Twin Equivalent Sudokus

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby hutman » Sat Dec 02, 2006 5:13 pm

gsf wrote:
yes, the two pseudo puzzles have 7539 and 77146 solutions respectively.


Oh my god! What a joke! A "puzzle" with 7539 and 77146 solutions! For goodness sake! Don't play such a silly prank on us! This forum is not the place for posting your junks. What do you think of us? You think all of us are supercomputers, gods or supermen? What is your motive? Yet you still have the cheeks to challenge someone to solve your junk. You think he is a god, a superman or a supercomputer?

At first when I saw your nice-looking "puzzle", I intended to include it in my future book on the history of sudoku. Hence I spent more than one whole day and one whole night trying to solve your junk, and in the end I was convinced that it has no unique solution at all. In other words, it is a junk, not a puzzle!

Gsf, you owe us an explanation as to why you post such junks on this forum. You owe those like me who had lost many hours of sleep and being made a monkey of by your silly prank a satisfactory explanation.
Now it is your turn to experience sleepless nights like us.

Starting from today, you have the moral responsibility to post one solution everyday until you have finished posting all the 77146 solutions. Let you go through the same terrible experience we have gone through.

Every time when I think of the many hours of sleep I had lost, my temperature would shoot up to 10 metres high:!:
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Postby ronk » Sat Dec 02, 2006 6:02 pm

hutman, you apparently did not read the entire thread before posting that rant.
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Postby gsf » Sat Dec 02, 2006 6:13 pm

hutman wrote:gsf wrote:
yes, the two pseudo puzzles have 7539 and 77146 solutions respectively.

What a joke! A "puzzle" with 7539 and 77146 solutions! For goodness sake! Don't play such a silly prank on us! This forum is not the place for posting your junks.

the twin puzzle problem statement is such that one or both of the component puzzles are not solvable independently
to eventually lead to a valid sudoku not solvable means that one or both
of the twins have multiple solutions (or equivalently, one or both are pseudopuzzles)

I looked at the problem statement as a generation challenge
which made me think about what would make twins hard to solve
(1) many solutions in both pseudopuzzles, my first post
(2) not so many solutions but with the twins almost identical, my final post

one thing this shows is that mathematically/algorithmically interesting problem instances
are not necessarily interesting for humans to solve by hand

as with anything scraped from the web verify before assuming
each of the twins look like valid sudoku, but because of the context in which
they were posted they need not be

along the same lines, consult a real doctor before making medical decisions

finally, I hope you respect the work done by the forum denizens and properly
attribute all of your scrapings in the book
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Postby tarek » Sat Dec 02, 2006 9:11 pm

gsf wrote:as with anything scraped from the web, verify before assuming
Especially if you are scraping from the sudoku VARIANTS section.

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Postby hutman » Sat Dec 02, 2006 9:38 pm

So far the common claim about sudoku is that it requires no mathematics but only logic to solve. However, the introduction of equivalent sudokus into the realm of puzzles has brought in the element of mathematics. The problems raised by you belong to the realm of mathematics, not puzzles. If you want to discuss such things, you should do it in mathematics magazines, forums or societies. If you ever find the answers to your questions (I doubt anybody can succeed in doing so), you would gain eternal fame in the world of mathematics.

From what you said -- "many solutions in both pseudopuzzles" -- it shows that you do not know what you are talking about. It also shows that you do not know what a puzzle is. It also shows that you are totally mixed up and confused about the whole issue. If you call something a puzzle, it means that it has a unique solution. Conversely, if something has many solutions (which means it has no unique solution at all), it is not a puzzle or has anything to do with puzzles. I can see that you are still trying to link "those freaks of yours" with puzzles by using the term of so-called "pseudopuzzles".

I can see that you are trying to test or challenge Henry Kwok. In the old days, when two people wanted to challenge each other, they went to some isolated place and had a duel with swords. In the end, they killed each other. That was all. Nobody would cry over it. However, when you do such thing in a public forum, you may indirectly hurt the innocent bystanders. For instance, I had lost many hours of sleep. My temperature is still boiling.

I could sense that you were trying to make two identical puzzles to test Henry Kwok, but in the end you failed to make a valid puzzle with a single solution. The result was a freak "puzzle" with multiple solutions.

