6174

Take any number with 4 non-repeating digits. Say 1562.

Step 1: Arrange the number in ascending and then descending order
Step 2: Subtract the smaller number from the bigger number

6521 - 1256 = 5265

Repeat the steps with your new number (the answer):

(5265 rearranged) 6552 - 2556 = 3996

(3996 rearranged) 9963 - 3699 = 6264

(6264 rearranged) 6642 - 2466 = 4176

(4176 rearranged) 7641 - 1467 = 6174

Try any 4-digit number with non-repeating digits, and you'll always get 6174.
Pretty cool, huh?

6174 is known as Kaprekar's constant. The math operation above, discovered by Indian mathematician D.R. Kaprekar, will reach 6174 after at most 7 steps (if you did more than 7 iterations, check your arithmetic).

Via

6 comments:

  1. Use your equal signs more carefully, surely (5265 = 6552 - 2556 = 3996) Is not a valid equation as 5265 is not equal to 3996..

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  2. anonymous, the poster isn't insinuating 5265 = 3996; he was saying that 5265 rearranged with the greatest number at the beginning is equivalent to 6552.

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  3. Yes exactly. But just to be perfectly clear, I have changed it. Thanks!

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  4. 7156

    7651-1567=6084

    8640-0468=8172

    8721-1278=7443

    7443-3447=3996

    9963-3699=6264

    6642-2466=4176

    7641-1467=6174

    awesome stuff!

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  5. I have to agree with the first anonymous poster, If you are writing "5265 = 6552 - 2556 = 3996", the you ARE implying that 5265 IS equal to 3996, no matter what your intentions were. That is what the equality sign means.

    But the original poster have now solved the "problem" in a nice way...

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  6. I have noticed that this works so long as all 4 digits don't repeat (obviously), but even up to 3 repeating digits will produce the result of 6174. Very interesting indeed.

    ReplyDelete