The New Sudoku Players' Forum

[djwillard]

I'm excited to find this forum! I am stuck on this one:

Original:
_3_5_487_
_____7__9
4_____5_6
_1_8__26_
____6____
_63__9_8_
8_1_____5
3__9_____
_964_8_3_

I got this far:
63_5_487_
1__6_7349
4_____5_6
91_8__26_
____6_95_
_63__9_8_
8_1____95
3__9____8
_964_8_3_

I have been staring at this for three days with no progress (I've filled in all possibilities for each number) so obviously am missing a technique.

Help with even just the next number would be most appreciated!
Regards,
DJ

[emm]

This is a pretty difficult puzzle. The solver lists these techniques required – locked candidates, naked pairs, naked triples, Xwing and colours before it places two more clues and gives up.

The best thing by far is to first learn these techniques yourself at Simple Sudoku's very-user-friendly site. Click on the blue words - they are the key to a door to a treasure house of knowledge - which is actually easier to find than it is so say quickly!

Hint : first step = locked candidates – look where the 4s go in box 3,6,9 - you may already know this, it's hard to tell without knowing what you have for the empty cells.

[djwillard]

Thanks for pointing me in a direction to go forward. I appreciate your response. Onward!

[tso]

This is a difficult puzzle that needed a variety of tactics. Neither Simple Sudoku nor SadMan can solve it completely.

Puzzles this complex will often, if not always, have alternate paths to the solution.

Code: Select all

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

It isn't clear which candidates you have already eliminated, so, starting from scratch:

Code: Select all

  6      3      29     | 5      129    4      | 8      7      12 
  1      258    258    | 6      28     7      | 3      4      9   
  4      278    2789   | 123    12389  123    | 5      12     6   
 ----------------------+----------------------+-------------------
  9      1      457    | 8      3457   35     | 2      6      347
  27     2478   2478   | 1237   6      123    | 9      5      1347
  257    6      3      | 127    12457  9      | 147    8      147
 ----------------------+----------------------+-------------------
  8      247    1      | 237    237    236    | 467    9      5   
  3      2457   2457   | 9      1257   1256   | 1467   12     8   
  257    9      6      | 4      1257   8      | 17     3      127

There is a naked triple of [123] in row three -- r3c468. Remove other 1's, 2's and 3's from r3c235.


Either r7c7 or r8c7 must be 4 -- eliminate the 4 in r6c7 ...
... which creates a naked pair of [17] in r69c7 eliminating 1's and 7's from r78c7.

... which forces a 7 in either r9c7 or r9c9, eliminating 7s from r9c15.

... Now the only place in column 1 for a 7 is row 5 or 6, both of which are in box 4 -- so you can eliminate 7's from the rest of box 4 (r45c23).


There is an X-Wing in 5's in r69c14. That is, the only place in row 6 and 9 that a 5 can go is in column 1 and 4. This eliminates the possibility of 5's elsewhere in both columns.

The updated grid at this point:

Code: Select all

  6      3      29     | 5     -129    4      | 8      7     +12 
  1      258    258    | 6      28     7      | 3      4      9   
  4      78     789    | 123    89     123    | 5     -12     6   
 ----------------------+----------------------+-------------------
  9      1      45     | 8      347    35     | 2      6      347
  27     248    248    | 1237   6      123    | 9      5      1347
  257    6      3      | 127    12457  9      | 17     8      147
 ----------------------+----------------------+-------------------
  8      247    1      | 237    237    236    | 46     9      5   
  3      2457   2457   | 9    +-127    1256   | 46    +12     8   
  25     9      6      | 4      125    8      | 17     3      127

The plus and minuses show "coloring" on the 1's ... both r8c8=1 and r8c8<>1 lead to r8c5<>1.

