Id like some feedback on whether this is pythonic enough, and if i can improve it. It works for positive numbers upto the range of 999,999,999,999 i. I aas solving a problem on hackerrank and the problem is as follows. Given a number, the task is to check if it is kaprekar number or not. Program to check for kaprekar number guide for school. Kaprekar, found number 6174 also known as kaprekar constant that will return the subtraction result when following this rules. 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. 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. 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 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. 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. 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. Kaprekar number are those number whose square, if split into parts and then add it, will be the same as the original number.
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. Given two positive integers and where is lower than, write a program to. Split the string representation of the square into two parts, and. 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.
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. The mystery and music of kaprekar constant 6174 renaissance. Consider n as a positive integer that has k number of digits. Write a program in java to input a number and check whether it is a kaprekar number or not. Modified kaprekar numbers hacker rank problem solution. Can you write the python code for a kaprekar number.
Kaprekar number programming java tutorial using eclipse. 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. The best known is probably that related to the number 6174, sometimes called kaprekars constant. Write a function that counts the number of iterations in kaprekars routine, which is as follows. 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. Hackerrank algorithms implementation modified kaprekar numbers solution. 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. Java program to check kaprekar number java tutorials and. We square to arrive at a number that is either digits long or digits long. This program performs kaprekars routine to automating the process. In number theory, a kaprekar number for a given base is a nonnegative integer, the representation of whose square in that base can be. Add these two digits and if the result is as same as n, then n is a kaprekar number. Kaprekar number programming java tutorial using eclipse subscribe. Masrul huda on 24 jun 2012 this is no more coding but the cyclist on 14 jun 2016.
Given a 4digit number that has at least two different digits, take that number s descending digits, and subtract that number s ascending digits. Write a java program to generate and show all kaprekar numbers less than. The series of kaprekar numbers is known as a006886, and begins as 1,9,45,55. Take any fourdigit number, with minimum of two different numbers 1122 or 5151 or 1001 or 4375 and so on. Square it and add the right n digits to the left n or n1 digits. Kaprekar is remembered today for a range of curious mathematical patterns that he discovered. The kaprekar method is very easy to use and is the following. This is a python module to convert number words eg.
The decimal n kaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10 n 1. Numbers having fewer than 4 digits are appended with leading 0s, resulting in all values converging to 6174. Manick srinivasan and ramkumar ramamoorthy sent me more computer results. Given a 4digit number that has at least two different digits, take that numbers descending digits, and subtract that numbers ascending digits. Kaprekar was an indian mathematician who came up with this beautiful result from number theory in 1946. Sep 29, 2014 a student talked about kaprekars constant 6174 during their my favorite presentation. If n kaprekars constant 6174 during their my favorite presentation. 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 sequences wells 1986 book defines kaprekar number roughly as follows. For example, given 6589, you should take 9865 5689, which is 4176. Explore the story behind the mysterious number 6174. 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.
It is named after dattaraya ramchandra kaprekar was an indian. Steps from wikipedia take any fourdigit number, using at least two different digits. Pdf a variant of kaprekar iteration and kaprekar constant. Calculate n kaprekar numbers code golf stack exchange. Sep 21, 2010 wolframs mathworld describes kaprekar numbers like this. Repeat this process with 4176 and youll get 7641 1467, which is 6174.
Modified kaprekar numbers discussions algorithms hackerrank. Jun 27, 2019 kaprekar number programming java tutorial using eclipse subscribe. 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. The number 6174 is the only unchanged mysterious number discovered by kaprekars operation.
Im new to python and as a first exercise, ive written a function module. Kaprekar steps code challenge matlab matlab programming. 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. The main object that the library deals with is a phonenumber object. A modified kaprekar number is a positive whole number n with d digits, such that when. What is kaprekar number definition and meaning math. If the resultant sum is k, then k is called a kaprekar number. Arrange the digits in descending and then in ascending order to get two fourdigit numbers, adding leading zeros if necessary. Mathematics and number based challenges developer insider. The best known is probably that related to the number 6174, sometimes called kaprekar s constant. How to prove kaprekars constant 6174 in layman terms.
How do you code a program to find kaprekar number answers. 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. It has always been a fascinating theorem, easily understood but hard to prove for amateurs, a lesser fermats last theorem. Write a program in c to find the deficient numbers integers between 1 to 100. The kaprekar series generator is a java application to help find all the kaprekar series for a specified number of digits. A modified kaprekar number is a positive whole number with a special property. 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. How to find kaprekar numbers within a given range using python. Kaprekars constant using c language programmingwithsantiago. 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. All natural numbers less than 10,000 except some with same digits can be reduced to 6174 in the followi. Write a program that calculates and outputs the first n kaprekar numbers, with n being in the range, but not limited to the range. Write a program in c to generate and show all kaprekar numbers less than. Wolframs mathworld describes kaprekar numbers like this consider an ndigit number k.
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. Apr 29, 2014 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. The number 6174 is the only unchanged mysterious number discovered by kaprekar s operation. 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. Kaprekar number is one of those gems, that makes mathematics fun. Iannucci the university of the virgin islands 2 john brewers bay st. Generate all possible chains leading to 6174, show their length and their patterns of convergence. Download discrepancies asked in computer programming. 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 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. 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. How to find kaprekar numbers within a given range using. This solution only tests for divisibility by 9, not whether the number is a kaprekar number.
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. Take any fourdigit number, using at least two different digits. 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. Discover the mystery behind the 6174 loop by using any four digit number. Jan 25, 2018 kaprekar is remembered today for a range of curious mathematical patterns that he discovered. 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. Write a function that counts the number of iterations in kaprekar s routine, which is as follows.