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enter image description here

Hint 1

This graph was chosen from a larger collection of graphs.

Hint 2

Among the graphs mentioned in Hint 1, this particular graph is specified by the collection $\{ 3284, 6235, 6685, 6619, 116 \}$.

Hint 3

The calculation-puzzle tag is included only to indicate that you need to calculate the final number, but this puzzle is not calculation-intensive.

Background on puzzle (Spoiler Alert)

I got the idea for this puzzle from a Numberphile, and decided to turn this into a graph puzzle with graphviz. The collection $\{ 3284, 6235, 6685, 6619, 116 \}$ was chosen at random.

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1 Answer 1

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The final node contains the number

6174

because

each node's "successor" is obtained by taking the difference between the largest and smallest numbers obtainable by rearranging its digits. That is: descending order minus ascending order. So e.g. 3284 is followed by 8432-2348. All numbers are treated as having four digits, so 116 means 0116 and is followed by 6110-0116.

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  • $\begingroup$ Interesting. Do all 4-digit numbers converge to that value (or to the trivial other value)? $\endgroup$
    – user3294068
    Commented Apr 23, 2020 at 19:35
  • $\begingroup$ Yes, it turns out that they do. $\endgroup$
    – Gareth McCaughan ♦
    Commented Apr 23, 2020 at 22:39
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    $\begingroup$ It holds for all 4-digits numbers where at least one digit is distinct. For example, 9999, 0000, 4444, etc, will not work. $\endgroup$
    – Galen
    Commented Apr 25, 2020 at 0:11

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