The New Sudoku Players' Forum

[bat999]

Hi
This is a puzzle generated by HoDoKu program.(Extreme 3092)

Code: Select all

.----------------.-------------------------.--------------------.
| 1468  68   467 | 1246789  14689  126789  | 346   234   5      |
| 4568  3    2   | 45678    4568   5678    | 1     9     46     |
| 9     56   46  | 3        1456   1256    | 7     8     246    |
:----------------+-------------------------+--------------------:
| 348   89   5   | 1489     2      189     | 349   6     13479  |
| 2346  269  1   | 4569     7      569     | 8     345   349    |
| 468   7    46  | 145689   3      15689   | 2     145   149    |
:----------------+-------------------------+--------------------:
| 2356  1    9   | 2567     56     4       | 36    23    8      |
| 236   4    8   | 1269     169    12369   | 5     7     12369  |
| 7     256  36  | 125689   15689  1235689 | 3469  1234  123469 |
'----------------'-------------------------'--------------------'

I hit a brick wall here...

Code: Select all

.---------------.-----------------------.---------------.
| 1     68   7  | 2689    4689   269    | 346  34   5   |
| 4568  3    2  | 568     4568   7      | 1    9    46  |
| 9     56   46 | 3       14     156    | 7    8    2   |
:---------------+-----------------------+---------------:
| 3     89   5  | 1489    2      189    | 49   6    7   |
| 246   269  1  | 4569    7      569    | 8    45   3   |
| 48    7    46 | 45689   3      5689   | 2    15   19  |
:---------------+-----------------------+---------------:
| 256   1    9  | 7       56     4      | 36   23   8   |
| 26    4    8  | 1269    169    3      | 5    7    169 |
| 7     256  3  | 125689  15689  125689 | 69   124  146 |
'---------------'-----------------------'---------------'

When I asked for a hint, HoDoKu came up with a forcing chain.
Here...

Hidden Text: Show

Forcing Chain Verity => r1c8=3
r6c6=5 r3c6<>5 r3c2=5 r9c2<>5 r7c1=5 r7c1<>2 r7c8=2 r7c8<>3 r1c8=3
r6c6=6 r6c3<>6 r6c3=4 r3c3<>4 r2c1=4 r2c1<>5 r7c1=5 r7c1<>2 r7c8=2 r7c8<>3 r1c8=3
r6c6=8 r6c1<>8 r2c1=8 r2c1<>5 r7c1=5 r7c1<>2 r7c8=2 r7c8<>3 r1c8=3
r6c6=9 r6c9<>9 r4c7=9 r4c7<>4 r1c7=4 r1c7<>3 r1c8=r1c8=3

That was all it needed, the puzzle solved without much trouble after that.

I can follow the forcing chain but I would not have found it myself.
Can anybody suggest an alternative (less convoluted) move that might have been easier to find?

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 1     Aa8-6aA   7        | 2689    4689    269      | 346b    34      5        |
| 4568    3       2        | 568     4568    7        | 1       9       46       |
| 9      b56     b46       | 3      d14     c156      | 7       8       2        |
|--------------------------+--------------------------+--------------------------|
| 3      B89B     5        | 1489    2       189      | 49      6       7        |
| 246    C269     1        | 4569    7       569      | 8       45      3        |
| 48      7       46       | 45689   3       5689     | 2       15      19       |
|--------------------------+--------------------------+--------------------------|
| 256D    1       9        | 7       56      4        | 36F     23E     8        |
|E26      4       8        |F1269   e169     3        | 5       7      G169      |
| 7      D256C    3        | 125689  15689   125689   | 69G     124     146      |
*--------------------------------------------------------------------------------*

Forcing Chain Contradiction in Box 9 Digit 9:

6 r1c2 - r3c23 = (6-1) r3c6 =  r3c5                         - 1 r8c5
6 r1c2 - 8 r1c2 = (8-9) r4c2 = (9-2) r5c2 = r9c2 - r8c1 = (2-1) r8c4  = r8c9 - 9 r8c9;

6 r1c2                                                   - 6 r1c7
6 r1c2 - (6=5) r3c2 - r9c2 = (5-2) r7c1 = (2-3) r7c8 = (3-6) r7c7 = r9c7     - 9 r9c7; => - 6 r1c2

I couldn't find any easy moves from your stuck position, however this one might be less convoluted than the Hodoku move (if you think so).

