.
Take any four digit number with at least two different digits. Kaprekars constant as a fixed point of iterative function. Here is a common problem in elementary school arithmetic. Id like some feedback on whether this is pythonic enough, and if. The output of shows that the only kaprekar constant for 7digit numbers with b. We subtracted the smaller integer from the larger, and repeated the process several times. Program to check for kaprekar number guide for school. It should be generalized to an arbitrary length and an arbitrary base, then if it is true that there are a finite number of fixed points, the conjecture that it holds for an arbitrary base give two kaprekar functions of the base and length less th. Sort four digits in ascending order and store result in a number asc. This paper discusses the kaprekar constant and kaprekar numbers in number theory. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special.
If the resultant sum is k, then k is called a kaprekar number. Sep 29, 2014 a student talked about kaprekars constant 6174 during their my favorite presentation. I would like to allow a user to run all reports and also just run a single report. Sixty years after its discovery and twenty years after kaprekars death, kaprekar constant 6174 continues to fascinate amateur.
How to prove kaprekars constant 6174 in layman terms quora. The 3digit kaprekar number constant is an amazing number. The only fourdigit numbers for which kaprekars routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. Kaprekar s constant this topic is locked from further discussion.
He showed that 6174 is reached in the limit as one repeatedly subtracts the highest and lowest numbers that can be constructed from a set of four digits that are not all identical. Use the merge statement to select rows from one or more sources for update or insertion into a table or view. There are three kaprekar constants for 10digit numbers 9753086421, 6333176664 and 9975084201. The concept of kaprekar numbers is not limited to base 10 i. Write a program in java to input a number and check whether it is a kaprekar number or not. Given any fourdigit number that consists of at least two different digits, if you form a number by arranging its digits in descending order, and subtract the number formed by arranging its digits in ascending order, and repeat, you should eventually arrive at 6174, kaprekar s constant. The process is iterative, such that the same procedure applies to the numbers obtained at each step.
This would provide me a folder full of the reports, but. Therefore b 2 and p is a mersenne prime number, since any 2adic kaprekar constant is the product of two suitable mersenne numbers by theorem 0. A modified kaprekar number is a positive whole number n with d digits, such that when. A kaprekar number is a number whose square when divided into two parts and such that sum of parts is equal to the original number and none of the parts has value 0. In mathematics, a natural number in a given number base is a kaprekar number if the representation of its square in that base can be split into two parts, where the second part has digits, that add up to the original number.
Note that the numbers and have the same digit sum and hence the same remainder modulo. Take any fourdigit number, using at least two different digits. On the number 495 a constant similar to kaprekar s constant. In particular, this establishes the correctness of an algorithm for generating the kaprekar. Subtract number larger number from smaller number, i. Kaprekar s constant of 6174 is notable for the following property. Pdf on the number 495 a constant similar to kaprekars. Write a program in c to check whether a given number is a kaprekar number or not. Kaprekar constant, or 6174, is a constant that arises when we take a 4digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. If you allow numbers with noughts at the beginning like 0342 or 0045, then the kaprekar number fits for any four digit number except for 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999. Why does alex clark, from the university of leicester, have a strange fascination with 163.
Let us look at some of the ideas which he introduced. Optionally, count and report the count of how many kaprekar numbers are less than 1,000,000. In fact, 9, 55 and 95121 are 1 kaprekar, 2 kaprekar and 5 kaprekar numbers, respectively. Either way, the end result is reached in a fairly small number of steps. In his booklet the mathematics of the new self numbers 1963 kaprekar studied the problem whether a. Talentsprint aptitude prep channel is designed to help aspirants get ready for various competitive exams including bank, ssc, railways, insurance, campus recruitment and other govt exams.