This allows a further coloring of 1's to remove r6c5:

Code: Select all

  6      3      29     | 5     -129    4      | 8      7     +12 
  1      258    258    | 6      28     7      | 3      4      9   
  4      78     789    | 123    89     123    | 5     -12     6   
 ----------------------+----------------------+-------------------
  9      1      45     | 8      347    35     | 2      6      347
  27     248    248    | 1237   6      123    | 9      5      1347
  257    6      3      | 127  +-12457  9      | 17     8      147
 ----------------------+----------------------+-------------------
  8      247    1      | 237    237    236    | 46     9      5   
  3      2457   2457   | 9       27   -1256   | 46    +12     8   
  25     9      6      | 4     +125    8      | 17     3      127

This shows that either r1c5 or r9c5 must be 1, eliminating other 1's from column 5.


There is now a naked triple of [237] in box 8 -- remove other 237s from that box.

At long last, this allows some actual placements by singles, leading to this updated grid:

Code: Select all

  6      3      29     | 5      129    4      | 8      7     +12 
  1      258    258    | 6      28     7      | 3      4      9   
  4      78     789    | 123    89    a123    | 5     -12     6   
 ----------------------+----------------------+-------------------
  9      1      45     | 8      347    35     | 2      6      347
+-27     248    248    | 1237   6     b123    | 9      5      1347
  257    6      3      | 127    2457   9      | 17     8      147
 ----------------------+----------------------+-------------------
  8      27     1      | 237    237    6      | 4      9      5   
  3      2457   2457   | 9      27     15     | 6     +12     8   
 +25     9      6      | 4      15     8      | 17     3     -127

A somewhat more complex coloring of 2's eliminates 2 from r5c1.
If r9c1 is 2 then r5c1<>2.
If r9c1<>2 then r3c8=2 then r3c6<>2 then r5c6=2 then r5c1<>2.
Therefore, r5c1<>2.

Another single is filled, bringing the grid to:

Code: Select all

  6     3     29    | 5    -129   4     | 8     7     12
  1     258   258   | 6    -28    7     | 3     4     9 
  4     78    789   |-123   89   -123   | 5    +12    6 
 -------------------+-------------------+----------------
  9     1     45    | 8     347   35    | 2     6     347
  7     248   248   | 123   6     123   | 9     5     134
  25    6     3     | 127   2457  9     | 17    8     147
 -------------------+-------------------+----------------
  8     27    1     | 237   237   6     | 4     9     5 
  3     2457  2457  | 9    +27    15    | 6     12    8 
  25    9     6     | 4     15    8     | 17    3    +127

Finally, we need a "Nishio":

[CORRECTION: Changed typo -- "r3c2=2" changed to "r3c8=2"]
If r8c5=2, then r9c9=2, then r3c8=2. But this leaves no place for a 2 in box 2.

Therefore, r8c5<>2.


The rest of the puzzle is solved with singles.

[gaby]

My solver cracks this puzzle, rating it a 2.5.2.1 (that's in the fiendish/extreme category on my site). It uses X-wing, colouring, nishio, block interactions, hidden pairs, number pairs and number chains. The main part of the solve is:

