Challenge: New set of 11 'Unsolvables'

Advanced methods and approaches for solving Sudoku puzzles

Postby StrmCkr » Thu Sep 14, 2006 12:12 am

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

puzzle #33

removed most of this post.
Last edited by StrmCkr on Tue May 01, 2018 6:08 am, edited 2 times in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 842
Joined: 05 September 2006

Postby Mike Barker » Thu Sep 14, 2006 3:11 am

#32 is longer than the last couple of solutions again using grouped strong links with overlap in the start and end nodes as key. This also has a grouped nice loop where two adjacent ALS share a common cell which doesn't contain the linking label.
    1) Naked Single (46)
    2) Locked Line/Box (12)
    3) Hidden Single (10)
    4) Grouped Nice Loops with 3 GSL/ALS (5)
    5) Grouped Nice Loops with 4 GSL/ALS (5)
    6) Nice Loops with 3 Strong Links/BV Cells (4)
    7) Finned X-wing (3)
    8) UR+2(X,D,B)/1SL (Type 4,...) (3)
    9) Nice Loops with 4 Strong Links/BV Cells (2)
    10) Strong Nice Loops with 4 GSL/BV Cells (2)
    11) Naked Triple (1)
    12) Locked Box/Box (1)
    13) Hidden Pair (1)
    14) Mutant Swordfish (1)
    15) Generalized WXYZ-wing (1)
    16) 4-node XY-ring (1)
    17) UR+3(X,C,N,U,E)/2SL (1)
    18) Advanced Colouring with 3 Links (1)
    19) Advanced Colouring with 5 Links (1)
    20) Grouped Advanced Colouring with 5 Links (1)
    21) Nice Loops with 5 Strong Links/BV Cells (1)
    22) A=2 cell ALS-xz rule (1)
    23) B=1 cell ALS-xy rule (1)
Code: Select all
Locked Row Line/Box: r3c46 => r3c9<>9
Locked Row Line/Box: r9c46 => r9c23<>5
Locked Row Line/Box: r5c78 => r5c26<>1
Locked Row Line/Box: r5c78 => r5c456<>3
Locked Column Line/Box Pair: r46c9 => r2c9<>5,r8c9<>6
Locked Column Line/Box: r89c8 => r5c8<>6
Naked Row Triple: r1c467 => r1c2<>68,r1c3<>2,r1c8<>8
Locked Row Line/Box: r2c12 => r2c5<>6
3-element Nice Loop: r4c6=1=r4c1-1-r6c1-6-r6c9=6=r4c9~6~r4c6 => r4c6<>6
3-element Nice Loop: r8c2=5=r8c3-5-r2c3-2-r9c3~7~r8c2 => r8c2<>7
4-element Nice Loop: r8c2=5=r8c3-5-r2c3-2-r2c9-9-r7c9=9=r7c2~9~r8c2 => r8c2<>9
4-element Strong Nice Loop: r7c1=1=r7c2=9=r7c9-9-r2c9-2-r2c13=2=r3c1~2~r7c1 => r7c1<>2
5-element Advanced Colouring: r1c3=4=r5c3=9=r8c3-9-r8c7=9=r2c7=1=r2c8=5=r1c8~5~r1c3 => r1c3<>5,r1c8<>4
Locked Row Line/Box: r3c89 => r3c2<>4
5-element Nice Loop: r2c3=5=r8c3=9=r7c2=1=r6c2-1-r6c1-6-r2c1=6=r2c2~5~r2c3 => r2c2<>5
B=1 cell ALS xy-rule: r1c7-2-r2c9-9-r7c4689 => r9c7<>8,r23c8<>8
4-element Nice Loop: r8c2-5-r1c2=5=r1c8-5-r2c8-1-r5c8~3~ => r8c8<>3
UR+3C/2SL (4,7): r38c89 => r8c9<>7
A=2 cell ALS xz-rule: r7c46-7-r89c7|r7c9 => r7c8<>3
3-element Grouped Nice Loop: r6c6=4=r6c2-4-ALS:r12389c2-6-r5c2=6=r5c456~6~r6c6 => r6c6<>6
+--------------------+-----------------------+------------------+
|    9   457*b   47  |   268     1       26  |   28    57    3  |
| 2368   368*b   25  |     4   238        7  | 1289    15   29  |
| 2378   378*b    1  |  2389     5      239  |    6    47  247  |
+--------------------+-----------------------+------------------+
|  167      2     3  |  5678   678       15  |    4     9   56  |
|    5   4679*  479  | 2679*c 267*c   2469*c |   13    13    8  |
|   16   1469*    8  |  3569    36  13459-6* |    7     2   56  |
+--------------------+-----------------------+------------------+
| 1378  13789     6  |   237     4       23  |    5    78  279  |
|  237    35*b 2579  |     1  2367        8  |  239   467  249  |