Mar 01, 2006 the number 6174 is a really mysterious number. This statement is a convenient way to combine multiple operations. For example applying kaprekar s operation to the three digit number 753 gives the following. Sep 21, 2010 wolframs mathworld describes kaprekar numbers like this. All kaprekar sequences will either reach one of these fixed points or will result in a repeating cycle. Kaprekar published a surprising result, concerning what is now known as kaprekar s process. All other kaprekars constant are nontrivial kaprekars constants. For three digit numbers the same phenomenon occurs. Pdf the decimal n kaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10n 1. Sort four digits in descending order and store result in a number desc.
You will reach 6174, which on repeating gives you 6174 again. Kaprekars constant, fixed point, iterative function, four digit numbers. Kaprekars constant is a studio and live collective who write, record and perform their own, origina. In 1949, kaprekar discovered an interesting property of the number 6174, which was subsequently named the kaprekar constant. How to prove kaprekars constant 6174 in layman terms. A modified kaprekar number is a positive whole number n with d digits, such that when we split its square into two pieces a right hand piece r with d digits and a left hand piece l that contains the remaining d or d. Arrange the digits in descending and then in ascending order to get two fourdigit numbers, adding leading zeros if necessary. I need to provide a weekly report package for my sales staff. In case if there is a constant on one side of the equation derive. D r kaprekar invented different number properties throughout his. Some properties of the kaprekar numbers and a means of generation. This number is special as we always get this number when following steps are followed for any four digit number such that all digits of number are not same, i.
All other fourdigit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. Is kaprekars constant useful for anything or is it just a. Clearly the only value for which this process is constant is 6174 but that doesnt explain why there should be convergence. We can calculate the result of kaprekar s operation using the standard method of subtraction applied to each column of this. Id like some feedback on whether this is pythonic enough, and if i can improve it. Iannucci the university of the virgin islands 2 john brewers bay st. Kaprekar s name today is wellknown and many mathematicians have found themselves intrigued by the ideas about numbers which kaprekar found so addictive. The mystery and music of kaprekar constant 6174 april 29, 2014 by girish arabale in mathematica in 1949, indian mathematician d. Perhaps the best known of kaprekar s results is the following which relates to the number 6174, today called kaprekar s constant.
Some properties of the kaprekar numbers and a means of. Kaprekar was an indian mathematician who came up with this beautiful result from number theory in 1946. Apr 29, 2014 the mystery and music of kaprekar constant 6174 april 29, 2014 by girish arabale in mathematica in 1949, indian mathematician d. Im new to python and as a first exercise, ive written a function module. I aas solving a problem on hackerrank and the problem is as follows. Naranan sixty years after its discovery and twenty years after kaprekar s death, kaprekar constant 6174 continues to fascinate amateur mathematicians, mathematics teachers and devotees of recreational and experimental mathematics. Kaprekar from devlali nashik came up with an interesting routine, the procedure now known as kaprekar routine. Combining the possibilities of derive and excel while studying bases. Dattatreya ramchandra kaprekar 19051986 was an indian recreational mathematician who described several classes of natural numbers including the kaprekar, harshad and self numbers and discovered the kaprekar constant, named after him. In number theory, kaprekars routine is an iterative algorithm that, with each iteration, takes a. A positive whole number n that has d number of digits is squared and split into two pieces, a righthand piece that has d digits and a lefthand piece that has remaining d or d1 digits. The main idea is that every number that our program takes sooner or later the result has to be 6174 following the kaprekar s routine. Series for 2digit numbers there is only one series for 2digit numbers 9 81 63 27 45 repeat series for 3digit numbers there is one kaprekar constant for 3digit numbers 495. You can specify conditions to determine whether to update or insert into the target table or view.
Kaprekar s constant using c language this project was based on the kaprekar s constant. The only 7digit kaprekar constant is 3203211 in base b4. The kaprekar number calculator there are many curious patterns in mathematics. Wolframs mathworld describes kaprekar numbers like this. Generate and show all kaprekar numbers less than 10,000. Media in category kaprekar s constant the following 5 files are in this category, out of 5 total.