You don't need to say a thing Part 5

Logic Level 3

Think of a 4 digit positive integer with at least two distinct digits. Follow these steps:

Step 1) Arrange the digits in descending order, and also arrange the digits in ascending order to get two four-digit integers, adding the leading zeros when necessary.
Step 2) Find the absolute difference between the two numbers you've found in step 1.
Step 3) Repeat Steps 1 to 2 six more times.

I know what number you have. What must it be?

Details and Assumptions :

  • As an explicit example, if your original number is 2770. Then the two numbers are 7720 and 0277, with a difference of 7443.


The answer is 6174.

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Chung Kevin by Chung Kevin , 45, Australia

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5 solutions

Akshat Sharda
Aug 10, 2015

See this,

Kaprekar's constant

5 Helpful 0 Interesting 0 Brilliant 0 Confused

i took 7890.... and at last 6174 was repeating.... I can't believe that only "13% could solve it"... and it should be a level 2 question.... not 3!!

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Its actually level 4 now....haha

Yatharth Chowdhury - 5 years, 4 months ago

I think that some people are just too lazy and click for a solution. Since its given that it doesn't change, anyone could just plug in 1122 and 2211 or something and get it

Brian Wang - 5 years, 8 months ago

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That's the difference between commoners and the community. Most of us don't plug in any value, but search for a logical or mathematical proof for the same.

Swapnil Das - 5 years, 3 months ago
Arnab Das
Aug 4, 2015

6174 is a very famous number. This number is known as the Kaprekar's constant. However there are some exceptions. 1000 has two distinct digits in it, it will will never generate 6174, same is with 1222. A detailed list of the exceptions is still not there on Wikipedia. Hope someone works on this:)

3 Helpful 0 Interesting 0 Brilliant 0 Confused

1000 and 1222 works too! You just need to add the leading zeroes (see my other comment).

Isn't this constant weird?

Chung Kevin - 5 years, 10 months ago

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Its Kaprekar's constant

Akshat Sharda - 5 years, 10 months ago
Siva Prasad
Sep 26, 2015

Yes..! its the Kaprekar's constant

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Kesudh Giri
Aug 2, 2015

Just went and did it with the given example, and got the answer!!! But doesnt work for some numbers when you subtract them and get a 3 digit number. Example: If i take 1222, 2221-1222=999. So, question's wrong matey!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes, you get a 3 digit number, but you need to add leading zero to 999 to get 0999 (like the given example).

So 9990 - 0999 = 8991

9981 - 1899 = 8082

8820 - 0288 = 8532

8532 - 2358 = 6174

Repeat another 2 more times, we get 6174.

Chung Kevin - 5 years, 10 months ago

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