Furthermore, I can see the introduction of the concept of "Equivalent Sudokus" by Henry Kwok has finally led us to the discovery of the "Mother of all Killers" or the "Mother of the Hangman of all Killers" in the form of "equivalent sudokus".

Such puzzles are like shuffling of a pack of cards. The more you shuffle the cards, the harder you get back the same type of cards you have obtained in the previous game. Hence if you include more transformations (like rearrangement of digits, shifting of lines, boxes, chutes, rotation of a grid to several quarter turns, reflection of digits across the main diagonal) in the making of such puzzles, the puzzles could turn up to be so difficult that it is almost impossible to solve by human efforts.

For me, I believe the puzzles can be solved by laboriously mapping all digits and examining all possible transformations. In the making of such difficult puzzles, the puzzle maker can guide the solvers by providing more hints and guidelines, and increase the number of starting digits to even more than 70 in both grids. But even that, the puzzles would still take a long time to solve.

You are right in saying that anybody can make such puzzles. But you must aware of these ethics in the puzzle world:

Firstly, never, never ask anybody to solve a puzzle which you know is beyond the ability of any human.

This is the same as if you were trying to test the intelligence of Einstein by asking such questions as "How many grains of sand are there on the beach? How many times had I gone to toilet last week?" It is definitely unfair to pose these types of questions to anybody as they can never be answered even by a genius like Einstein.

Secondly, never, never ask anybody to solve a puzzle for which you yourself also do not know how to do.

For example, if you tell somebody that he would be rewarded with a million dollars if he could answer a million-dollar question. After scratching his head for sometime, that person replies: "I admit defeat, but please tell me the answer." Then you admit: "I myself also do know how to do." That is totally ridiculous. You have made yourself a laughingstock. If you don't know the answer, don't ask.

That person will definitely get the impression that you are trying to be funny with him, that you are playing the fool with him, that you are insulting his intelligence, that you are treating him like a cuckoo. No wonder his temperature would rise to 10 metres high.

What is the object of asking somebody to solve a puzzle? It is not to show how clever you are. In asking somebody to solve a puzzle, you have to ensure that your puzzle has an answer and that you yourself know how to demonstrate the solution. When somebody fails to solve your puzzle, don't laugh as though you were standing on the top of the world. You should feel frustrated instead.

You are right to say that "one thing this shows is that mathematically/algorithmically interesting problem instances are not necessarily interesting for humans to solve by hand." It appears that Henry Kwok is also aware of this. He has been very careful to ensure that his puzzles are solvable by not having to much "shuffling" in the equivalent puzzles. His puzzles are all very simple with one or two transformations only.

Making a difficult and silly "puzzle" is not your monopoly. Anybody, including me, can also make such puzzles. I am too happy if you can pay me ten times the hours of sleep I had lost by accepting my challenge to solve my difficult "puzzles". But a word of warning in advance: I myself know neither the solution nor the method of solving. So don't curse and swear when you discover that you have been made a cuckoo:!:
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Postby gsf » Sat Dec 02, 2006 10:25 pm

hutman wrote:... rants ...

step back
take a deep breath
note that you are in the Sudoku variants thread group
further note that you are in the Twin Equivalent Sudokus thread
now read the entire thread from the first post
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Postby udosuk » Sun Dec 03, 2006 6:34 am

I'm amazed at hutman's ability to rant for so many words... Frankly I don't even have the time and energy to read them...:)

I don't see what's the problem of gsf posting his puzzles, which all have unique solutions... I don't think it's his fault that some careless minds misinterpreted the rules and wasted hours trying to solve them as separate sudokus...

But gsf, as some point I assume you still need to post the actual method to convert one of the grids to another, such as the permutation of digits and which bands/stacks/rows/columns get permuted...:?:
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Postby hutman » Sun Dec 03, 2006 6:37 am

gsf wrote:
...yes, the two pseudo puzzles have 7539 and 77146 solutions respectively...here's a variation where only one clue differs between the twins, 424 and 213 solutions for the pseudo puzzles...note that you are in the Sudoku variants thread group. further note that you are in the Twin Equivalent Sudokus thread. now read the entire thread from the first post.

