A kaprekar number is a number whose square when divided into two parts the sum of those parts is equal to the original number and none of the parts has value 0. The number 6174 is the only unchanged mysterious number discovered by kaprekar s operation. Modified kaprekar numbers hacker rank problem solution. Manick srinivasan and ramkumar ramamoorthy sent me more computer results. Steps from wikipedia take any fourdigit number, using at least two different digits. Given a number, the task is to check if it is kaprekar number or not. Kaprekars constant using c language programmingwithsantiago. Iannucci the university of the virgin islands 2 john brewers bay st. How to prove kaprekars constant 6174 in layman terms. 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. The main object that the library deals with is a phonenumber object. The best known is probably that related to the number 6174, sometimes called kaprekars constant. Take any fourdigit number, using at least two different digits. Write a function that counts the number of iterations in kaprekar s routine, which is as follows.
Wolframs mathworld describes kaprekar numbers like this consider an ndigit number k. It has always been a fascinating theorem, easily understood but hard to prove for amateurs, a lesser fermats last theorem. Program to check for kaprekar number guide for school. The series of kaprekar numbers is known as a006886, and begins as 1,9,45,55. It works for positive numbers upto the range of 999,999,999,999 i. Given a 4digit number that has at least two different digits, take that numbers descending digits, and subtract that numbers ascending digits. Kaprekar sequences wells 1986 book defines kaprekar number roughly as follows. Kaprekar number programming java tutorial using eclipse subscribe. The kaprekar routine arranges four digits zeros are appended to the number if its less than 4 digits in descending and ascending order, subtracts those two numbers, and repeats the process until the difference is 0 degenrate case or 6174 kaprekar s constant. The kaprekar routine arranges four digits zeros are appended to the number if its less than 4 digits in descending and ascending order, subtracts those two numbers, and repeats the process until the difference is 0 degenrate case or 6174 kaprekars constant. Calculate n kaprekar numbers code golf stack exchange. How to find kaprekar numbers within a given range using python.
A kaprekar number is an ndigit number k that, when the first n or n1 digits of k2 are added to the second n the digits of n2, the result is n examples. This solution only tests for divisibility by 9, not whether the number is a kaprekar number. Kaprekar was an indian mathematician who came up with this beautiful result from number theory in 1946. Split the string representation of the square into two parts, and. The mystery and music of kaprekar constant 6174 renaissance. If you square it, then split the number into two integers and sum those integers, you have the same value you started with. Mathematics and number based challenges developer insider. A modified kaprekar number is a positive whole number with a special property.
The number 6174 is the only unchanged mysterious number discovered by kaprekars operation. Pdf a variant of kaprekar iteration and kaprekar constant. A kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number e. I aas solving a problem on hackerrank and the problem is as follows. A 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. 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. We square to arrive at a number that is either digits long or digits long. Repeat this process with 4176 and youll get 7641 1467, which is 6174.
If the resultant sum is k, then k is called a kaprekar number. For example, given 6589, you should take 9865 5689, which is 4176. This is a python module to convert number words eg. Kaprekar, found number 6174 also known as kaprekar constant that will return the subtraction result when following this rules. Arrange the digits in descending and then in ascending order to get two fourdigit numbers, adding leading zeros if necessary. Kaprekar number programming java tutorial using eclipse. The best known is probably that related to the number 6174, sometimes called kaprekar s constant. Masrul huda on 24 jun 2012 this is no more coding but the cyclist on 14 jun 2016. Jan 25, 2018 kaprekar is remembered today for a range of curious mathematical patterns that he discovered. 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. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. How do you code a program to find kaprekar number answers. In number theory, a kaprekar number for a given base is a nonnegative integer, the representation of whose square in that base can be. If we take the four digits of 6174 and form two new numbers by arranging them in descending and ascending order, we get 7641 and 1467.
The kaprekar method is very easy to use and is the following. 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. Have fun with this math trick and discover why all the 4 digit numbers on subtracting using the kaprekar operation reach to the mysterious number 6174. Kaprekar is remembered today for a range of curious mathematical patterns that he discovered.
