The New Sudoku Players' Forum

[netvope]

I think the puzzle is almost solved and it probably needs only one or two moves. For many of the remaining cells, if you pick a number for one random cell, you will be able to proceed to the complete solution with elementary techniques. However that would be considered cheating I guess

[daj95376]

My solver doesn't find anything simpler than a 7-cell XY-Chain followed by a 6-cell XY-Loop for the next two steps.

Code: Select all

 +--------------------------------------------------------------+
 |  15    57    17    |  8     2     3     |  9     4     6     |
 |  2     46    3     |  46    5     9     |  1     7     8     |
 |  46    8     9     |  1     46    7     |  5     23    23    |
 |--------------------+--------------------+--------------------|
 |  7     9     2     |  46    1     5     |  346   8     34    |
 |  8     3     46    |  9     7     2     |  46    5     1     |
 |  46    1     5     |  3     46    8     |  2     9     7     |
 |--------------------+--------------------+--------------------|
 |  15    26    8     |  57    3     14    |  47    26    9     |
 |  3     2457  147   |  57    9     6     |  8     12    245   |
 |  9     4567  1467  |  2     8     14    |  347   136   345   |
 +--------------------------------------------------------------+
 # 45 eliminations remain

(7=1)r1c3-(1=5)r1c1-(5=1)r7c1-(1=4)r7c6-(4=7)r7c7-(7=5)r7c4-(5=7)r8c4 => r8c3<>7

(4=6)r5c3-(6=4)r5c7-(4=7)r7c7-(7=5)r7c4-(5=1)r7c1-(1=4)r8c3-loop => r9c3<>14, r49c7<>4


This doesn't solve the puzzle, but it does allow less difficult techniques to complete the puzzle.

[netvope]

Thanks. Those chains/loops are difficult to find! (at least for me)

What solver did you use?

[daj95376]

What solver did you use?

I wrote my own solver. It's not interactive, but it gets the job done on many puzzles.

Regards, Danny

[tarek]

My solver doesn't bring out anything pretty
Danny's 1st elimination can be done using double implication chains

Code: Select all

*--------------------------------------------------------*
| 15    57    17   | 8     2     3    | 9     4     6    |
| 2     46    3    | 46    5     9    | 1     7     8    |
| 46    8     9    | 1     46    7    | 5     23    23   |
|------------------+------------------+------------------|
| 7     9     2    | 46    1     5    | 346   8     34   |
| 8     3     46   | 9     7     2    | 46    5     1    |
| 46    1     5    | 3     46    8    | 2     9     7    |
|------------------+------------------+------------------|
| 15    26    8    | 57    3     14   | 47    26    9    |
| 3     2457  147  | 57    9     6    | 8     12    245  |
| 9     4567  1467 | 2     8     14   | 347   136   345  |
*--------------------------------------------------------*
Candidates in r9c6 will force r8c3<>7 (Double implication chains)
r9c6=1: r9c6=1 => r7c6=4 => r7c7=7 => r7c4=5 => r8c4=7 => r8c3<>7
r9c6=4: r9c6=4 => r7c6=1 => r7c1=5 => r1c1=1 => r1c3=7 => r8c3<>7
Threfore r8c3<>7

[netvope]

Cool!

Sounds like everyone write his/her own solver

Perhaps I should write one too

[aran]

Code: Select all

 
*-----------------------------------------------------------*
 | 15    57    17    | 8     2     3     | 9     4     6     |
 | 2     46    3     | 46    5     9     | 1     7     8     |
 | 46    8     9     | 1     46    7     | 5     23    23    |
|-------------------+-------------------+-------------------|
 | 7     9     2     | 46    1     5     | 346   8     34    |
 | 8     3     46    | 9     7     2     | 46    5     1     |
 | 46    1     5     | 3     46    8     | 2     9     7     |
 |-------------------+-------------------+-------------------|
 | 15    26    8     | 57    3     14    | 47    26    9     |
 | 3     2457  147   | 57    9     6     | 8     12    245   |
 | 9     4567  1467  | 2     8     14    | 347   136   345   |
 *-----------------------------------------------------------*