|    4   378*b   27  | 23567     9     2356  |   23  3678    1  |
+--------------------+-----------------------+------------------+
Common 3-element Grouped Nice Loop: r9c7-2-ALS:r159c3-9-ALS:r89c3|r8c12~3~ => r9c2<>3,r8c7<>3
+---------------------+---------------------+------------------+
|    9    457    47*b |   268     1     26  |   28    57    3  |
| 2368    368     25  |     4   238      7  | 1289    15   29  |
| 2378    378      1  |  2389     5    239  |    6    47  247  |
+---------------------+---------------------+------------------+
|  167      2      3  |  5678   678     15  |    4     9   56  |
|    5   4679   479*b |  2679   267   2469  |   13    13    8  |
|   16   1469      8  |  3569    36  13459  |    7     2   56  |
+---------------------+---------------------+------------------+
| 1378  13789      6  |   237     4     23  |    5    78  279  |
| 237*c   35*c 2579*c |     1  2367      8  | 29-3   467  249  |
|    4   78-3   27*bc | 23567     9   2356  |   23* 3678    1  |
+---------------------+---------------------+------------------+
Locked Row Line/Box: r9c78 => r9c46<>3
UR+2D/1SL (7,8): r79c28 => r7c2<>8
UR+2D/1SL (2,9): r28c79 => r8c9<>9
4-element Strong Nice Loop: r7c2=1=r6c2-1-r6c1-6-r6c5-3-r8c5=3=r7c46~3~r7c2 => r7c2<>3
3-element Grouped Nice Loop: ALS:r1c23-5-ALS:r89c2|r9c3|r78c1-1-ALS:r46c1~7~ => r3c1<>7
+--------------------+--------------------+------------------+
|     9   457*   47* |  268     1     26  |   28    57    3  |
|  2368   368    25  |    4   238      7  | 1289    15   29  |
| 238-7   378     1  | 2389     5    239  |    6    47  247  |
+--------------------+--------------------+------------------+
|  167*c    2     3  | 5678   678     15  |    4     9   56  |
|     5  4679   479  | 2679   267   2469  |   13    13    8  |
|   16*c 1469     8  | 3569    36  13459  |    7     2   56  |
+--------------------+--------------------+------------------+
| 1378*b  179     6  |  237     4     23  |    5    78  279  |
|  237*b  35*b 2579  |    1  2367      8  |   29   467   24  |
|     4   78*b  27*b | 2567     9    256  |   23  3678    1  |
+--------------------+--------------------+------------------+
Overlap 3-element Grouped Nice Loop: ALS:r7c1468-1-ALS:r46c1|r5c23-4-ALS:r1357c6~2~ => r9c6<>2
+--------------------+--------------------+------------------+
|    9    457    47  |  268     1    26*c |   28    57    3  |
| 2368    368    25  |    4   238      7  | 1289    15   29  |
|  238    378     1  | 2389     5   239*c |    6    47  247  |
+--------------------+--------------------+------------------+
| 167*b     2     3  | 5678   678     15  |    4     9   56  |
|    5  4679*b 479*b | 2679   267  2469*c |   13    13    8  |
|  16*b  1469     8  | 3569    36  13459  |    7     2   56  |
+--------------------+--------------------+------------------+
| 1378*   179     6  |  237*    4    23*c |    5    78* 279  |
|  237     35  2579  |    1  2367      8  |   29   467   24  |
|    4     78    27  | 2567     9   56-2  |   23  3678    1  |
+--------------------+--------------------+------------------+
3-element Grouped Nice Loop: ALS:r78c1|r9c23-1-ALS:r6c15-3-r2c5=3=r2c12~3~ => r3c1<>3
+--------------------+--------------------+------------------+
|     9   457    47  |  268     1     26  |   28    57    3  |
| 2368*c 368*c   25  |    4   238*     7  | 1289    15   29  |
|  28-3   378     1  | 2389     5    239  |    6    47  247  |
+--------------------+--------------------+------------------+