Code: Select all

5 -> [r5,c8] Candidate appears once in c8
9 -> [r7,c8] Candidate appears once in c8
9 -> [r5,c7] Candidate appears once in c7
3 -> [r2,c7] Candidate appears once in c7
8 -> [r8,c9] Candidate appears once in c9
6 -> [r1,c1] Candidate appears once in r1
1 -> [r2,c1] Candidate appears once in c1
9 -> [r4,c1] Candidate appears once in c1
6 -> [r2,c4] Candidate appears once in r2
4 -> [r2,c8] Candidate appears once in r2
4 <- [r6,c7] b9 only has 4 in c7
1 <- [r8,c7] Number Pair in c7 {1,7}, in {[r6,c7][r9,c7]}
7 <- [r7,c7] Number Pair in c7 {1,7}, in {[r6,c7][r9,c7]}
7 <- [r8,c7] Number Pair in c7 {1,7}, in {[r6,c7][r9,c7]}
7 <- [r9,c1] b9 only has 7 in r9
7 <- [r9,c5] b9 only has 7 in r9
7 <- [r5,c2] c1 only has 7 in b4
7 <- [r4,c3] c1 only has 7 in b4
7 <- [r5,c3] c1 only has 7 in b4
1 <- [r3,c5] Number Chains in r3 {1,2,3}, in {[r3,c4][r3,c6][r3,c8]}
2 <- [r3,c2] Number Chains in r3 {1,2,3}, in {[r3,c4][r3,c6][r3,c8]}
2 <- [r3,c3] Number Chains in r3 {1,2,3}, in {[r3,c4][r3,c6][r3,c8]}
2 <- [r3,c5] Number Chains in r3 {1,2,3}, in {[r3,c4][r3,c6][r3,c8]}
3 <- [r3,c5] Number Chains in r3 {1,2,3}, in {[r3,c4][r3,c6][r3,c8]}
5 <- [r4,c5] X-Wing in 5's: r6,r9
5 <- [r8,c5] X-Wing in 5's: r6,r9
1 <- [r6,c5] Coloured cells: [r1,c5]=1a, [r3,c8]=1a, [r1,c9]=1b, [r8,c8]=1b, [r9,c7]=2a, [r6,c7]=2b. If 1b excludes 2a, the intersection of 1a and 2b prohibits 1 at [r6,c5]
1 <- [r8,c5] Nishio won't allow 1 in [r8,c5]
2 <- [r9,c5] Hidden Pair in b8 {1,5}, in {[r9,c5],[r8,c6]}
2 <- [r8,c6] Hidden Pair in b8 {1,5}, in {[r9,c5],[r8,c6]}
6 <- [r8,c6] Hidden Pair in b8 {1,5}, in {[r9,c5],[r8,c6]}
6 -> [r7,c6] Candidate appears once in c6
4 -> [r7,c7] One number possible in cell
6 -> [r8,c7] One number possible in cell
2 <- [r5,c1] Coloured cells: [r9,c1]=1a, [r1,c9]=1a, [r8,c8]=1a, [r9,c9]=1b, [r3,c8]=1b, [r3,c6]=2a, [r5,c6]=2b. If 1b excludes 2a, the intersection of 1a and 2b prohibits 2 at [r5,c1]
7 -> [r5,c1] One number possible in cell
2 <- [r7,c2] Nishio won't allow 2 in [r7,c2]


The rest is basic logic.

Gaby
http://vanhegan.net/sudoku/

[Crazy Girl]

Another single is filled, bringing the grid to:

Code: Select all

  6     3     29    | 5    -129   4     | 8     7     12
  1     258   258   | 6    -28    7     | 3     4     9 
  4     78    789   |-123   89   -123   | 5    +12    6 
 -------------------+-------------------+----------------
  9     1     45    | 8     347   35    | 2     6     347
  7     248   248   | 123   6     123   | 9     5     134
  25    6     3     | 127   2457  9     | 17    8     147
 -------------------+-------------------+----------------
  8     27    1     | 237   237   6     | 4     9     5 
  3     2457  2457  | 9    +27    15    | 6     12    8 
  25    9     6     | 4     15    8     | 17    3    +127

Finally, we need a "Nishio":

If r8c5=2, then r9c9=2, then r3c2=2. But this leaves no place for a 2 in box 2.

Therefore, r8c5<>2.

The rest of the puzzle is solved with singles.

Do you mean R7C2 = 2, as the options for r3c2 are {7, 8}

Can you explain what a "Nishio" is as I've only ever heard of it but not how to apply it and what it proves in this puzzle. Is it a sort of chain that leads to a contradiction ?

[Hud]

I dubbed the puzzle into my Pappocom program and was surprised to see it come up as "very hard". I solved it without any heroic measures in 20 minutes. I know what it's like to get hopelessly stuck for extended periods of time though. I often start from "scratch" again to see if I end up at the same place and usually, something emerges. Nice to see a fellow Arizonian and Phoenician on board.

[tso]

Another single is filled, bringing the grid to:

Code: Select all

  6     3     29    | 5    -129   4     | 8     7     12
  1     258   258   | 6    -28    7     | 3     4     9 
  4     78    789   |-123   89   -123   | 5    +12    6 
 -------------------+-------------------+----------------
  9     1     45    | 8     347   35    | 2     6     347
  7     248   248   | 123   6     123   | 9     5     134
  25    6     3     | 127   2457  9     | 17    8     147
 -------------------+-------------------+----------------
  8     27    1     | 237   237   6     | 4     9     5 
  3     2457  2457  | 9    +27    15    | 6     12    8 
  25    9     6     | 4     15    8     | 17    3    +127

Finally, we need a "Nishio":

If r8c5=2, then r9c9=2, then r3c2=2. But this leaves no place for a 2 in box 2.

