Anonymous at Sat, 25 May 2024 22:14:45 UTC No. 16193221

WOOOOOAHHHH I CONTRICTED POSSIBLE CHOICES AND SOMETHING REPEATED I'M GOOOOOOONING
fucking mathcels need to be institutionalized

Anonymous at Sat, 25 May 2024 22:25:17 UTC No. 16193242

>>>/tg/

Anonymous at Sat, 25 May 2024 22:47:14 UTC No. 16193275

>>16193213
If there is no proof, then I am not interested.

Anonymous at Sat, 25 May 2024 23:11:38 UTC No. 16193299

>>16193275
>If there is no proof, then I am not interested

I guess you missed the colorful picture.

https://www.sudokuweb.org/

Generate as many solved Soduko states that you desire. Example, just the rows...

Index 000 (no unique unpaired numbers)
598 217 346 == 598 . 217 . 346
127 436 859 == 859 . 127 . 436
634 589 127 == 589 . 127 . 634

Index 159
713 894 265 == 26(5) . 8(9)4 . 7(1)3
269 375 418 == 26(9) . 4(1)8 . 37(5)
485 621 793 == 62(1) . 48(5) . 7(9)3

Index 279
951 743 682 == (9)51 . (7)43 . 68(2)
876 152 934 == 15(2) . (9)34 . 8(7)6
342 968 571 == 5(7)1 . 34(2) . (9)68

Anonymous at Sat, 25 May 2024 23:32:36 UTC No. 16193328

Now just the columns.
598 217 346
127 436 859
634 589 127

713 894 265
269 375 418
485 621 793

951 743 682
876 152 934
342 968 571

But let's rotate them 90 degrees
For easier text formatting.

Index 157
697 583 241 == 69(7) . (5)83 . 24(1)
452 619 837 == 6(1)9 . 83(7) . 4(5)2
381 247 695 == 69(5) . 38(1) . 24(7)

Index 126
769 451 328 == 7(6)9 . 45(1) . 3(2)8
138 972 456 == 97(2) . 45(6) . (1)38
245 836 719 == 7(1)9 . (2)45 . 83(6)

Index 285
874 395 162 == (8)74 . 39(5) . 16(2)
923 168 574 == (5)74 . 9(2)3 . 16(8)
516 724 983 == 7(2)4 . 9(8)3 . (5)16

Anonymous at Sun, 26 May 2024 08:54:47 UTC No. 16193787

>>16193213
Please elaborate

Anonymous at Sun, 26 May 2024 09:09:51 UTC No. 16193799

>>16193213
Cool

Anonymous at Sun, 26 May 2024 23:28:51 UTC No. 16194953

>>16193213
This writeup is ambiguously-worded. What is a "leftover"? Does "indexing" refer to hashing or otherwise uniquely identifying a sudoku? Are six triplets needed, or not? Does "indexing" offer shortcuts to solving a sudoku?

Anonymous at Sun, 26 May 2024 23:44:09 UTC No. 16194989

What is OP trying to say? I'm too much of a brainlet to even understand the point.

Anonymous at Mon, 27 May 2024 00:16:05 UTC No. 16195021

Neat. Do you have a proof that it happens in all cases, or have you just observed it in a large number of cases?

Anonymous at Mon, 27 May 2024 00:29:52 UTC No. 16195043

>>16194953
>This writeup is ambiguously-worded. What is a "leftover"? Does "indexing" refer to hashing or otherwise uniquely identifying a sudoku? Are six triplets needed, or not? Does "indexing" offer shortcuts to solving a sudoku?

Should be pretty obvious.
Let's go with the second example.

2nd row
Index 159
713 894 265 == 26(5) . 8(9)4 . 7(1)3
269 375 418 == 26(9) . 4(1)8 . 37(5)
485 621 793 == 62(1) . 48(5) . 7(9)3

Of the three 3x3 squares in that row.
We have 713 next square has 375 and next square has 793. What is common? Well, the three numbers all have a 7 & 3. What is uncommon, the three numbers sets have 1, 5, 9.

If we examine the other three sets, they too have pairs of numbers 4 & 8, and 2 & 6. What are the uncommon numbers? 1, 5, 9.

Because these numbers are uncommon they make the index for that row, you can put them in any order, but 157 is lowest to highest.

In the 000 row, there are no uncommon numbers, each of the three 3x3 squares is a permutation of the previous square.

I bring up the law of Transposition because if you exchanged all the number 9 values with all the number 8 values, the indexes for rows would become 000, 158, 278 instead of 000, 159, 279.

By this method you can index unknown Sudoku Solutions instantly.

>Does "indexing" offer shortcuts to solving a sudoku?

Solving Sudoku puzzles
This knowledge is generally only good for MID-SOLVING Sudoku puzzles. As you need at least 45% of the solution (36 solved squares) visible to utilize this knowledge. Early stage Sudokus are not solvable using only this knowledge unless you know the index values. The GEMINI AI says these index values can be used by themselves to generate a unique Sudoku solution.

