## This cannot be solved by logic

Advanced methods and approaches for solving Sudoku puzzles

### This cannot be solved by logic

On many hard, or very hard puzzles, there is often a point in the game where logic no longer comes into play. Then trial and error must be used - i.e guessing on of two numbers and continuing the puzzle to see whether it fails somewhere down the line or not. Surely claims that all Sudoku puzzles can be solved by logic alone are false? Any comments?
Guest

I've solved many hard and very hard puzzles and never came to such a point...

It seems to me that you are missing some techniques... Perhaps it would be a good idea to post a puzzle on which you are stuck?
Animator

Posts: 469
Joined: 08 April 2005

Can anyone give me a hand with this puzzle? I've come to the trial and error stage. Logic doesn't seem to work for me....

Code: Select all
`9-- 7-8 -4547- -95 ---85- -42 -7-649 581 723237 964 158--- 273 4967-- 856 -34--- --9 -673-- --7 ---`

cheers
Guest

Posts: 312
Joined: 25 November 2005

Take a close look at the number 1.

If you look carefully then you know where it has to go in column 1.

(Also, can you do me a favor? Next time you post a grid, then please include the category...)
Animator

Posts: 469
Joined: 08 April 2005

Which logic must be used for this one?

000700800000040030000009001600500000010030040005001007500200600030080090007000002

or as a grid:
Code: Select all
`--- 7-- 8-- --- -4- -3- --- --9 --1 6-- 5-- --- -1- -3- -4- --5 --1 --7 5-- 2-- 6-- -3- -8- -9- --7 --- --2`

It is proved to have an unique solution, but it seems it can be calculated only with brute force.
Vereth

Posts: 2
Joined: 01 July 2008

Vereth The puzzle you have given is extremely hard. It may be a transformation of an already known puzzle in the hardest puzzles thread, I'm sure someone can easily verify that. It requires nested forcing moves.
Glyn

Posts: 357
Joined: 26 April 2007

### 10.6

Vereth wrote:Which logic must be used for this one?

Code: Select all
` . . . 7 . . 8 . .  . . . . 4 . . 3 .  . . . . . 9 . . 1  6 . . 5 . . . . .  . 1 . . 3 . . 4 .  . . 5 . . 1 . . 7  5 . . 2 . . 6 . .  . 3 . . 8 . . 9 .  . . 7 . . . . . 2 `

SuDoku Explainer 1.2.1 rates it 10.6

Pat

Posts: 3674
Joined: 18 July 2005

Pat It's what I would call a 'breeze' for Sudoku Explainer (where the breeze refers to the processor fan).
Glyn

Posts: 357
Joined: 26 April 2007

Code: Select all
` ...7..8......4..3......9..16..5......1..3..4...5..1..75..2..6...3..8..9...7.....2   c258  Swordfish (finned)              <> 7    [r3c1]   -or- r258    Swordfish (finned)              <> 7    [r3c1]  5r3c7  5r5c9  4r8c9  4r3c7             <> 5    [r3c7]   (chain) +--------------------------------------------------------------------------------+ |  12349   24569   123469  |  7       1256    2356    |  8       256     4569    | |  12789   256789  12689   |  168     4       2568    |  2579    3       569     | |  2348    245678  23468   |  368     256     9       |  247     2567    1       | |--------------------------+--------------------------+--------------------------| |  6       24789   23489   |  5       279     2478    |  1239    128     389     | |  2789    1       289     |  689     3       2678    |  259     4       5689    | |  23489   2489    5       |  4689    269     1       |  239     268     7       | |--------------------------+--------------------------+--------------------------| |  5       489     1489    |  2       179     347     |  6       178     348     | |  124     3       1246    |  146     8       4567    |  1457    9       45      | |  1489    4689    7       |  13469   1569    3456    |  1345    158     2       | +--------------------------------------------------------------------------------+`

At this point, just test the five different possibilities for '7'. It may be Brute Force, but is nested forcing chains/nets really any better?

Code: Select all
` ...7..8......4.73..7...9..16..57....71..3..4...5..1..75..2..67..3..87.9...7.....2 ...7..8...7..4..3......9.716..5.7...71..3..4...5..1..75..27.6...3..8.79...7.....2 ...7..8...7..4..3......9.716..57....71..3..4...5..1..75..2.76...3..8.79...7.....2 ...7..8...7..4..3......97.16..57....71..3..4...5..1..75..2..67..3..87.9...7.....2 *** ...7..8..7...4..3......9.7167.5......1..37.4...5..1..75..27.6...3..8.79...7.....2`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Vereth wrote:Which logic must be used for this one?