Therefore, r8c5<>2.

The rest of the puzzle is solved with singles.

Do you mean R7C2 = 2, as the options for r3c2 are {7, 8}

Sorry, that was a typo. I've corrected it in the original post. It should read "r3c8=2" The + marks the cells that must be 2 if r8c5=2, the - marks cells that the + cells eliminate.

Can you explain what a "Nishio" is as I've only ever heard of it but not how to apply it and what it proves in this puzzle. Is it a sort of chain that leads to a contradiction ?

Nishio is asking the question "If I place one instance of this number in a cell, will I be able to place all 9 instances of this number?" If you cannot, then you can eliminate that possibility. It's been described as trial and error limited to a single digit, however, *because* it is limited to a single digit, it can be performed by human solvers by simple inspection without needing to write anything down. It is a paper and pen solving method that predates many of the advanced tactics discussed in this forum. It *might* be a forcing chain, it *might* be a forcing net ... ultimately, it does not matter. See here for some puzzles that can be solved with Nishio.

[tso]

I dubbed the puzzle into my Pappocom program and was surprised to see it come up as "very hard". I solved it without any heroic measures in 20 minutes. I know what it's like to get hopelessly stuck for extended periods of time though. I often start from "scratch" again to see if I end up at the same place and usually, something emerges. Nice to see a fellow Arizonian and Phoenician on board.

You've dubbed it in incorrectly. Pappocom rejects this puzzle as "INVALID".

[Hud]

tso, you're right and the crow isn't as tasty as the turkey. I copied the grid to a paper having another one on it and dubbed the wrong one in. Man, there's always something; sorry. I was feeling pretty smart though lol.

[Guest]

Code: Select all

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


[tso]

Bestplayer:

*Please* stop posting just the solutions to puzzles. Anyone here can go to 100 different websites or use two dozen pieces of software to find the solution. The name of the forum is "solving techniques". Most of the time, the poster already knows the answer, but they want to find a logical way to the solution -- and learn something that will help them solve the next one without needing help.

[Tom Sawyerer]

The best thing by far is to first learn these techniques yourself at Simple Sudoku's very-user-friendly site. Click on the blue words - they are the key to a door to a treasure house of knowledge - which is actually easier to find than it is so say quickly!

Thank you very much for the link which helped me alot in solving the sudoku puzzles.

[Max Beran]

There's a repetitive cycle that forces a "1" into r1c9 taking in (1)r1c3(9)r3c3(7)r8c3(-7)r8c5(-2)r8c8(2)r3c8 and back to (1)r1c9. Once you've got that the rest follows with standard methods. Note that this involves both strong and weak edges as r8c5 is not bilocation so thanks as ever to Jeff for making this technique so available.

Max Beran

[QBasicMac]

I got this far and couldn't proceed without T&E.

If there is something "simple" I am missing, such as a hidden triple or quad or a swordfish, please tell me in great detail where it is.

If, instead, complex stuff is required such as coloring, just tell me that complex stuff is required. I am not interested in learning those techniques. T&E is simpler.

Thanks,

Mac

Solution So Far

Code: Select all

63- 5-4 87-
1-- 6-7 349
4-- --- 5-6
91- 8-- 26-
--- -6- 95-
-63 --9 -8-
8-1 --- -95
3-- 9-- --8
-96 4-8 -3-


Pencilmarks So Far

Code: Select all

-         -         29        -         129       -         -         -         12       
-         258       258       -         28        -         -         -         -       
-         278       2789      123       12389     123       -         12        -       
-         -         45        -         3457      35        -         -         347     
27        248       248       1237      -         123       -         -         1347     
257       -         -         127       12457     -         17        -         147     
-         247       -         237       237       236       46        -         -       
-         2457      2457      -         127       1256      46        12        -       
25        -         -         -         125       -         17        -         127