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. Jun 27, 2019 kaprekar number programming java tutorial using eclipse subscribe. Consider n as a positive integer that has k number of digits. Sep 29, 2014 a student talked about kaprekars constant 6174 during their my favorite presentation. Write a program that calculates and outputs the first n kaprekar numbers, with n being in the range, but not limited to the range. Id like some feedback on whether this is pythonic enough, and if i can improve it. Python programming 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. Now given a number, your task is to check if it is kaprekar number or not. 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.
Generate all possible chains leading to 6174, show their length and their patterns of convergence. Numbers having fewer than 4 digits are appended with leading 0s, resulting in all values converging to 6174. Find the square of the number n and separate the resulting number into two parts right hand side with k digits and left hand side k or k1 digits. Kaprekar number are those number whose square, if split into parts and then add it, will be the same as the original number. Download discrepancies asked in computer programming. Given a 4digit number that has at least two different digits, take that number s descending digits, and subtract that number s ascending digits. This program performs kaprekars routine to automating the process. Discover the mystery behind the 6174 loop by using any four digit number. Write a java program to generate and show all kaprekar numbers less than. You can create this from a string representing a phone number using the parse function, but you also need to specify the country that the phone number is being dialled from unless the number is in e. Write a program in java to input a number and check whether it is a kaprekar number or not.
The number of steps required for the kaprekar routine to reach a fixed point for values of n 0 to 9999, partitioned into rows of length 100. Given two positive integers and where is lower than, write a program to. In number theory, kaprekar s routine is an iterative algorithm that, with each iteration, takes a natural number in a given number base, creates two new numbers by sorting the digits of its number by descending and ascending order, and subtracts the second from the first to yield the natural number for the next iteration. In mathematics, a kaprekar number for a given base is a nonnegative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. How to find kaprekar numbers within a given range using. It is named after dattaraya ramchandra kaprekar was an indian. All natural numbers less than 10,000 except some with same digits can be reduced to 6174 in the followi. A modified kaprekar number is a positive whole number n with d digits, such that when. What is kaprekar number definition and meaning math. A modified kaprekar number is a positive whole number n n with d d digits, such that when we split its square into two pieces a right hand piece r r with d d digits and a left hand piece l l that contains the remaining d d or d. Take any fourdigit number, with minimum of two different numbers 1122 or 5151 or 1001 or 4375 and so on. Write a function that counts the number of iterations in kaprekars routine, which is as follows. Explore the story behind the mysterious number 6174. Kaprekar number is one of those gems, that makes mathematics fun.
If n kaprekars constant 6174 during their my favorite presentation. Hackerrank algorithms implementation modified kaprekar numbers solution. Write a program in c to generate and show all kaprekar numbers less than. Add these two digits and if the result is as same as n, then n is a kaprekar number. Say 45, if we square it we get 2025 that is 45 2 2025, and split it as 20 and 25 then add it, will get 45. The decimal n kaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10 n 1. Kaprekar steps code challenge matlab matlab programming. Square it and add the right n digits to the left n or n1 digits. Can you write the python code for a kaprekar number.
So, say, you want to find all the kaprekar series for 5digit numbers there are three of them, just ask the generator to generate all the series for 5digit numbers and voila. N is a kaprekar number if it has d digits, and if you take n 2 and divide it into two pieces each d digits in size and add them together, you get n. Im new to python and as a first exercise, ive written a function module. In number theory, a kaprekar number for a given base is a nonnegative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. Write a program in c to find the deficient numbers integers between 1 to 100. Well, to the can you bit id say that every common programming language in the world would have the ability to do simple arithmetics and array which is about what is required to find a kaprekar number, and other ideas of recreational mathematics. A kaprekar number is an ndigit number k that, when the first n or n1 digits of k2 are added to the second n the digits of n2, the result is n. The kaprekar series generator is a java application to help find all the kaprekar series for a specified number of digits.