000700800000040030000009001600500000010030040005001007500200600030080090007000002

It can be solved with nets of AICs crossing AHS or ALS, but it is a long long way.
champagne
2017 Supporter

Posts: 6702
Joined: 02 August 2007
Location: France Brittany

Glyn wrote:Vereth The puzzle you have given is extremely hard. It may be a transformation of an already known puzzle in the hardest puzzles thread, I'm sure someone can easily verify that. It requires nested forcing moves.

It has popped up before here.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Great work! Thanks to all!

daj95376 wrote:
Code: Select all
` ...7..8......4..3......9..16..5......1..3..4...5..1..75..2..6...3..8..9...7.....2   c258  Swordfish (finned)              <> 7    [r3c1]   -or- r258    Swordfish (finned)              <> 7    [r3c1]  5r3c7  5r5c9  4r8c9  4r3c7             <> 5    [r3c7]   (chain) +--------------------------------------------------------------------------------+ |  12349   24569   123469  |  7       1256    2356    |  8       256     4569    | |  12789   256789  12689   |  168     4       2568    |  2579    3       569     | |  2348    245678  23468   |  368     256     9       |  247     2567    1       | |--------------------------+--------------------------+--------------------------| |  6       24789   23489   |  5       279     2478    |  1239    128     389     | |  2789    1       289     |  689     3       2678    |  259     4       5689    | |  23489   2489    5       |  4689    269     1       |  239     268     7       | |--------------------------+--------------------------+--------------------------| |  5       489     1489    |  2       179     347     |  6       178     348     | |  124     3       1246    |  146     8       4567    |  1457    9       45      | |  1489    4689    7       |  13469   1569    3456    |  1345    158     2       | +--------------------------------------------------------------------------------+`

At this point, just test the five different possibilities for '7'. It may be Brute Force, but is nested forcing chains/nets really any better?

Code: Select all
` ...7..8......4.73..7...9..16..57....71..3..4...5..1..75..2..67..3..87.9...7.....2 ...7..8...7..4..3......9.716..5.7...71..3..4...5..1..75..27.6...3..8.79...7.....2 ...7..8...7..4..3......9.716..57....71..3..4...5..1..75..2.76...3..8.79...7.....2 ...7..8...7..4..3......97.16..57....71..3..4...5..1..75..2..67..3..87.9...7.....2 *** ...7..8..7...4..3......9.7167.5......1..37.4...5..1..75..27.6...3..8.79...7.....2`

Maybe testing the 7's could be simplified by using the Pattern Overlay Method?
Vereth

Posts: 2
Joined: 01 July 2008

This doesn't really belong here but since we were just discussing Sue de Coq elsewhere here are two Sue de Coqs in my solver's solution:

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`.---------------------.----------------------.---------------------.| 1349  B25     134-69|  7     A1256  A236   | 8     B256    4-69  || 189    257    689   | C18     4      2568  | 279    3      569   || 348    257    3468  | C38     256    9     | 247    2567   1     |:---------------------+----------------------+---------------------:| 6      489    3489  |  5      7      248   | 1239   128    389   || 7      1      2     |  9      3      68    | 5      4      68    || 3489   489    5     |  48     26     1     | 239    268    7     |:---------------------+----------------------+---------------------:| 5      489    1489  |  2      19     347   | 6      178    348   || 2      3      14    |  6      8      457   | 147    9      45    || 1489   6      7     |  134    159    345   | 134    158    2     |'---------------------'----------------------'---------------------'Sue de Coq: r1c56 - {12356} (r1c28 - {256}, r23c4 - {138}) => r1c39<>6`

Code: Select all
`.------------------.------------------.-------------------.| 1349  25    39   | 7     125   36   |  8     56    49   || 189   27    689  | 18    4     56   |  27    3     59   || 348   257   368  | 38    25    9    |  247   567   1    |:------------------+------------------+-------------------:| 6     49    349  | 5     7     2    |  39    1     8    || 7     1     2    | 9     3     8    |  5     4     6    || 389   89    5    | 4     6     1    |  39    2     7    |:------------------+------------------+-------------------:| 5     489   1489 | 2     19    47   |  6    C78    3    || 2     3    B14   | 6     8     -457 | A147   9    A45   || 89    6     7    | 13    59    34   |  14   C58    2    |'------------------'------------------'-------------------'Sue de Coq: r8c79 - {1457} (r8c3 - {14}, r79c8 - {578}) => r8c6<>4`
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

Anonymous wrote:Can anyone give me a hand with this puzzle? I've come to the trial and error stage. Logic doesn't seem to work for me....

Code: Select all
`9-- 7-8 -4547- -95 ---85- -42 -7-649 581 723237 964 158--- 273 4967-- 856 -34--- --9 -673-- --7 ---`

cheers

I am not conversant with the terminology used for puzzles such as this; however, I have come up with some mathematical techniques that allow me to solve some of these puzzles. Therefor, I will explain the terminology that I use and go from there.