I have read the entire thread from the beginning to the end. I find nothing in the thread that gives you the moral right to post something that insults the intelligence of others. If you can prove that I have missed anything in the thread that gives you the moral right to post such rubbish, you are welcome to point that out to me.

Your so-called "solutions" in the above quote may mislead others into thinking that there is a common solution in each pair of your freaks. They may have the notion that in your first pair of freaks, both of them may share more than one common solution or even 7539 common solutions. In the second pair of your freaks, they may think that both may share more than one common solution or even 213 solutions.

However, the actual fact is that each pair of "psudo puzzles" does not share any common solution. This is the fact which you yourself either do not know or hide to mislead others into thinking that the freaks you posted are valid "Twin Equivalent Sudokus".

You have pointed out that we are "in the Twin Equivalent Sudokus thread". It means that ethically you should not post any other "puzzles" except valid "Twin Equivalent Sudokus". There is no relevant link between each component in each pair of your "pseudo puzzles". Hence how can you dump those things down here which is reserved for valid "Twin Equivalent Sudokus"?

You have also pointed out that we are in the Sudoku variants thread group. However, being in the Sudoku variants thread group does not mean that you are given the license to throw all ethics aside by posting something that can mislead others into wasting a lot of their precious time. At the end of their agony and frustration, they suddenly realise they have been played like monkeys by someone who may be laughing loudly now with the feeling of being on top of the world and thinking himself as another Einstein.

Your so-called "pseudo puzzles" are analogous to asking others to answer such silly questions or heed crazy commands like "How many drops of water can I get from that cup of water? How many kilograms of food have I eaten last month? Find a way to bring me to the moon without using a spaceship, etc".

If you disagree with me that your so-called "psedo puzzles"are invalid "Twin Equivalent Sudokus", you are welcome to disclose your "common solution". That perhaps will lower my temperature a few metres:!:
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Postby Shintaro » Sun Dec 03, 2006 6:54 am

My friend told me that he is afraid that he may become the next target for hutman to vent his agony and frustration at having lost many precious hours of sleep in solving the "puzzles". He said that he is busy preparing a number of grids for the explanation of the walkthrough of his twin puzzles. They should be ready for me to post on the forum within the next 36 hours.:D
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Postby gsf » Sun Dec 03, 2006 7:22 am

the honus is on the original poster(s) to post solution techniques

here are the canonical grid for both twins and the solution for both twins
(there exists number/col/chute permutations that map each twin solution to the canonical solution)
there are no other solutions to either twin pseudopuzzle that have the same canonical solution

with this I'm done with this thread
Code: Select all
1 2 3 | 4 5 6 | 7 8 9
4 5 6 | 7 8 9 | 1 3 2
7 8 9 | 1 3 2 | 5 6 4
------+-------+------
2 3 7 | 8 9 5 | 4 1 6
5 1 8 | 2 6 4 | 9 7 3
9 6 4 | 3 1 7 | 2 5 8
------+-------+------
3 7 1 | 9 4 8 | 6 2 5
6 9 2 | 5 7 3 | 8 4 1
8 4 5 | 6 2 1 | 3 9 7

6 8 1 | 5 9 4 | 2 7 3
2 3 5 | 7 6 1 | 8 4 9
4 9 7 | 3 2 8 | 6 1 5
------+-------+------
7 4 6 | 1 3 2 | 5 9 8
8 5 9 | 4 7 6 | 1 3 2
1 2 3 | 8 5 9 | 4 6 7
------+-------+------
3 1 2 | 9 4 5 | 7 8 6
9 6 4 | 2 8 7 | 3 5 1
5 7 8 | 6 1 3 | 9 2 4

6 8 1 | 5 9 4 | 2 7 3
9 3 5 | 7 2 8 | 6 4 1
4 2 7 | 3 6 1 | 8 9 5
------+-------+------
7 4 6 | 1 3 2 | 5 8 9
8 5 9 | 4 7 6 | 1 3 2
2 1 3 | 8 5 9 | 4 6 7
------+-------+------
3 9 4 | 2 8 5 | 7 1 6
1 6 2 | 9 4 7 | 3 5 8
5 7 8 | 6 1 3 | 9 2 4
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Postby RW » Sun Dec 03, 2006 7:13 pm

hutman wrote:For example, if you tell somebody that he would be rewarded with a million dollars if he could answer a million-dollar question. After scratching his head for sometime, that person replies: "I admit defeat, but please tell me the answer." Then you admit: "I myself also do know how to do." That is totally ridiculous. You have made yourself a laughingstock.