Mid-Stage Sudoku puzzles become easier in that you don't have to guess numbers as hard or have multiple elimination options. Once you know a number pairing exists of the 3 values possible per row or column, it's easier to eliminate impossible pairings.

Anonymous at Mon, 27 May 2024 00:55:17 UTC No. 16195058

>>16195021 (me)
After thinking about it, I see a proof. Consider three 3x3 squares in a row. Any particular digit must occur once in each of the 3x3 squares, and it must occur in a different row in each of the three 3x3 squares. The number of ways of choosing a row in each square is 6, and there are 9 digits we have to make such a choice for. Think of the 6 choices of rows in each square as 6 buckets that we have to put the 9 digits into.

We can split into two cases: Either every bucket contains at most 2 digits, or there is a bucket with 3 digits. It's not possible to put more than three digits in a bucket.

1) every bucket contains at most 2 digits
Since there are 9 digits and 6 buckets, there must be at least 3 buckets with 2 digits in them; these are the digit pairs sought. Note that the remaining 3 buckets must have at most one digit each, because otherwise there would be a row of a 3x3 square with 4 digits in it.

2) there is a bucket with 3 digits
These 3 digits occupy a full row of each 3x3 square. For the remaining digits, there are only 2 ways remaining to choose a row in each of the 3x3 squares. In the bucket analogy, that's 2 buckets that it remains possible to put digits into. So we get 3 buckets with 3 digits each in them, with the rest of the buckets empty. This is the case of three triplets.

Anonymous at Mon, 27 May 2024 01:48:22 UTC No. 16195120

>>16195058
>After thinking about it, I see a proof.

Excellent,you see what I see.
These new Sudoku Rules actually remove some difficulty by elimination of illogical or impossible pairings.

Here is another example partial Sudoku (easy level) with notes. And how I achieved my deductions. The trick is to realize that if you've got a normal column or row, not a 000 strip, the logic can make concrete predictions very fast.

Although, a 000 strip can also grant extra predictable benefits. Note the unusual Sudoku puzzles like math Sudokus can become drastically easier knowing Sudoku Indexing.

Anonymous at Mon, 27 May 2024 01:58:57 UTC No. 16195129

Made a goof, middle row chunk of the 9x9 square text is duplicated, creating nonsense.

Using the crude ass ANDROID phone document editor so this is slow, and painful versus using XARA or SERIF desktop apps. Reposting fixed image. Sorry. Android phones tend to be laggy and lock up depending on software and hardware.

Anonymous at Mon, 27 May 2024 02:00:11 UTC No. 16195130

>>16193299
A colorful picture is not a proof. And examples are not a proof.
>>16195043
Bro, nobody gives a fuck about gemini.

Anonymous at Mon, 27 May 2024 02:05:01 UTC No. 16195136

>>16195120
>>16195129
Can you post the original sudoku problem without anything filled in so it's easier to follow along by trying it on my own?

Anonymous at Mon, 27 May 2024 02:11:52 UTC No. 16195140

>>16195130
>A colorful picture is not a proof. And examples are not a proof.

Fun thing about absence of logic being an inductive proof. This is 4Chan, home of shitposting for giggles, but not the only home. Autism (uncontrollable emotional outbursts) & Asperger's (high functioning low emotion) is that INTENSE ANGER over such a self-evident proof is VERY AMUSING rather than enraging.

My logical deduction is that you are an Elgin Air Force Base Bot or an Israeli Bot or a India Pajeet Proxy. Since the first two have better logical AI systems, I deduce you are from India and a very low paid Pajeet.

Extremely amusing.
This isn't an insult, merely an obvious logical prediction based on your absence of logic and inability to exercise wit or humor which is common with high IQ 4Channers.

Anonymous at Mon, 27 May 2024 02:21:55 UTC No. 16195154

>>16195136
>Can you post the original sudoku problem without anything filled in so it's easier to follow along by trying it on my own?

The Sudoku was generated using
https://www.sudokuweb.org/

Cheap and quick way to get puzzle + solution.
Unfortunately, the INDEXING has a low utility value for early stage Sudoku Solving (17 of 81 squares known), but genuinely makes mid stage (34 to 56) very easy as it wipes out the 2 or 3 path choices in possible solutions as the wrong solutions become immediately obvious as being impossible.

My curiosity and discovery came from creating a SUDOKU GLOBE concept. Imagine a Solved Sudoku with a 3x9 chunk missing (row or column) and creating a completed Sudoku then chop off another 3x9 chunk and repeat. Essentially an "infinite Sudoku Grid" but obviously not infinite. Part of this was identifying if this could actually be achieved and the limits. The rest was just simple obvious deduction of where that leads.