Looking at cells r7c1+r8c3+r8c4, using XYwing logic : if r8c3 is not 4, then r7c4 is not 5
thus establishing the strong link 4r8c3=7r7c4
1. 4r8c3=7r7c4-(7=4)r7c7 : =><4>r8c9
2. 4r8c3=7r7c4-(7=5)r8c4-(5=2)r8c9-(2=1)r8c8 : =><1>r8c3
3. 4r8c3=(7-5)r7c4=(5-1)r7c1=1r1c1-(1=7)r1c3 : =><7>r8c3
singles to end

[Elzo Nguyen]

Sorry, I have intetion to retreave my idea.
Thaks

[denis_berthier]

 



Hi netvope,

There's also a short solution with whips of maximum length 4

***** SudoRules version 15b.1.12-W *****
...8239462.3.59178.891.75..792.15.8.83.972.51.153.8297..8.3...93...968..9..28....
48 givens, 88 candidates and 345 nrc-links
whip[1]: c8n6{r9 .} ==> r7c7 <> 6, r9c7 <> 6
whip[1]: c6n4{r9 .} ==> r7c4 <> 4, r8c4 <> 4
whip[2]: c1n1{r7 r1} - c1n5{r1 .} ==> r7c1 <> 4
whip[2]: c1n5{r7 r1} - c1n1{r1 .} ==> r7c1 <> 6
whip[2]: r7n6{c8 c2} - r7n2{c2 .} ==> r7c8 <> 1
whip[2]: r7n6{c2 c8} - r7n2{c8 .} ==> r7c2 <> 7, r7c2 <> 4, r7c2 <> 5
whip[4]: r7n1{c1 c6} - r7n4{c6 c7} - r5c7{n4 n6} - c3n6{r5 .} ==> r9c3 <> 1
whip[3]: b8n7{r8c4 r7c4} - r7n5{c4 c1} - b7n1{r7c1 .} ==> r8c3 <> 7
whip[3]: r7n4{c7 c6} - r7n1{c6 c1} - r8c3{n1 .} ==> r8c9 <> 4
whip[1]: r8n4{c2 .} ==> r9c3 <> 4, r9c2 <> 4
whip[3]: r9c3{n7 n6} - r5c3{n6 n4} - b7n4{r8c3 .} ==> r8c2 <> 7
singles to the end
GRID SOLVED. W = 4, MOST COMPLEX RULE = Whip[4]
571823946
243659178
689147532
792415683
836972451
415368297
168534729
324796815
957281364

[pjb]

I think the puzzle is almost solved and it probably needs only one or two moves. For many of the remaining cells, if you pick a number for one random cell, you will be able to proceed to the complete solution with elementary techniques. However that would be considered cheating I guess

I implemented POM analysis, as nicely explained in Sudopedia (http://www.sudopedia.org/wiki/Pattern_Overlay_Method), into my solver (www.philsfolly.net.au). As described at Sudopedia, It has a simple mode and a multi-digit mode. When I put this puzzle into my solver, it solves the puzzle using the multi-digit method in two steps. It shows how pattern analysis is a useful and overlooked technique.

pjb

[daj95376]

When I put this puzzle into my solver, it solves the puzzle using the multi-digit method in two steps. It shows how pattern analysis is a useful and overlooked technique.

I presume that you are referring to:

Code: Select all

 +--------------------------------------------------------------+
 |  15    57    17    |  8     2     3     |  9     4     6     |
 |  2     46    3     |  46    5     9     |  1     7     8     |
 |  46    8     9     |  1     46    7     |  5     23    23    |
 |--------------------+--------------------+--------------------|
 |  7     9     2     |  46    1     5     |  346   8     34    |
 |  8     3     46    |  9     7     2     |  46    5     1     |
 |  46    1     5     |  3     46    8     |  2     9     7     |
 |--------------------+--------------------+--------------------|
 |  15    26    8     |  57    3     14    |  47    26    9     |
 |  3     2457  147   |  57    9     6     |  8     12    245   |
 |  9     4567  1467  |  2     8     14    |  347   136   345   |
 +--------------------------------------------------------------+
 # 45 eliminations remain