Like Paul Wolfskehl made himself a laughingstock in 1906 for offering the reward of 100,000 Marks to the first person to prove or disprove Fermat's last theorem?

hutman, before writing your next post, maybe you should think a while about what you are saying, who you are accusing and on what grounds. gsf's puzzles are perfectly valid "Twin Equivalent Puzzles", they are solvable by logic alone (even though quite complex logic), and the problem has one unique solution. I have absolutely no idea from where you got the impression that this wouldn't be the case.

If you feel insulted by someone posting puzzles other than standard sudokus, then stay away from the variants section. If you liked the shape of gsf's puzzles, then maybe you'd rather solve this normal sudoku, with one unique solution, created by Ocean:
Code: Select all
 +-------+-------+-------+
 | . . 1 | . . . | 2 . . |
 | . 3 . | . . . | . 4 . |
 | 4 . . | . 5 . | . . 6 |
 +-------+-------+-------+
 | . . . | 1 . 2 | . . . |
 | . 6 . | . 7 . | . 3 . |
 | . . . | 8 . 9 | . . . |
 +-------+-------+-------+
 | 3 . . | . . . | . . 5 |
 | . 5 . | . 4 . | . 6 . |
 | . . 8 | . . . | 9 . . |
 +-------+-------+-------+


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Postby Shintaro » Mon Dec 04, 2006 10:40 am

Twin A
Code: Select all
 7 2 . | 3 . . | . . 8
 3 . . | . 8 5 | . . 2
 . . . | 2 6 . | . . 3
-------+-------+------
 . . . | . 5 . | 2 3 .
 . . 3 | 6 2 . | . . 1
 . . 2 | . 3 . | . . .
-------+-------+------
 2 3 . | 5 9 6 | . . .
 . . 9 | . . 2 | 3 . .
 . 6 . | 8 . 3 | . 2 9


Twin B
Code: Select all
 . . 6 | . . . | . . 2
 . . . | . . . | . . 4
 . . . | . 3 . | . 7 5
-------+-------+------
 . . . | . 5 . | . . .
 5 . . | 3 . . | 2 . 9
 . . . | . . 9 | 5 4 .
-------+-------+------
 . . 4 | 1 8 3 | . . .
 . 3 . | . . . | 4 . 8
 8 9 . | . . 4 | . . .


Thanks to Pat for posting the above two grids.:)

We notice that digit 6 corresponds to digit 3 in column 4, column 5 and column 6 of twin A and twin B respectively. We expect is a linkage in the pair of linked puzzles which by definition must have a single unique solution. Furthermore, this is the only linkage we can find, that is with 3 digits in one grid correspond to 3 digits in another grid. Hence this must be the starting point for tackling the puzzle.

We can write the correspondence in this way: 6 --> 3.

As a result of this correspondence, column 4, column 5, column 6, row 3, row 5 and row 7 are all "fixed" in position. Fixing a row means that all the digits in the same row must remain within the row. However, a digit can shift to another position in the same row but in a different column within the same box. Similarly, fixing a column means that all the digits in the same column must remain within the column. However, a digit can shift to another position in the same column but in a different row within the same box. As column 4, column 5 and column 6 intersect with row 7 in both grids, this means that all the digits in the first row of box 8 in both grids are fixed in position. This is because all the digits occupy the points of intersections of column 4, column 5 and column 6 with row 7. Hence we have the following correspondence for the three digits in the first row of box 8:

Twin A --> twin B

5 --> 1
9 --> 8
6 --> 3

As row 7 is fixed, it means that only row 8 and row 9 can interchange with each other within the block of rows. On examining row 8 and row 9 in both grids, we find 6 in row 9 of twin A and 3 in row 8 of twin B. This implies that row 8 and row 9 of twin A can be interchanged with each other to produce twin B. This can be shown by interchanging the row 8 and row 9 to produce the new grid for twin A:

Twin A
Code: Select all
 7 2 . | 3 . . | . . 8
 3 . . | . 8 5 | . . 2
 . . . | 2 6 . | . . 3
-------+-------+------
 . . . | . 5 . | 2 3 .
 . . 3 | 6 2 . | . . 1
 . . 2 | . 3 . | . . .
-------+-------+------
 2 3 . | 5 9 6 | . . .
 . 6 . | 8 . 3 | . 2 9
 . . 9 | . . 2 | 3 . .