I've written it as a forcing chain contradiction net (when read from left to right). However you can read it from right to left, reverse the parity of the nodes and it becomes a Kraken Box 9 Digit 9.

You can also read the first leg from left to right, reverse the parity of the nodes in the second leg and read it from right to left and it becomes a discontinuous loop.

Any way you look at this move you can remove the 6 from r1c2. With subsequent singles this gets you to here:

Code: Select all

*--------------------------------------------------------------------------------*
| 1       8       7        | 269     469     269      | 36      34      5        |
| 456     3       2        | 568     4568    7        | 1       9       46       |
| 9      a56     b46       | 3       14      16-5     | 7       8       2        |
|--------------------------+--------------------------+--------------------------|
| 3       9       5        | 18      2       18       | 4       6       7        |
| 246     26      1        | 469     7       69       | 8       5       3        |
| 8       7      c46       | 456     3      d56       | 2       1       9        |
|--------------------------+--------------------------+--------------------------|
| 256     1       9        | 7       56      4        | 36      23      8        |
| 26      4       8        | 1269    169     3        | 5       7       16       |
| 7       256     3        | 12568   1568    12568    | 9       24      146      |
*--------------------------------------------------------------------------------*

W Wing : (5=6) r3c2 - r3c3 = r6c3 - (6=5) r6c6 => - 5 r3c6; stte

Leren

[JC Van Hay]

Solution based on the properties of the 1/1-Plot and 2/2-Plot : here there is only one given for the digit 6, B6 has only 2 solutions, r1c7 and r9c8 and r2c1 each contain 3 members of 3 bilocals, ...

1. Solving B6 => Kraken 1C4 -> [4r4c7==9r6c9==9r4c2]-9r4c7; 5 Singles

Code: Select all

+-----------------+-------------------------+--------------------+
| 1     68     7  | 2689      4689   269    | 346    34     5    |
| 4568  3      2  | 568       4568   7      | 1      9      46   |
| 9     56     46 | 3         14     156    | 7      8      2    |
+-----------------+-------------------------+--------------------+
| 3     8(9)   5  | 89(14)    2      189    | -9(4)  6      7    |
| 246   6(29)  1  | 4569      7      569    | 8      45     3    |
| 48    7      46 | 45689     3      5689   | 2      5(1)   (19) |
+-----------------+-------------------------+--------------------+
| 256   1      9  | 7         56     4      | 36     23     8    |
| 6(2)  4      8  | 69(12)    169    3      | 5      7      169  |
| 7     56(2)  3  | 25689(1)  15689  125689 | 69     24(1)  146  |
+-----------------+-------------------------+--------------------+
9r4c7
4r4c7=4r4c4
9r6c9=======1r6c9
            1r6c8=1r9c8
9r4c2===================9r5c2
                        2r5c2=2r9c2
                              2r8c1=2r8c4
      1r4c4=======1r9c4=============1r8c4


2. Solving C8 => Kraken r6c6 -> [5r3c1==4r3c1==8r3c1]-5r2c1; stte

Code: Select all

+---------------------+--------------------+-------------+
| 1        68    7    | 2689   4689  269   | 36  34  5   |
| 6-5(48)  3     2    | 568    4568  7     | 1   9   46  |
| 9        6(5)  (46) | 3      14    16(5) | 7   8   2   |
+---------------------+--------------------+-------------+
| 3        89    5    | 189    2     189   | 4   6   7   |
| 246      269   1    | 469    7     69    | 8   5   3   |
| 4(8)     7     4(6) | 4568   3     (568) | 2   1   9   |
+---------------------+--------------------+-------------+
| 256      1     9    | 7      56    4     | 36  23  8   |
| 26       4     8    | 1269   169   3     | 5   7   16  |
| 7        256   3    | 12568  1568  12568 | 9   24  146 |
+---------------------+--------------------+-------------+
5r2c1
5r3c1=5r3c6
4r3c1=======4r3c3
            6r3c3=6r6c3
8r3c1===================8r6c1
      5r6c6=======6r6c6=8r6c6

[bat999]

Hi
Neither of those two replies seem (imho) to be any improvement on HoDoKu's hint.