|   167     2     3  | 5678   678     15  |    4     9   56  |
|     5  4679   479  | 2679   267   2469  |   13    13    8  |
|   16*b 1469     8  | 3569   36*b 13459  |    7     2   56  |
+--------------------+--------------------+------------------+
|  1378*  179     6  |  237     4     23  |    5    78  279  |
|   237*   35  2579  |    1  2367      8  |   29   467   24  |
|     4    78*   27* | 2567     9     56  |   23  3678    1  |
+--------------------+--------------------+------------------+
Overlap 4-element Grouped Nice Loop: r2c9-9-ALS:r7c14689-1-ALS:r6c15-3-ALS:r2c35789~2~ => r2c1<>2
+--------------------+--------------------+--------------------+
|     9   457    47  |  268     1     26  |    28    57     3  |
| 368-2   368   25*d |    4  238*d     7  | 1289*d  15*d  29*d |
|    28   378     1  | 2389     5    239  |     6    47   247  |
+--------------------+--------------------+--------------------+
|   167     2     3  | 5678   678     15  |     4     9    56  |
|     5  4679   479  | 2679   267   2469  |    13    13     8  |
|   16*c 1469     8  | 3569   36*c 13459  |     7     2    56  |
+--------------------+--------------------+--------------------+
| 1378*b  179     6  | 237*b    4    23*b |     5   78*b 279*b |
|   237    35  2579  |    1  2367      8  |    29   467    24  |
|     4    78    27  | 2567     9     56  |    23  3678     1  |
+--------------------+--------------------+--------------------+
Mutant Swordfish (r19c1/c7b27, fins=r9c4|r3c1): r1c467|r9c347|r38c1 => r3c4<>2
+-------------------+---------------------+------------------+
|    9   457    47  |   268*    1     26* |   28*   57    3  |
|  368   368    25  |     4   238      7  | 1289    15   29  |
|   28#  378     1  | 389-2     5    239  |    6    47  247  |
+-------------------+---------------------+------------------+
|  167     2     3  |  5678   678     15  |    4     9   56  |
|    5  4679   479  |  2679   267   2469  |   13    13    8  |
|   16  1469     8  |  3569    36  13459  |    7     2   56  |
+-------------------+---------------------+------------------+
| 1378   179     6  |   237     4     23  |    5    78  279  |
|  237*   35  2579  |     1  2367      8  |   29   467   24  |
|    4    78    27* |  2567#    9     56  |   23* 3678    1  |
+-------------------+---------------------+------------------+
5-element Grouped Advanced Colouring: r3c1=2=r2c3=5=r2c8=1=r2c7=8=r1c7=2=r1c46~2~ => r3c6<>2
4-element Grouped Nice Loop: r6c5-6-r5c456=6=r5c2-6-ALS:r12389c2-4-r6c2=4=r6c6~3~r6c5 => r6c6<>3
+-------------------+----------------------+------------------+
|    9  457*c   47  |   268     1      26  |   28    57    3  |
|  368  368*c   25  |     4   238       7  | 1289    15   29  |
|   28  378*c    1  |   389     5      39  |    6    47  247  |
+-------------------+----------------------+------------------+
|  167     2     3  |  5678   678      15  |    4     9   56  |
|    5  4679*  479  | 2679*b 267*b  2469*b |   13    13    8  |
|   16  1469*    8  |  3569    36* 1459-3* |    7     2   56  |
+-------------------+----------------------+------------------+
| 1378   179     6  |   237     4      23  |    5    78  279  |
|  237   35*c 2579  |     1  2367       8  |   29   467   24  |
|    4   78*c   27  |  2567     9      56  |   23  3678    1  |
+-------------------+----------------------+------------------+
4-element Grouped Nice Loop: ALS:r39c2-3-r2c12=3=r2c5-3-r6c5-6-ALS:r5c3456~7~ => r5c2<>7
+--------------------+---------------------+------------------+
