{"id":44,"date":"2016-01-09T15:31:49","date_gmt":"2016-01-09T15:31:49","guid":{"rendered":"http:\/\/muthu.co\/?p=44"},"modified":"2021-01-02T14:06:15","modified_gmt":"2021-01-02T14:06:15","slug":"the-mysterious-and-beautiful-6174","status":"publish","type":"post","link":"http:\/\/write.muthu.co\/the-mysterious-and-beautiful-6174\/","title":{"rendered":"The mysterious and beautiful 6174"},"content":{"rendered":"

My favorite will always be 1.618 (The Golden Ratio) but 6174 fascinated me recently mainly because of the mystery it carries.<\/p>\n

It was in 1949 when an Indian\u00a0mathematician named D. R. Kaprekar, devised a process now known as Kaprekar’s operation. This was published in “Scripta Mathematica<\/a>” which was a quarterly journal published by Yeshiva University. This was the only magazine which was believed to be edited by masters for laymen at that time.<\/p>\n

So whats the big deal?\u00a0Pick any four digit number where all the numbers are not same for example 2500. Now rearrage the digits to get the largest and the smallest number that it can make. Subtract the smallest number from the largest to get a new number, repeat this operation for every new number. All this seems simple isn’t it? But how is it a beautiful pattern? Karpekar discovered that this process actually led to a surprising result.<\/p>\n

Lets take 2500 for instance and see how it turns out to be beautiful. The smallest number that you can make up with 2500 is 25 and the largest being 5200.<\/p>\n

5200 – 0025 = 5175
\n7551 – 1557 = 5994 (Made from 5175 the result of previous subtraction)
\n9954 – 4599 = 5355
\n5553 – 3555 = 1998
\n9981 – 1899 = 8082
\n8820 – 0288 = 8532
\n8532 – 2358 = 6174
\n7641 – 1467 = 6174<\/p>\n

When we reach 6174 the operation repeats itself, returning 6174 every time. Karpekar called it the kernel of this operation.<\/p>\n

Lets try another number,<\/p>\n

9990 – 999 = 8991
\n9981 – 1899 = 8082
\n8820 – 288 = 8532
\n8532 – 2358 = 6174 ( Reached 6174 again! )<\/p>\n

Why is it special?<\/strong>
\nEvery 4 digit number combination will end up in 6174. <\/p>\n","protected":false},"excerpt":{"rendered":"

My favorite will always be 1.618 (The Golden Ratio) but 6174 fascinated me recently mainly because of the mystery it carries. It was in 1949 when an Indian\u00a0mathematician named D. R. Kaprekar, devised a process now known as Kaprekar’s operation. This was published in “Scripta Mathematica” which was a quarterly journal published by Yeshiva University. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[54],"_links":{"self":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/44"}],"collection":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/comments?post=44"}],"version-history":[{"count":1,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/44\/revisions"}],"predecessor-version":[{"id":1674,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/44\/revisions\/1674"}],"wp:attachment":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/media?parent=44"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/categories?post=44"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/tags?post=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}