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Four-Digit Number (Posted on 2003-04-26) Difficulty: 4 of 5
Find a four-digit number with four different digits, that is equal to the number formed by its digits in descending order minus the number formed by its digits in ascending order.

See The Solution Submitted by Ravi Raja    
Rating: 3.1667 (6 votes)

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Some Thoughts re: Interesting! | Comment 7 of 14 |
(In reply to Interesting! by Bryan)

In fact, take any four digits, consecutive or not, and so long as they are not all equal, and keep repeating the process, and you will eventually get 6174 after at most 7 iterations.

For example, start with 2631. Applying this procedure produces successive values of 5085, 7992, 7173, 6354, 3087, 8352 and then 6174 interminably.

It even works considering smaller number as having leading zeros: 343 produces (via 0343) 3996, 6264, 4176, 6174.

Of course if all the digits are the same, then you get all zeros right away and that's the end, but only one digit need be different, as in 1112 leading to 0999, 8991, 8082, 8532, 6174.

  Posted by Charlie on 2003-04-27 04:06:07

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