Is this what happens with puzzles like this, test all the candidates in a cell and try to draw a conclusion from the results?

If so, how do we figure out which cells to try first (or is it pot luck)?

@ JC Van Hay
I don't understand any of this sentence...
"Solution based on the properties of the 1/1-Plot and 2/2-Plot..."

[JC Van Hay]

Neither of those two replies seem (imho) to be any improvement on HoDoKu's hint.

Hodoku forcing chain verity is a 10 constraints chain; a further 7 constraints chain is needed to solve the puzzle.
This is to be compared with the 11 and 3 constraints chains of Leren and my 7 and 5 constraints chains.
Where is the no improvement ? What were you expecting ?

Is this what happens with puzzles like this, test all the candidates in a cell and try to draw a conclusion from the results?

Sorry, but to solve any puzzle, i.e to find all its solutions whether it be 0 or 1 or several, all the candidates in a constraint has to be tested.

If so, how do we figure out which cells to try first (or is it pot luck)?

I illustrated the "how to" in my solution. So what kind of further information do you need ?
In SE less than 9.2 puzzles, for example, all you first need is to visualize all the X and XY Chains and their couplings. The best initial starting constraint then lies in the "middle" of these interconnected chains. And this has absolutely nothing to do with lucky guess !

@ JC Van Hay
I don't understand any of this sentence...
"Solution based on the properties of the 1/1-Plot and 2/2-Plot..."

N/N-Plot is the set of all the constraints containing N candidates.

[bat999]

...What were you expecting ?

The question asked to suggest a move "that might have been easier to find".
Neither of the replies addressed the question.

[JasonLion]

A five constraint chain is easier to find (on average) than a ten constraint chain. That doesn't mean it is easy to find in any absolute sense, just "easier". That looks to me like an answer to your question.

Based on your recent comment, perhaps there aren't any "easier" ways to solve the puzzle (by your personal criteria). It is going to take some serious chains regardless.

A possibly better answer is that you really ought to look into the 1/1-Plot and 2/2-Plot mentioned earlier. By drawing all of the obvious strong links that might be used in a chain, it often becomes clear where to search in more detail for a useful chain; without having to methodically try every possible chain in the puzzle one by one.

[bat999]

"...Solution based on the properties of the 1/1-Plot and 2/2-Plot..."
"...you really ought to look into the 1/1-Plot and 2/2-Plot mentioned earlier..."

Is the advice that threads such as "Nice loops for advanced level players - b/b plot" is the way to go.
Here ---> http://forum.enjoysudoku.com/nice-loops-for-advanced-level-players-b-b-plot-t2143.html

It might enable me to decide which square(s) to investigate first, instead of pot luck?

Then test all of the candidates in the square to see if the results lead to a conclusion...

Is that it?

Testing all the candidates in square r6c6 => - 4 r1c8 (Hodoku)
Testing all the candidates in square r1c2 => - 6 r1c2 (Leren)
" Solving B6" and "Solving C8" don't mean anything to me in Van Hay's post, but the outcomes are => - 9 r4c7 and => -5 r2c1.

[JasonLion]

I don't know of any good tutorial, so that is a relatively good place to start. Try it both by doing a full plot as described, and by just doing steps 1 through 4, checking to see if you can visualize most of the rest. The goal is to start being able to visualize the possible interconnections of links, getting a sense of where the available chains are and what regions of the board they interconnect. Longer term you want to experiment with drawing less and less, while still visualizing the full diagram.

