Twin Equivalent Sudokus

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby tarek » Thu Nov 30, 2006 9:31 am

Shintaro wrote:If I am not wrong, you have to convince him and perhaps many others by showing your working step by step just like the way high school students prove mathematical theorems in schools.:D

I'm afraid that you are wrong there shintaro...... gsf is the one that showed us how this puzzles in its current format is solved.... it is you that needs to show us how you solve these puzzles ......

How many Twins did you post ? 3+ (and on many forums under different aliases, even in other languages)

how many did you show a walkthrough solution for ? the answer is 0.

This discussion should go no further if you don't do that..... I am a programmer myself & frankly without you showing us how this was handcrafted, then I myself would claim that I would make better twins than the ones you supplied & that your dexterity skills can be easily matched:idea:

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re: "Twin Equivalent Sudokus" - puzzle Three

Postby Pat » Thu Nov 30, 2006 12:28 pm

Shintaro wrote:puzzle Three


A. [ 19 clues ]

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




B. [ 19 clues ]

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




Can tarek or anyone else help to post on the forum the two original grids with all the available clues they can find by the usual sudoku strategy?
Then we can try to spot any interesting pattern or any telltale sign or link between the twin puzzles.


OK, Shintaro, this is what we have - now show us the logical way to solve it


A. [ 33 ]

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




B. [ 24 ]

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 | . . .



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Postby Shintaro » Thu Nov 30, 2006 2:17 pm

tarek wrote:
how many did you show a walkthrough solution for ? the answer is 0.

Tarek, you have forgotten the occasion on Nov 23 when I used the technique (taught by my friend) to map the digits in one box of the original puzzle onto the digits in another box of the equivalent puzzle to prove that the last row of boxes did not interchange with the first row of boxes.

In the normal practice of the puzzle world, there is no need for a puzzle maker to reveal the solution or the steps leading to the solution. Just visit any puzzle website or read any puzzle book, how many of them had revealed the answers? The request only comes when somebody suspects that even the puzzle maker does not know the answer himself. Of course, this is ridiculous. As a maker of the puzzle, he should already know every clue and every line of reasoning in the puzzle.

The best reward for a puzzle maker is to see somebody provide a solution and show the steps leading to the solution, not himself. Otherwise why the need to publish his puzzle? He might as well sit at home every night solving his own puzzle himself.

Tarek's request is similar to one story I know. A chef had baked a new type of cake and invited some friends to his house to have a taste of it, hoping to get some comments from his friends on the new cake. After eating the cake, everybody kept silent except one friend commented that the cake tasted sweet enough.

To the disappointment of the chef, however, another friend told him to eat his own cake so as to prove to everybody the existence of sugar in the cake. Of course, it was ridiculous for the chef to eat his own cake so as to find out whether there was sugar in it. As the maker of the cake, he should already know what ingredients he had used to bake the cake, how many grams of sugar he had added to it, etc.

What would delight him was to hear the comments of others, not to get the request to eat his own cake so as to prove the existence of sugar in the cake. In the end, the chef suspected that he had forgotten to add sugar during the process of baking, so he finally ate his own cake.

I have to thank Pat for her help in posting the grids with all the available clues. You won't be disappointed as the steps leading to the solution would be revealed either by me (taught by my friend) or somebody else within a few days.:)
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Postby tarek » Thu Nov 30, 2006 4:13 pm

Shintaro wrote:As a maker of the puzzle, he should already know every clue and every line of reasoning in the puzzle.
I hope so, the variation in puzzles submitted to date is big. I would be interested if somebody would provide a line of reasoning for the last twins. I will step back now & leave it for others as my chain of reasoning includes plenty of T&E

Shintaro wrote:Otherwise why the need to publish his puzzle? He might as well sit at home every night solving his own puzzle himself.
sometimes a puzzle maker needs to reveal how the solution was reached to show that the methods were consistant with "a chain of resoaning to reach a solution".....

Forgive me, but let me show you how EASY it is to create such twins.....

1. Take a valid minimal puzzle
2. Remove one clue --------> multiple solutions [by using electronic solvers, u can choose a clue that when removed will give a small number of possible solutions]
3. Return to the original puzzle & remove another clue ---------> multiple solutions [again you can choose the best one to pick]
4. look at all solutions available by step 2 & 3, if there are only 2 similar solutions which are the same as the parent solution then you have a valid puzzle.........
5. scramble puzzles & you've got the twins......

That is a chain of reasoning for creating a puzzle which is VALID....Do I know the chain of reasoning to get me from the Twins to the parent ? No

providing a chain of reasoning to get to the original puzzle from the Twins is DIFFERENT, that is why I asked for a walkthrough for the 3rd.

I'm afraid that providing a solution is not a proof that the puzzle maker knows the chain of reasoning to get from the twins to the parent.

