4 ms·

This seems obviously related to the standard manual accounting trick employed when isolating an error in a double ledger - the first thing you do is look to see

This seems obviously related to the standard manual accounting trick employed when isolating an error in a double ledger - the first thing you do is look to see if the error is evenly divisible by 9. If it is, you've transposed 2 or more numbers somewhere. To prove why this is so: For any numbers x and y: The correct value is 10x + y The transposed value is x + 10y The difference is (10x - x) + (y - 10y) Reduces to 9x - 9y Factors to 9(x - y)

AnotherGoodName 3y ago
Yes i think there's two components to this and that's the first part. Each digit sum on the left and right side converges to 18. Each side of the equation a - rev_a = b has digit sums to that iteratively get closer to each other (sometimes stay the same distance but never getting further). Additionally that convergence only happens at 18. Eg. 5200 (sums to 7) - 0025 = 5175 (sums to 18, 11 apart) 7551 (sums to 18) - 1557 = 5994 (sums to 27, 9 apart) 9954 (sums to 27) - 4599 = 5355 (sums to 18, 9 apart) 5553 (sums to 18) - 3555 = 1998 (sums to 27, 9 apart) 9981 (sums to 27) - 1899 = 8082 (sums to 18, 9 apart) 8820 (sums to 18) - 0288 = 8532 (sums to 18, 0 apart) 8532 (sums to 18) - 2358 = 6174 (sums to 18, 0 apart) 7641 (sums to 18) - 1467 = 6174 (sums to 18, 0 apart) I think this is the first clue. The digits can only be equal on each side when they are 18 and the sum of each side progressively gets closer on each side, eventually equalling each other which has to happen at 18. I think if you dive in it's a variation of the classic 'digits sum to 0 mod 9'. Then once the digits on each side sum to 18 i think they must converge onto 6174 from there. So first we have digits always converging to have the same digit sum on each side and that convergence is always when the digit sum is 18 on each side of the equation. I think property is going to be provable by the classic mod 9 rules but it'd take some work. Then i believe we have a second property kicking in that all 4 digit numbers that have digits that sum to 18 on both sides of this equation will converge on 6174. This is a more limited set of numbers. Only numbers of the form a - a_rev = b that have digits that sum to 18 for both a and b need to be considered since we can separately see the convergence to 18 on both sides above.
- devilsAdv0cate 3y ago
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chrismorgan 3y ago
Why is the correct value 10x + y?
- roenxi 3y ago
  Say the correct value is 42. He broke the number down into 10x4 + 2. It is just writing the correct number in a form that emphasises the important elements for the transposition.
  - chrismorgan 3y ago
    Oh, transposed two or more digits, got it.
- sally_glance 3y ago
  Probably because swapping two digits causes that (times ten moves the digit one place to the left). For example if you accidentally swapped 210,00 to 120,00: 20x10 + 10 is the correct number, 20 + 10x10 is the swapped one.
  - pajko 3y ago
    2x100 + 1x10 + 0x0, 1x100 + 2x10 + 0x0
skrebbel 3y ago
> obviously It’s not obvious to me at all, I had to think pretty hard about it.
devilsAdv0cate 3y ago
[dead]

AnotherGoodName 3y ago

Yes i think there's two components to this and that's the first part. Each digit sum on the left and right side converges to 18. Each side of the equation a - rev_a = b has digit sums to that iteratively get closer to each other (sometimes stay the same distance but never getting further). Additionally that convergence only happens at 18. Eg. 5200 (sums to 7) - 0025 = 5175 (sums to 18, 11 apart) 7551 (sums to 18) - 1557 = 5994 (sums to 27, 9 apart) 9954 (sums to 27) - 4599 = 5355 (sums to 18, 9 apart) 5553 (sums to 18) - 3555 = 1998 (sums to 27, 9 apart) 9981 (sums to 27) - 1899 = 8082 (sums to 18, 9 apart) 8820 (sums to 18) - 0288 = 8532 (sums to 18, 0 apart) 8532 (sums to 18) - 2358 = 6174 (sums to 18, 0 apart) 7641 (sums to 18) - 1467 = 6174 (sums to 18, 0 apart) I think this is the first clue. The digits can only be equal on each side when they are 18 and the sum of each side progressively gets closer on each side, eventually equalling each other which has to happen at 18. I think if you dive in it's a variation of the classic 'digits sum to 0 mod 9'. Then once the digits on each side sum to 18 i think they must converge onto 6174 from there. So first we have digits always converging to have the same digit sum on each side and that convergence is always when the digit sum is 18 on each side of the equation. I think property is going to be provable by the classic mod 9 rules but it'd take some work. Then i believe we have a second property kicking in that all 4 digit numbers that have digits that sum to 18 on both sides of this equation will converge on 6174. This is a more limited set of numbers. Only numbers of the form a - a_rev = b that have digits that sum to 18 for both a and b need to be considered since we can separately see the convergence to 18 on both sides above.

devilsAdv0cate 3y ago
[dead]

chrismorgan 3y ago

Why is the correct value 10x + y?

roenxi 3y ago
Say the correct value is 42. He broke the number down into 10x4 + 2. It is just writing the correct number in a form that emphasises the important elements for the transposition.
- chrismorgan 3y ago
  Oh, transposed two or more digits, got it.
sally_glance 3y ago
Probably because swapping two digits causes that (times ten moves the digit one place to the left). For example if you accidentally swapped 210,00 to 120,00: 20x10 + 10 is the correct number, 20 + 10x10 is the swapped one.
- pajko 3y ago
  2x100 + 1x10 + 0x0, 1x100 + 2x10 + 0x0

skrebbel 3y ago

> obviously It’s not obvious to me at all, I had to think pretty hard about it.

devilsAdv0cate 3y ago

[dead]