I number the boxes, with the upper left box being box #1 and the lower right box being box #81.

By writing down (or whatever) the numbers that are not automatically eliminated because they are already present in the same row, column or 3 X 3 that each respective open box is in, I generated the following Raw Possibility Matrix (God, I hope I got this right--there's probably a web site or a download or something that'll do this automatically--and if not I can write one--but I don't know where it is):

Code: Select all
`-----------------------------------------------------------|  9  |  126 | 1236   #  7  | 136 | 8 #  236  |  4  |  5  |-----------------------------------------------------------|  4  |   7  | 1236   # 136 |  9  | 5 # 23368 | 138 | 129 |-----------------------------------------------------------|  8  |   5  |  136   # 136 |  4  | 2 #  369  |  7  |  19 |===========================================================|  6  |   4  |    9   #  5  |  8  | 1 #   7   |  2  |  3  |-----------------------------------------------------------|  2  |   3  |    7   #  9  |  6  | 4 #   1   |  5  |  8  |-----------------------------------------------------------| 15  |   18 |  158   #  2  |  7  | 3 #   4   |  9  |  6  |===========================================================|  7  |   12 |   12   #  8  |  5  | 6 #  29   |  3  |  4  |-----------------------------------------------------------| 15  |  128 |  12458 # 134 | 123 | 9 #  25   |  6  |  7  |-----------------------------------------------------------|  3  | 1269 | 124568 #  14 | 12  | 7 # 2589  | 18  | 129 |-----------------------------------------------------------`

Please check boxes 56 and 57. These can only hold the values of 1 or 2. Since this is the case, no other boxes in that 3 X 3 or row can hold either of those values.

Code: Select all
`-----------------------------------------------------------|  9  |  126 |  1236  #  7  | 136 | 8 #  236  |  4  |  5  |-----------------------------------------------------------|  4  |   7  |  1236  # 136 |  9  | 5 # 23368 | 138 | 129 |-----------------------------------------------------------|  8  |   5  |  136   # 136 |  4  | 2 #  369  |  7  |  19 |===========================================================|  6  |   4  |    9   #  5  |  8  | 1 #   7   |  2  |  3  |-----------------------------------------------------------|  2  |   3  |    7   #  9  |  6  | 4 #   1   |  5  |  8  |-----------------------------------------------------------| 15  |   18 |  158   #  2  |  7  | 3 #   4   |  9  |  6  |===========================================================|  7  |   12 |   12   #  8  |  5  | 6 #  9    |  3  |  4  |-----------------------------------------------------------| 15  |    8 |   458  # 134 | 123 | 9 #  25   |  6  |  7  |-----------------------------------------------------------|  3  |  69  |   4568 #  14 | 12  | 7 # 2589  | 18  | 129 |-----------------------------------------------------------`

Using this information, one can easily establish that box 65 must contain the number 8 (its raw possibilities are only 1, 2 or 8).

This removes the possibility of any other box in that row, column or 3 X 3 containing the number 8.

Code: Select all
`-----------------------------------------------------------|  9  |  126 | 1236  #  7  | 136 | 8 #  236  |  4  |  5  |-----------------------------------------------------------|  4  |   7  | 1236  # 136 |  9  | 5 # 23368 | 138 | 129 |-----------------------------------------------------------|  8  |   5  |  136  # 136 |  4  | 2 #  369  |  7  |  19 |===========================================================|  6  |   4  |    9  #  5  |  8  | 1 #   7   |  2  |  3  |-----------------------------------------------------------|  2  |   3  |    7  #  9  |  6  | 4 #   1   |  5  |  8  |-----------------------------------------------------------| 15  |   1  |  158  #  2  |  7  | 3 #   4   |  9  |  6  |===========================================================|  7  |   12 |    12 #  8  |  5  | 6 #  9    |  3  |  4  |-----------------------------------------------------------| 15  |    8 |   45  # 134 | 123 | 9 #  25   |  6  |  7  |-----------------------------------------------------------|  3  |  69  |   456 #  14 |  12 | 7 # 2589  | 18  | 129 |-----------------------------------------------------------`

Because of this, box number 47 must contain the number 1 (it is in the same column as box 65, and its raw possibilities are 1 and 8).

This removes the number 1 from the possibilities in the row, column and 3 X 3 in which box 47 is found.