 template '5' = r1c1,r2c5,r3c7,r4c6,r5c8,r6c3,r7c4,r8c2,r9c9   contains r7c4
 template '5' = r1c1,r2c5,r3c7,r4c6,r5c8,r6c3,r7c4,r8c9,r9c2   contains r7c4
 template '5' = r1c2,r2c5,r3c7,r4c6,r5c8,r6c3,r7c1,r8c4,r9c9   contains r1c2

 template '7' = r1c2,r2c8,r3c6,r4c1,r5c5,r6c9,r7c4,r8c3,r9c7   conflict
 template '7' = r1c2,r2c8,r3c6,r4c1,r5c5,r6c9,r7c7,r8c4,r9c3
 template '7' = r1c3,r2c8,r3c6,r4c1,r5c5,r6c9,r7c4,r8c2,r9c7
 template '7' = r1c3,r2c8,r3c6,r4c1,r5c5,r6c9,r7c7,r8c4,r9c2

 for '7' = { r1c2,r2c8,r3c6,r4c1,r5c5,r6c9,r7c4,r8c3,r9c7 }, '5' fails for { r1c2,r7c4 }

         Templates (A: 1)                <> 7    r8c3

 template '4' = r1c8,r2c2,r3c5,r4c4,r5c7,r6c1,r7c6,r8c3,r9c9
 template '4' = r1c8,r2c2,r3c5,r4c4,r5c7,r6c1,r7c6,r8c9,r9c3
 template '4' = r1c8,r2c4,r3c1,r4c7,r5c3,r6c5,r7c6,r8c2,r9c9
 template '4' = r1c8,r2c4,r3c1,r4c7,r5c3,r6c5,r7c6,r8c9,r9c2
 template '4' = r1c8,r2c4,r3c1,r4c9,r5c3,r6c5,r7c6,r8c2,r9c7
 template '4' = r1c8,r2c4,r3c1,r4c9,r5c3,r6c5,r7c7,r8c2,r9c6   conflict

 template '7' = r1c2,r2c8,r3c6,r4c1,r5c5,r6c9,r7c7,r8c4,r9c3   contains r7c7
 template '7' = r1c3,r2c8,r3c6,r4c1,r5c5,r6c9,r7c4,r8c2,r9c7   contains r8c2
 template '7' = r1c3,r2c8,r3c6,r4c1,r5c5,r6c9,r7c7,r8c4,r9c2   contains r7c7

 for '4' = { r1c8,r2c4,r3c1,r4c9,r5c3,r6c5,r7c7,r8c2,r9c6 }, '7' fails for { r7c7,r8c2 }

         Templates (A: 2)                <> 4    r7c7,r9c6


[ronk]

When I put this puzzle into my solver, it solves the puzzle using the multi-digit method in two steps. It shows how pattern analysis is a useful and overlooked technique.

I presume that you are referring to: ...

Why do you think the POM should be limited to two (digit) layers in this case? Might not the use of additional layers result in shorter chains or simpler patterns?

BTW did your look for the chains or networks that produce your eliminations?

[daj95376]

Why do you think the POM should be limited to two (digit) layers in this case? Might not the use of additional layers result in shorter chains or simpler patterns?

pjb said that he used the multi-digit POM described in Sudopedia -- which uses two digits from what I read. Lots of other things might apply, but I was only interested in searching for what pjb might have used. Since my results cracked the puzzle in two steps -- ala pjb -- I was satisfied with the results.

BTW did your look for the chains or networks that produce your eliminations?

I did not search for chains/networks for the POM eliminations. In that respect, I was satisfied with the two steps in my first reply for this thread. I'll probably check now since you mentioned it.

[daj95376]

The XY-Chain in my first reply accounts for r8c3<>7.

That leaves this Kraken Row [r8] on <4> -- which is sufficient for r7c7,r9c6<>4.

Code: Select all

(4-7)r8c2 = r8c4 - r7c4 = (7-4)r7c7
(4  )r8c3 - r5c3 = r5c7 - (  4)r7c7
(4  )r8c9               - (  4)r7c7


[SudoQ]

Since my results cracked the puzzle in two steps -- ala pjb -- I was satisfied with the results.

My solver think that the fact that r7c6<>1 is a one-step solution, but I don't know if it is?