|    9    457    47  |   268     1     26  |   28    57    3  |
| 368*b  368*b   25  |     4   238*     7  | 1289    15   29  |
|   28    378*    1  |   389     5     39  |    6    47  247  |
+--------------------+---------------------+------------------+
|  167      2     3  |  5678   678     15  |    4     9   56  |
|    5  469-7  479*c | 2679*c 267*c 2469*c |   13    13    8  |
|   16   1469     8  |  3569    36*  1459  |    7     2   56  |
+--------------------+---------------------+------------------+
| 1378    179     6  |   237     4     23  |    5    78  279  |
|  237     35  2579  |     1  2367      8  |   29   467   24  |
|    4     78*   27  |  2567     9     56  |   23  3678    1  |
+--------------------+---------------------+------------------+
4-element Grouped Nice Loop: ALS:r39c2-3-r2c12=3=r2c5-3-ALS:r6c15-1-ALS:r7c1468~7~ => r7c2<>7
+--------------------+-------------------+------------------+
|     9   457    47  |  268     1    26  |   28    57    3  |
|  368*b 368*b   25  |    4   238*    7  | 1289    15   29  |
|    28   378*    1  |  389     5    39  |    6    47  247  |
+--------------------+-------------------+------------------+
|   167     2     3  | 5678   678    15  |    4     9   56  |
|     5   469   479  | 2679   267  2469  |   13    13    8  |
|   16*c 1469     8  | 3569   36*c 1459  |    7     2   56  |
+--------------------+-------------------+------------------+
| 1378*d 19-7     6  | 237*d    4   23*d |    5   78*d 279  |
|   237    35  2579  |    1  2367     8  |   29   467   24  |
|     4    78*   27  | 2567     9    56  |   23  3678    1  |
+--------------------+-------------------+------------------+
4-element Grouped Nice Loop: ALS:r2c35789-3-r6c5-6-r5c456=6=r5c2-6-ALS:r34678c1~8~ => r2c1<>8
+--------------------+---------------------+------------------+
|     9   457    47  |   268     1     26  |   28    57    3  |
|  36-8   368    25* |     4   238*     7  | 1289*   15*  29* |
|   28*c  378     1  |   389     5     39  |    6    47  247  |
+--------------------+---------------------+------------------+
|  167*c    2     3  |  5678   678     15  |    4     9   56  |
|     5   469*  479  | 2679*b 267*b 2469*b |   13    13    8  |
|   16*c 1469     8  |  3569    36*  1459  |    7     2   56  |
+--------------------+---------------------+------------------+
| 1378*c   19     6  |   237     4     23  |    5    78  279  |
|  237*c   35  2579  |     1  2367      8  |   29   467   24  |
|     4    78    27  |  2567     9     56  |   23  3678    1  |
+--------------------+---------------------+------------------+
3-element Advanced Colouring: r7c9=7=r3c9=2=r3c1=8=r7c1~7~r7c9 => r7c1<>7
Column Finned X-Wing: r48c1|r458c5 => r4c4<>7
3-element Nice Loop: r8c1=2=r3c1=8=r7c1-8-r9c2~7~r8c1 => r8c1<>7
UR+2B/1SL (5,6): r46c49 => r6c4<>6
3-element Nice Loop: r6c2=1=r7c2=9=r8c3-9-r5c3~4~r6c2 => r6c2<>4
WXYZ-wing: r2c12|r3c2, r9c2 => r1c2<>7
Column Finned X-Wing: r39c2|r37c9 => r9c8<>7
4-node XY-ring (r1c3-4-r1c2-5-r2c3-2-r9c3-7-r1c3) => r8c3<>2,r8c3<>7
Locked Row Line/Box: r9c23 => r9c4<>7
Hidden Row Pair: r8c58 => r8c5=67,r8c8=67
Locked Row Line/Box: r7c46 => r7c1<>3
Row Finned X-Wing: r3c19|r8c17 => r7c9<>2
Locked Column Line/Box: r89c7 => r12c7<>2
Locked Row Box/Box: r2c39|r3c19 => r2c5<>2
Last edited by Mike Barker on Sat Jan 26, 2008 1:01 pm, edited 2 times in total.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby StrmCkr » Thu Sep 14, 2006 5:54 am