Twin B
Code: Select all
 . . 6 | . . . | . . 2
 . . . | . . . | . . 4
 . . . | . 3 . | . 7 5
-------+-------+------
 . . . | . 5 . | . . .
 5 . . | 3 . . | 2 . 9
 . . . | . . 9 | 5 4 .
-------+-------+------
 . . 4 | 1 8 3 | . . .
 . 3 . | . . . | 4 . 8
 8 9 . | . . 4 | . . .


After exchanging row 8 with row 9 in twin A, we find the following correspondence in row 8 of both grids tallying with what we have discovered so far:

Twin A --> twin B
6 --> 3
9 --> 8

Such tally with earlier findings implies that exchanging the rows is a correct move. Hence we can fix the position of row 8. AS row 7 and row 8 are fixed, it implies that the row 9 is now fixed in twin A.

As 2 and 4 occupy the points of intersection of column 6 and row 9 in in twin A and twin B respectively, it implies that they are fixed in position. It also implies that 2 in twin A is corresponding to 4 in twin B.

Twin A --> twin B
2 --> 4

On examining column 9 of both grids, we find that the following correspondence tallies with what we have discovered so far:

Twin A --> twin B
2 --> 4
9 --> 8

This implies that column 9 in twin A is fixed in position. Since 2 and 4 correspond to each other in row 2 of twin A and twin B respectively, it implies that row 2 is fixed in position. Since row 2 and row 3 are fixed in position, row 1 is also fixed in position. In other words, there is no exchange of rows in the first three rows of twin A to produce twin B. Since the following fixed rows -- row 1, row 2, row 3, row 5 and row 8 intersect with the fixed column 9, we get the correspondence for the following digits which occupy the points of intersection.

Twin A --> twin B
8 --> 2
2 --> 4
3 --> 5
1 --> 9
9 --> 8

On examining row 4 of both grids, we find that 5 corresponds to 5. This is illogical as we already discovered the following correspondence between 3 and 5.

Twin A --> twin B
3 --> 5

As 2 occupies the point of intersection of fixed row 5 and fixed column 5, it is fixed in position. Row 4 and row 6, however, are not fixed in position. The discrepancy 5 --> 5 implies that row 4 can be exchanged with with row 6 in twin A. Interchanging row 4 and row 6 in twin A, we get the following equivalent grids:

Twin A
Code: Select all
 7 2 . | 3 . . | . . 8
 3 . . | . 8 5 | . . 2
 . . . | 2 6 . | . . 3
-------+-------+------
 . . 2 | . 3 . | . . .
 . . 3 | 6 2 . | . . 1
 . .   | . 5 . | 2 3 .
-------+-------+------
 2 3 . | 5 9 6 | . . .
 . 6 . | 8 . 3 | . 2 9
 . . 9 | . . 2 | 3 . .


Twin B
Code: Select all
 . . 6 | . . . | . . 2
 . . . | . . . | . . 4
 . . . | . 3 . | . 7 5
-------+-------+------
 . . . | . 5 . | . . .
 5 . . | 3 . . | 2 . 9
 . . . | . . 9 | 5 4 .
-------+-------+------
 . . 4 | 1 8 3 | . . .
 . 3 . | . . . | 4 . 8
 8 9 . | . . 4 | . . .
 


Now we have the following correspondence between 3 and 5 in row 4 of twin A and twin B respectively.

Twin A --> twin B
3 --> 5

Since this tallies with what we have discovered so far, we implies that it is correct to exchange row 4 and row 6. Hence we can fix the position of row 4 and row 6. Note that 3 and 5 are fixed in position now because they occupy the point of intersection of fixed row 4 and fixed column 5. Looking at row 6 again, we discover the following discrepancy in correspondence:

Twin A --> twin B
2 --> 5 (false)
3 --> 4 (false)

This correspondence does not tally with what we have discovered so far. As column 7 and column 8 of twin A are not fixed in position, we can interchange them to get the right correspondence for the digits in row 6. Swapping column 7 and column 8 in twin A, we get the following equivalent grids:

Twin A
Now we have the following correspondence between 3 and 5 in row 4 of twin A and twin B respectively.

