Can anyone share the proof for the following?

Today when I was surfing the internet I stumbled across this video.This was fasinating.

Take any 3 digit number, rearrange the numbers to form the largest number and the smallest number possible.

Subtract the two, repeat the process and eventually you will end at the number 495.

If you do this with any 4 digit number you get 6174.

I really wanted to know the proof of this. Can anybody please share the proof?Please

Note by Shriniketan Ruppa
3 months, 1 week ago

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1 vote

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The algebraic proof is pretty intricate, and I'm too tired for LaTeX\LaTeX, so here's a table of values.

Ved Pradhan - 3 months, 1 week ago

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If ac=0a-c=0 or ac=1a-c=1, the values leave 3 digit numbers and approach zero.

For four digit numbers, a similar proof can be used, but it might take more time.

Ved Pradhan - 3 months, 1 week ago

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Kaprekar's constant

Pi Han Goh - 3 months, 1 week ago

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I think it is a result by iteration.

Zakir Husain - 3 months ago

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Some number which don't get to 495495:111,222,333,444,555,666,777,888,999111,222,333,444,555,666,777,888,999

Zakir Husain - 3 months ago

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@Zakir Husain : As you can see if you look in the reply to my comment, the numbers that don't converge to 495 are numbers where the difference between the biggest and smallest numbers are 1 or 0. For the numbers where this is 1 or 0, the sequence converges to 0.

Ved Pradhan - 3 months ago

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