removed.
Last edited by StrmCkr on Tue May 01, 2018 6:09 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 842
Joined: 05 September 2006

Postby udosuk » Thu Sep 14, 2006 6:52 am

Code: Select all
.1.|...|.5.
7.8|...|...
..2|6.8|3..
---+---+---
9..|3.5|A.7
...|...|...
8..|4.2|..6
---+---+---
..9|7.1|2..
..3|...|4..
.8.|...|.9.

Okay, let's follow your logic for once...

Consider cell A (r4c7).

A=(45)-(2+3+4+5+6+7+9)=9
=1+8|2+7|3+6|4+5|1+2+6|1+3+5|2+3+4
Only 1+8|1+2+6|1+3+5 contain "unseen" candidates by A

1+8 are both "unseen" by A, therefore 8 must be broken up to other numbers:
8=1+7|2+6|3+5|1+2+5|1+3+4
Only 1+7|1+2+5|1+3+4 contain "unseen" candidates by A

But A couldn't be 1+(1+7)|1+(1+2+5)|1+(1+3+4) (duplication of 1)

So A must be 1!

But we know from the final solution, r4c7=8. Therefore your logic has given us a wrong conclusion.
Therefore your logic is flawed.
Case closed.
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby StrmCkr » Thu Sep 14, 2006 8:24 am

removed.
Last edited by StrmCkr on Tue May 01, 2018 6:09 am, edited 2 times in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 842
Joined: 05 September 2006

Postby udosuk » Thu Sep 14, 2006 8:35 am

Here is what you wrote above:
StrmCkr wrote:A4 = (45) - (8+7+6+5+4+3+1)
A4 = (11)

11 | (9+2), (8+3), (8+2+1), (7+4), (7+3+1), (6+5), (6+4+1), (6+3+2), (5+4+2), (5+3+2+1)

remove known numbers

11| (9+2), (5+4+2), (5+3+2+1)
check logic on (paired unknowns)
(9+2)
9 = (8+1), (7+2), (6+3), (5+4),(5+3+1) (remove the known number solutions
9 = (7+2) is the only known number in possible summations is the 2 we can apply logic to this
since in the original equation 2 was not seen by the cell A4, 9 was not directly revealed. thus eliminated the 9 as the solution.

there fore the only valid solution is A4(2)

From that example, 2 was the number with no "break downs", and you decided to keep it and eliminate 9. Here you decide to keep 8 and eliminate 1... So in fact there is no logic... Just whatever you like...

I saw and still see all these stuffs as a hoax... Inconsistent "logic" really throws me off...:(
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby StrmCkr » Thu Sep 14, 2006 8:51 am

removed
Last edited by StrmCkr on Tue May 01, 2018 6:09 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 842
Joined: 05 September 2006

Postby Myth Jellies » Thu Sep 14, 2006 3:30 pm

Dang, Mike, what techniques don't you have in that thing? (I don't want to waste my time looking for something the computer has already scoured.:) )

Just to make sure I understand these "Almost Swordfish" steps.

Is it true that...

The rule is that a potential swordfish and the group of candidates that could break it up in one dimension (rows, columns) are strongly linked (one or the other must be true)...

...and, the potential swordfish and any candidates that it would eliminate are weakly linked (one or the other must be false).


Of course this rule applies to all seafood...the swordfish in the rule is just a generic NxN swordfish.

Taking your example from puzzle 23...

Code: Select all
 *-----------------------------------------------------------------------------*
 | 5       3479    479     | 8       679     2       | 1       346     3469    |
 |X379    X6       2       | 1       4      x379     | 39      5      X8       |
 | 1       3489    489     | 56      569     359     | 3469    7       2       |
 |-------------------------+-------------------------+-------------------------|
 | 348     2348    5       | 9       1       6       | 7       234     34      |
 | 3467    23479   4679    | 257     8      A57      | 234569  1       34569   |
 |X679    X279     1       | 3      x257     4       | 8       26     X569     |
 |-------------------------+-------------------------+-------------------------|
 | 2       5       46789   | 67      679     789     | 346     3468    1       |
 | 4678    1       4678    | 2567    3       578     |D2456    9      B467     |
 |X679    X789     3       | 4       2569    1       |D256     268   CX567     |
 *-----------------------------------------------------------------------------*

Your chain is:
Almost Row Swordfish (r2c6|r6c5-7-r5c6-5-, r9c9-7-r9c9=5=r56c9): r2c16|r6c125|r9c129 => r5c7<>5
which, if I wanted to make an AIC would be
5[A]=7[A]-7[x]=7swordfish[X]-7[B]=7[C]-5[C]=5[D] => r5c6 <> 5

Just trying to clarify this, because the concept is fairly new, especially to the other sites.
Myth Jellies
 