Twin A --> twin B
3 --> 5

Since this tallies with what we have discovered so far, we implies that it is correct to exchange row 4 and row 6. Hence we can fix the position of row 4 and row 6. Note that 3 and 5 are fixed in position now because they occupy the point of intersection of fixed row 4 and fixed column 5. Looking at row 6 again, we discover the following discrepancy in correspondence:

Twin A --> twin B
2 --> 5 (false)
3 --> 4 (false)

This correspondence does not tally with what we have discovered so far. As column 7 and column 8 of twin A are not fixed in position, we can interchange them to get the right correspondence for the digits in row 6. Swapping column 7 and column 8 in twin A, we get the following equivalent grids:


Twin A
Code: Select all
 7 2 . | 3 . . | . . 8
 3 . . | . 8 5 | . . 2
 . . . | 2 6 . | . . 3
-------+-------+------
 . . 2 | . 3 . | . . .
 . . 3 | 6 2 . | . . 1
 . .   | . 5 . | 3 2 .
-------+-------+------
 2 3 . | 5 9 6 | . . .
 . 6 . | 8 . 3 | 2 . 9
 . . 9 | . . 2 | . 3 .


Twin B
Code: Select all
 . . 6 | . . . | . . 2
 . . . | . . . | . . 4
 . . . | . 3 . | . 7 5
-------+-------+------
 . . . | . 5 . | . . .
 5 . . | 3 . . | 2 . 9
 . . . | . . 9 | 5 4 .
-------+-------+------
 . . 4 | 1 8 3 | . . .
 . 3 . | . . . | 4 . 8
 8 9 . | . . 4 | . . .
 


Now the correspondence of the digits in row 6 of both grids tallies with what we have discovered so far:

Twin A --> twin B
2 --> 4
3 --> 5

By now all the rows and columns except the first three columns in twin A have been fixed. Looking at column 2 of both grids, we notice that 6 in twin A maps correctly to 3 in twin B.

Twin A --> twin B
6 --> 3

With this correct mapping or correspondence, we can fix column 2. Looking at column 1 of both grids, we cannot map any digit in that column for both grids. However we can map the digits in column 1 of twin A and column 3 of twin B. Swapping the column 1 and column 3 of twin A, we get the following equivalent grids.

Twin A
Code: Select all
 . 2 7 | 3 . . | . . 8
 . . 3 | . 8 5 | . . 2
 . . . | 2 6 . | . . 3
-------+-------+------
 2 . . | . 3 . | . . .
 3 . . | 6 2 . | . . 1
 . .   | . 5 . | 3 2 .
-------+-------+------
 . 3 2 | 5 9 6 | . . .
 . 6 . | 8 . 3 | 2 . 9
 9 . . | . . 2 | . 3 .


Twin B
Code: Select all
 . . 6 | . . . | . . 2
 . . . | . . . | . . 4
 . . . | . 3 . | . 7 5
-------+-------+------
 . . . | . 5 . | . . .
 5 . . | 3 . . | 2 . 9
 . . . | . . 9 | 5 4 .
-------+-------+------
 . . 4 | 1 8 3 | . . .
 . 3 . | . . . | 4 . 8
 8 9 . | . . 4 | . . .


Now looking at column 1 of both grids, we can find the following correspondence which tallies with what we have discovered so far:

Twin A --> twin B
3 --> 5
9 --> 8

With such correspondence that tallies with the previous findings, we can fix column 1 of twin A. Since column 1 and column 2 are fixed in twin A, this implies that column 3 of twin A is also fixed. Now looking at column 3 of both grids, we can map the following digits in twin A and twin B:

Twin A --> twin B
7 --> 6
2 --> 4

Note that the mapping of 7 in twin A to 6 in twin B is new. Digit 7 in twin A must be equivalent to digit 6 in twin B because column 3 is fixed in position. So far We have mapped all the digits except digit 4 in twin A:

Twin A --> twin B
1 --> 9
2 --> 4
3 --> 5
4 --> ?
5 --> 1
6 --> 3
7 --> 6
8 --> 2
9 --> 8

The only digit left in twin B that has not been mapped to other digits is 7. Hence, 4 in twin A must map to 7 in twin B.