Code: Select all
`-----------------------------------------------------------|  9  |   26 | 1236  #  7  | 136 | 8 #  236  |  4  |  5  |-----------------------------------------------------------|  4  |   7  | 1236  # 136 |  9  | 5 # 23368 | 138 | 129 |-----------------------------------------------------------|  8  |   5  |  136  # 136 |  4  | 2 #  369  |  7  |  19 |===========================================================|  6  |   4  |    9  #  5  |  8  | 1 #   7   |  2  |  3  |-----------------------------------------------------------|  2  |   3  |    7  #  9  |  6  | 4 #   1   |  5  |  8  |-----------------------------------------------------------|   5 |   1  |   58  #  2  |  7  | 3 #   4   |  9  |  6  |===========================================================|  7  |    2 |   12  #  8  |  5  | 6 #  9    |  3  |  4  |-----------------------------------------------------------| 15  |    8 |   45  # 134 | 123 | 9 #  25   |  6  |  7  |-----------------------------------------------------------|  3  |  69  |   456 #  14 |  12 | 7 # 2589  | 18  | 129 |-----------------------------------------------------------`

Because of this, box 46 must contain the number 5--its raw possibilities are 1 and 5. Also because of this, box 56 must contain the number 2--it is in the same row as box 47.

Look at the lower left 3 X 3 carefully.

The 5 in box 46 removes that possibility from all other boxes in its column.

Code: Select all
`-----------------------------------------------------------|  9  |   26 | 1236  #  7  | 136 | 8 #  236  |  4  |  5  |-----------------------------------------------------------|  4  |   7  | 1236  # 136 |  9  | 5 # 23368 | 138 | 129 |-----------------------------------------------------------|  8  |   5  |  136  # 136 |  4  | 2 #  369  |  7  |  19 |===========================================================|  6  |   4  |    9  #  5  |  8  | 1 #   7   |  2  |  3  |-----------------------------------------------------------|  2  |   3  |    7  #  9  |  6  | 4 #   1   |  5  |  8  |-----------------------------------------------------------|   5 |   1  |    58 #  2  |   7 | 3 #   4   |  9  |  6  |===========================================================|  7  |    2 |   12  #  8  |   5 | 6 #  9    |  3  |  4  |-----------------------------------------------------------| 1   |    8 |   45  # 134 | 123 | 9 #  25   |  6  |  7  |-----------------------------------------------------------|  3  |  69  |  456  #  14 |  12 | 7 # 2589  | 18  | 129 |-----------------------------------------------------------`

Thus, box 64 must contain the number 1--it is in the same column as box 46, and its raw possibilities are 1 and 5.

Because box 56 contains the number 2, this removes the possibility that any other box in its row contains that number.

Code: Select all
`-----------------------------------------------------------|  9  |   26 | 1236  #  7  | 136 | 8 #  236  |  4  |  5  |-----------------------------------------------------------|  4  |   7  | 1236  # 136 |  9  | 5 # 23368 | 138 | 129 |-----------------------------------------------------------|  8  |   5  |  136  # 136 |  4  | 2 #  369  |  7  |  19 |===========================================================|  6  |   4  |    9  #  5  |  8  | 1 #   7   |  2  |  3  |-----------------------------------------------------------|  2  |   3  |    7  #  9  |  6  | 4 #   1   |  5  |  8  |-----------------------------------------------------------|   5 |   1  |    58 #  2  |  7  | 3 #   4   |  9  |  6  |===========================================================|  7  |    2 |  *1*  # 8   |  5  | 6 #  9    |  3  |  4  |-----------------------------------------------------------| *1* |    8 |   45  # 134 | 123 | 9 #  25   |  6  |  7  |-----------------------------------------------------------|  3  |  69  |   456 #  14 | 12  | 7 # 2589  | 18  | 129 |-----------------------------------------------------------`

Therefor, box 57 must contain the number 1--it is in the same 3 X 3 as box 56, and its raw possibilities are 1 and 2.

But this is impossible. Box 57 cannot contain the number 1 because box 64, in the same 3 X 3, was already shown to contain the number 1.

Therefor, I conclude that there is an error in your existing solution to this puzzle. Please provide the raw puzzle.
cpu.write

Posts: 1
Joined: 06 July 2008

cpu.write Unfortunately what you call the Raw Possibility Matrix is incorrect. Here is the actual scenario. You can try it again from here. It is very straightforward.

This puzzle was posted 3 years ago so it is really a dormant thread.

Code: Select all
`.---------------------.---------------------.---------------------.| 9      126    1236  | 7      13     8     | 236    4      5     || 4      7      1236  | 136    9      5     | 2368   18     12    || 8      5      136   | 136    4      2     | 369    7      19    |:---------------------+---------------------+---------------------:| 6      4      9     | 5      8      1     | 7      2      3     || 2      3      7     | 9      6      4     | 1      5      8     || 15     18     158   | 2      7      3     | 4      9      6     |:---------------------+---------------------+---------------------:| 7      129    12    | 8      5      6     | 29     3      4     || 15     128    12458 | 134    123    9     | 258    6      7     || 3      12689  124568| 14     12     7     | 2589   18     129   |'---------------------'---------------------'---------------------'`
Glyn

Posts: 357
Joined: 26 April 2007