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Postby Shintaro » Thu Nov 30, 2006 6:52 pm

Tarek, thank you for your message. My friend said that he has great admiration for your curiosity in the pursuit of knowledge. You are partially right in saying "how EASY it is to create such twins". Hence, it is possible to create two equivalent puzzles using your 5-step method. However, the products will usually turn out to be shoddy or trivial with many redundant clues.

In addition to your five steps, there is an impotant factor. It is the human factor, not the machine factor. The puzzle maker needs to have the heart and spirit of an artist, not a businessman. My friend usually takes many hours to create a puzzle. He checks and rechecks his puzzle until he is satisfied that it is flawless and has a solution. In addition, he takes great pain to reduce as many redundant clues as possible. When he submits his puzzles to the websites for publication, the editors/owners of those websites would check them again until they are satisfied.

Now returning to the term (parent) you use for the twin puzzles. Biologically and logically, it is wrong to treat the relationship between two equivalent puzzles as parent and child. How can a parent and her child be considerd as twins?

Two equivalent puzzles are essentially one and the same puzzle. Hence twin A and twin B can be transformed into each other. It is not necessary to start solving a puzzle from twin A. We can also do it from twin B. Perhaps it is more appropriate to treat each twin puzzle as the mirror image of each other.

As a warm up to finding a "human solution" to the puzzles, has anybody noticed any special pattern in the arrangement of certain digits in the middle column of boxes of both grids?:)
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Postby gsf » Thu Nov 30, 2006 7:50 pm

now I'm cranky

I bent the twin problem statement by allowing chute reflection on the middle chute column
it makes room for artistic symmetry
(that's a big hint for this puzzle by the way)

here's a twin puzzle for your book
Code: Select all
. . 1 | . . . | 2 . .
. . . | . 6 . | . 4 .
4 . . | . . . | . . 5
------+-------+------
. . . | 1 . 2 | . . .
. 5 . | . 7 . | . 3 .
. . . | 8 . 9 | . . .
------+-------+------
3 . . | . 4 . | . . 6
. . . | . . . | . 5 .
. . 8 | . . . | 9 . .

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

edit: I missed a number permutation -- now the twins only differ in two clues
now stop trying to get us to write it
(with apologies if you and/or your friend aren't writing a book)
Last edited by gsf on Sat Dec 02, 2006 3:18 am, edited 1 time in total.
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Postby ronk » Thu Nov 30, 2006 8:39 pm

Shintaro, are you and friend Henry Kwok one and the same person?

Shintaro wrote:Someone had noticed the interest generated by this variant and had suggested to my friend to make this variant a regular feature in this forum by providing at least one or two new puzzles of this type once a month.

Was this "someone" you also?
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Postby Shintaro » Fri Dec 01, 2006 2:38 am

gsf, good try. You are really artistic. It really needs to be "cranky" sometimes to be creative and innovative. It will be a perfect symmetry if box 1 and box 7 contain 3 digits each in both grids, and also if the single digit in box 8 of both grids is placed in the middle cell of the box. Please try again to give us the perfect symmetry.

ronk, that "someone" is waiting for you at another website http://www.sudoku.org.uk/discus/messages/1289/3102.html?1164393348.

I cannot beat him in inventing puzzles, but I am happy that I can beat him in the English language. He had expected very tough questions in this forum. Since he knows that I can express better than him in English, he requests for my help to post his puzzles and answer all questions on his behalf.

With regard to making his puzzles a regular feature here, I am afraid that he may have already changed his mind about it. Making a really good puzzle is not that easy. My friend found the going quite taxing. Moreover, he also has to spend considerable time to make puzzles for the websites where he has committed himself to making regular contribution. Hence, he will have nothing more for me to post in this thread after a few more puzzles. Most likely, we shall leave it to gsf and tarek to continue this thread.:D
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Postby gsf » Fri Dec 01, 2006 4:16 am

Shintaro wrote:Please try again to give us the perfect symmetry.
Most likely, we shall leave it to gsf and tarek to continue this thread.

you ignored the fact that both twins have the same pattern
how would your friend solve this?
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Postby Shintaro » Fri Dec 01, 2006 11:26 pm

Sorry, I didn't even care to examine it carefully at first because I expected you to make a proper puzzle solvable by humans, not the machine. In the case of my friend, he was really disappointed that nobody can give a convincing step-by-step explanation of the solution. He has tried his best to give as many clues as possible because he is worrying that in the end he has to solve the puzzle himself.

In his opinion, puzzles are for everybody to enjoy. He considers it a failure on his part that his puzzle has not been solved convincingly, just like what a joker feels when nobody except himself laughs at his joke.

He will take his hat off to you if you can explain the solution of your puzzle and his puzzle in a convincing step-by-step manner, without resorting to "machine solution" or unconvincing high-sounded language.:)
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Postby RW » Sat Dec 02, 2006 1:09 am

Shintaro wrote:
tarek wrote:how many did you show a walkthrough solution for ? the answer is 0.