Effectively you are drawing the strong links first, then interconnecting them with weak links. Then you move to finding possible end points among the available chains, scanning for something that has an elimination. At more advanced levels you also scan for places where the chains can be extended using more complex techniques (that you presumably already spotted before looking for chains).

At first it is going to feel a bit tedious, but with practice you get better at visualizing the available links and narrowing in on end points likely to result in eliminations.

One associated technique that is worth mentioning: It is possible to scan the board for cells that if solved with cause the whole puzzle to to be solved. Given such a cell, you can work backwards, finding the end points that would solve it, and then finding a way to make a chain that connects those end points. Practicing basic chains as described above makes this much simpler to do.

[bat999]

I don't know of any good tutorial...

Funny that.

The "Nice loops for advanced level players - b/b plot" thread is 10 years old. The illustration images are frogs.

If this "properties of the 1/1-Plot and 2/2-Plot" is such a useful technique, I wonder why it's not better documented?

[JasonLion]

Chains are a very advanced technique, of interest to a relatively small number of people. Tutorial authors almost invariably start writing up the simplest techniques first. They then continue writing for a while before stopping. Invariably they stop before explaining everything. Another tendency is to explain the logical/proof aspects of a technique, with relatively few people going into the practical aspects of searching for ways to use the technique. No one that I know of has gotten much beyond the point of explaining the logic of chains. Relatively few even get to that point. These days, not very many people are still writing about Sudoku, so it seems unlikely that anyone will get around to explaining the practical aspects of finding chains in a proper tutorial.

Of course, there might be something out there somewhere that I haven't seen. And it is worth mentioning the book: The Hidden Logic of Sudoku, which goes into the logical/proof aspects especially throughly.

[bat999]

That's all well and good JasonLion, but it's not getting the baby bathed.

When I started this thread I had a hint from HoDoKu...
Look at square r6c6...
Make chains from all the candidates...
The answer is 3 every time, bingo!


What I am no wiser about is why to look at square r6c6 first without just taking pot luck.

Van Hay made reference to "the properties of the 1/1-Plot and 2/2-Plot".

I don't feel inclined to study the "very advanced technique" in that old thread.

Maybe somebody else can contribute to this thread with alternative methods that are less "advanced".

PS JasonLion
Does your book "The Hidden Logic of Sudoku" explain how to decide which square to investigate first without just taking pot luck?

[JasonLion]

"The Hidden Logic of Sudoku" is not my book. It is by Denis Berthier, another forum member. And, no it doesn't go into which cell to investigate first. It is very much a logic and proof book, which means that it is more likely to say things like "there is a cell such that . . ." and just assume you can find it on your own.

[eleven]

Bat,

you asked an old question, which has no general answer, because it depends on the solver's preferences, what will be tried next.
For example: while i try to get as far as possible without entering any candidates, others like Marty (where is he ?) fill them in, as soon as the simple things are done.
Or while i almost never look for swordfish, others would never continue with chains (simple or not) without having scanned the puzzle for all possible ones.
Many ignore ALS's or deadly patterns, others find very complicated ones ...

What you like, you will practise and spot easier.

JC and Jason gave some hints, how it could be done to find useful chains. E.g. David has his own methods.

Personally i try this or that, but i refuse to do it in a mechanical/systematical way.
The reason, why i don't like 3way-chains from a cell is indeed, because i never would go through them one by one, in the hope to find something useful. If i found one, then always from the other side, by following a digit into a contradiction.

As Jason mentioned, there are the basic possibilities to start, where many links can be combined - or e.g. at an (almost) pattern, and then look where it can lead to, or you go through candidates, which if eliminated would advance the puzzle (e.g. by giving you a number), and then try to find a way to do it.


Concerning the book, it is by denis_berthier, who is contributor here, so you can dive into one of his threads. I did not read it, but i don't think it will answer your question.

[bat999]

Hi eleven, thanks for your comments.
In the above puzzle I had exhausted all my tools such as Swordfish.
What would be your thought process to find a move from my stuck position?