Twin A --> twin B
4 --> 7

With all the equivalent digits found, we can substitute them in twin A and twin B as shown in the grids below:

Twin A
Code: Select all
 . 2 7 | 3 . . | . . 8
 . . 3 | . 8 5 | . . 2
 . . . | 2 6 . | . 4 3
-------+-------+------
 2 . . | . 3 . | . . .
 3 . . | 6 2 . | 8 . 1
 . . . | . 5 1 | 3 2 .
-------+-------+------
 . 3 2 | 5 9 6 | . . .
 . 6 . | 8 . 3 | 2 . 9
 9 1 . | . . 2 | . 3 .


Twin B
Code: Select all
 . 4 6 | 5 . . | . . 2
 . . 5 | . 2 1 | . . 4
 . . . | 4 3 . | . 7 5
-------+-------+------
 4 . . | . 5 . | . . .
 5 . . | 3 4 . | 2 . 9
 . . . | . 1 9 | 5 4 .
-------+-------+------
 . 5 4 | 1 8 3 | . . .
 . 3 . | 2 . 5 | 4 . 8
 8 9 . | . . 4 | . 5 .


Using the usual sudoku strategy, we finally obtain the solutions for the twin puzzles as shown below:

Twin A
Code: Select all
 6 2 7 | 3 4 9 | 5 1 8
 4 9 3 | 1 8 5 | 7 6 2
 1 8 5 | 2 6 7 | 9 4 3
-------+-------+------
 2 5 1 | 7 3 8 | 4 9 6
 3 7 9 | 6 2 4 | 8 5 1
 8 4 6 | 9 5 1 | 3 2 7
-------+-------+------
 7 3 2 | 5 9 6 | 1 8 4
 5 6 4 | 8 1 3 | 2 7 9
 9 1 8 | 4 7 2 | 6 3 5


Twin B
Code: Select all
 3 4 6 | 5 7 8 | 1 9 2
 7 8 5 | 9 2 1 | 6 3 4
 9 2 1 | 4 3 6 | 8 7 5
-------+-------+------
 4 1 9 | 6 5 2 | 7 8 3
 5 6 8 | 3 4 7 | 2 1 9
 2 7 3 | 8 1 9 | 5 4 6
-------+-------+------
 6 5 4 | 1 8 3 | 9 2 7
 1 3 7 | 2 9 5 | 4 6 8
 8 9 2 | 7 6 4 | 3 5 1
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re: solving Puzzle Three

Postby Pat » Mon Dec 04, 2006 12:41 pm

Shintaro wrote:We notice that digit 6 corresponds to digit 3 in column 4, column 5 and column 6 of twin A and twin B respectively.

We expect is a linkage in the pair of linked puzzles which by definition must have a single unique solution.

Furthermore, this is the only linkage we can find, that is with 3 digits in one grid correspond to 3 digits in another grid.

Hence this must be the starting point for tackling the puzzle.

We can write the correspondence in this way: 6 --> 3.




      so we start with a good guess--
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Postby RW » Mon Dec 04, 2006 1:49 pm

Shintaro, Pat is right. You start with a guess, that in fact has no logical reasoning to back it up as the columns/rows within the chutes can be swapped. Working from this guess on you eventually find a solution, but you cannot know if this is the only solution. Most people here think that a good solution should always use proof by contradiction, it should show that all other options are false. Your solution is equal to using a backdoor in a normal puzzle, guess a value and solve it from there.

I would also like to point out that the "logic" you used relies very heavily on the fact that the chutes haven't been swapped. This was never mentioned in the rules and therefore a solution cannot use that as a given fact.

IMO this puzzle remains unsolved. Proper solutions are still welcome.

RW
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Postby hutman » Mon Dec 04, 2006 2:01 pm

gsf, don't run away leaving your joke behind. You still haven't show us how you can deal with the joke of yours by human means without resorting to machines.:)
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