Tarek, you have forgotten the occasion on Nov 23 when I used the technique (taught by my friend) to map the digits in one box of the original puzzle onto the digits in another box of the equivalent puzzle to prove that the last row of boxes did not interchange with the first row of boxes.

Shintaro, first you said "Once you manage to find all the available digits in both grids, the solution will be staring at you in the face", then after I asked you several times to post this solution you posted 51 lines of text that ultimately excluded the possibility of two chutes being equal... That's not "staring in your face". IMHO your technique is pure Trial&Error - pick a box and try "If box A = box B then...". Of course I knew of the possibility to map boxes like that before you posted that solution, but I had no interest in doing so, because of the laborious T&E aspect. Instead I found a way to solve the whole puzzle (and the next one you posted) in a couple of minutes, by simply looking at the given information, without having to think "if this then that".

Now you keep saying that you have a way to solve the third puzzle. If it's by using the same technique as you used to solve the first, it will be a lot more laborious and a lot more T&E involved, because of the swapped columns/rows.

tarek wrote:Show us a way Shintaro to solve this without T&E then you have a point.... I'm afraid if that is not the case then it is very easy for anyone to create such puzzles......

I agree with tarek. If you don't have a way to solve it without T&E, then it is very easy for anyone to create such puzzles.

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Postby udosuk » Sat Dec 02, 2006 1:33 am

Shintaro wrote:Sorry, I didn't even care to examine it carefully at first because I expected you to make a proper puzzle solvable by humans, not the machine. In the case of my friend, he was really disappointed that nobody can give a convincing step-by-step explanation of the solution. He has tried his best to give as many clues as possible because he is worrying that in the end he has to solve the puzzle himself.

Shintaro wrote:He will take his hat off to you if you can explain the solution of your puzzle and his puzzle in a convincing step-by-step manner, without resorting to "machine solution" or unconvincing high-sounded language.:)

If I might barge in a little, perhaps Shintaro could send a PM (private message) to gsf or RW including his "step-by-step explanation of the solution", and let them decide if it's a "convincing" one (I'm assuming gsf or RW won't mind)... That way, he doesn't need to worry about spoiling the fun for the others... Similarly, gsf could send Shintaro a logical walkthrough (if there is any) for his puzzle via PM and still allow other potential solvers the chance to crack it by themselves...:idea:
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Postby gsf » Sat Dec 02, 2006 4:13 am

udosuk wrote:Similarly, gsf could send Shintaro a logical walkthrough (if there is any) for his puzzle

not my job or anyone else on the list except the original positer
we have yet to see anything that makes this look different from a "do my homework" request

also, I constructed the puzzle to foil the techniques that look for similar
boxes between the twins -- because the twins have identical patterns that
work is already done -- and for this puzzle gets you nowhere
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Postby udosuk » Sat Dec 02, 2006 7:57 am

gsf, does that means this puzzle:
Code: Select all
. . 1 | . . . | 2 . .
. . . | . 6 . | . 4 .
4 . . | . . . | . . 5
------+-------+------
. . . | 1 . 2 | . . .
. 5 . | . 7 . | . 3 .
. . . | 8 . 9 | . . .
------+-------+------
3 . . | . 4 . | . . 6
. . . | . . . | . 5 .
. . 8 | . . . | 9 . .

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

... has a unique solution but probably cannot be solved by human without extensive trial & error steps (which is what we call "Ruudiculous" in killer sudoku community)?:?:

Also, who is the "original positer"? Is it you who created and posted this puzzle, or Shintaro who introduced this concept to us?
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Postby gsf » Sat Dec 02, 2006 8:46 am

udosuk wrote:... has a unique solution but probably cannot be solved by human without extensive trial & error steps (which is what we call "Ruudiculous" in killer sudoku community)?:?:

yes, the two pseudo puzzles have 7539 and 77146 solutions respectively
udosuk wrote:Also, who is the "original positer"? Is it you who created and posted this puzzle, or Shintaro who introduced this concept to us?

yeah, that's not a word
the guy or friend who said "here's a puzzle I invented, tell me how to solve it"

here's a variation where only one clue differs between the twins, 424 and 213 solutions for the pseudo puzzles,
probably still too complex to do by hand, but nice to look at
btw, the parent is one of the diagonal puzzles in the hardest list
Code: Select all
. . 1 | . . . | 2 . .
. 3 . | . 6 . | . 4 .
4 . . | . . . | . . 5
------+-------+------
. . . | 1 . 2 | . . .
. 5 . | . 7 . | . 3 .
. . . | 8 . 9 | . . .
------+-------+------
3 . . | . . . | . . 6
. 6 . | . . . | . 5 .
. . 8 | . 1 . | 9 . .

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