@LionJim, 6174.

[Tgar]

Go.

 

[LionJim]

I’m going to pick a random 4-digit number, 7532, note that the digits are decreasing, then subtract from this the number you get by rearranging the digits from low to high.
7532-2357=5,175. Rearrange from high to low and repeat.
7551-1557=5,994
9954-4599=5,355
5553-3555=1,998
9981-1899=8,082
8820-288=8,532
8532-2358=6,174.

Kaprekar’s Constant. Notice that if you do the same procedure with 6174, you get
7641-1467=6,174. There are some restrictions (like 1111 won’t work) but when you start with four different digits you’ll always arrive at 6174 within seven steps.

Number theory, not my thing. I don’t remember ever seeing this before. I wouldn’t have the foggiest idea how to prove this, maybe/probably a brute force proof.

 

[Tgar]

I’m going to pick a random 4-digit number, 7532, note that the digits are decreasing, then subtract from this the number you get by rearranging the digits from low to high.
7532-2357=5,175. Rearrange from high to low and repeat.
7551-1557=5,994
9954-4599=5,355
5553-3555=1,998
9981-1899=8,082
8820-288=8,532
8532-2358=6,174.

Kaprekar’s Constant. Notice that if you do the same procedure with 6174, you get
7641-1467=6,174. There are some restrictions (like 1111 won’t work) but when you start with four different digits you’ll always arrive at 6174 within seven steps.

Number theory, not my thing. I don’t remember ever seeing this before. I wouldn’t have the foggiest idea how to prove this, maybe/probably a brute force proof.

@laKavosiey-st lion How about our math wizard!

 

[DaytonRickster]

I’m going to pick a random 4-digit number, 7532, note that the digits are decreasing, then subtract from this the number you get by rearranging the digits from low to high.
7532-2357=5,175. Rearrange from high to low and repeat.
7551-1557=5,994
9954-4599=5,355
5553-3555=1,998
9981-1899=8,082
8820-288=8,532
8532-2358=6,174.

Kaprekar’s Constant. Notice that if you do the same procedure with 6174, you get
7641-1467=6,174. There are some restrictions (like 1111 won’t work) but when you start with four different digits you’ll always arrive at 6174 within seven steps.

Number theory, not my thing. I don’t remember ever seeing this before. I wouldn’t have the foggiest idea how to prove this, maybe/probably a brute force proof.

Dude, you are the math man!

 

[LionJim]

Dude, you are the math man!

Wikipedia math articles are excellent. Like I said, I don’t recall seeing this before. I do have the ability to explain, though.

 

[laKavosiey-st lion]

@laKavosiey-st lion How about our math wizard!

F that, after a 2 hour morning meeting I’m off to mammoth (bringing son2, surprisings son1)
no time for brain power SPRING BREAK MF!!

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