Posts: 593
Joined: 19 September 2005

Postby Mike Barker » Thu Sep 14, 2006 7:39 pm

I've no experience with AIC's however I think it should look something like
5[A]=7[A]-7[x]=7swordfish[X]-7[B]-5[B]=5[C]-5[A] => r5c7 <> 5
Code: Select all
Almost Row Swordfish (r2c6|r6c5-7-r5c6-5-, r9c9-7-r9c9=5=r56c9): r2c16|r6c125|r9c129 => r5c7<>5
+---------------------+------------------+----------------------+
|     5   3479    479 |     8   679    2 |       1   346   3469 |
|  X379      6      2 |     1     4 x379 |      39     5      8 |
|     1   3489    489 |    56   569  359 |    3469     7      2 |
+---------------------+------------------+----------------------+
|   348   2348      5 |     9     1    6 |       7   234     34 |
|  3467  23479   4679 |   257     8  A57 | -234569     1 C34569 |
|  X679   X279      1 |     3  x257    4 |       8    26   C569 |
+---------------------+------------------+----------------------+
|     2      5  46789 |    67   679  789 |     346  3468      1 |
|  4678      1   4678 |  2567     3  578 |    2456     9    467 |
|  X679   X789      3 |     4  2569    1 |     256   268   B567 |
+---------------------+------------------+----------------------+

As you can tell by my nomenclature I tend to think of the links as radiating out from the fish in a nice loop fashion and the elimination based on a discontinuous nice loop. There can actually be more than two of these radiating links and the links can be chains. Because my solver currently limits these links to a single ALS or GSL (grouped strong link), I haven't worried about continuous nice loop possibilities. The write up for all this is here. This technique should not be a surprise to the UK crowd since I first saw it over there in Anne's post for Ruud's #5000, though its been extended to include GSL.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby StrmCkr » Thu Sep 14, 2006 8:19 pm

removed
Last edited by StrmCkr on Tue May 01, 2018 6:10 am, edited 1 time in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 842
Joined: 05 September 2006

Postby AndrewStuart » Sat Sep 16, 2006 12:01 pm

Contratulations Mike, I didn't think these would be felled so quickly. My hit rate for the 1465 is 850, so well done on both counts. I'll have to digest your solutions before putting up the credit but first pass I can see some very nice extended strategies. Super stuff.
AndrewStuart
 
Posts: 21
Joined: 28 December 2005

Unsolvable #33

Postby gurth » Mon Sep 18, 2006 8:38 am

u33

PROLOGUE

This is supposed to be the hardest of the Unsolvables, so I am not going to waste time explaining techniques contained in SSTS (the Simple Sudoku Technique Set). When I use a forcing net, starting with a candidate x such as 5e4 and proceeding by SSTS to a contradiction, I am not going to list the SSTS steps, I am merely going to state " ? 5e4, (SSTS), ?? -5e4." Anyone interested in the details of those steps merely has to use SS to trace them.

As usual, I concentrate on developing the technique of Forcing Nets. Here I have one novel technique to offer !


GURTH'S (MULTIPLE) ELIMINATION TECHNIQUE

When "bifurcating" to start a Forcing Net, it is customary to *place* a candidate in some cell and then prove a contradiction, thus allowing elimination of the placed candidate.

What is *not* customarily done (nor ever, as far as I have seen!) is to *eliminate* a candidate in some cell and then prove a contradiction, thus allowing *placement* of the eliminated candidate !!!

Why is it not customarily done? For no good reason. Simply because nobody has thought of doing it.

I have already described this idea at [url]http://forum.enjoysudoku.com/viewtopic.php?t=4830[\url]. This is Gurth's Elimination Technique. (GET).

Furthermore, one can go further : instead of trying a single elimination in a cell, one can try either :

(1) A multiple elimination of candidates in one cell. (A good reason for this would be to create a locked set.)

(2) A multiple elimination of candidates x in a row, column or box.

In both cases (1) and (2), proving a contradiction will allow elimination of the non-eliminated candidates !!! This is Gurth's Multiple Elimination Technique. (GMET).


SOLUTION OF U33

(1) (AIC: 7h2=k3 - k7=h8 - c8=a7 - a6=e6) -7e2.

(2) ? -9c2, (SSTS) ?? 9c2. (An example of GET).

(3) ? 9a5, (SSTS) ?? -9a5.

(4) ? 9b5, (SSTS) ?? -9b5.

(5) ? 3a5, (SSTS) ?? -3a5.

(6) ? 3a6 (==3b2==3e1), (SSTS) ?? -3a6, -3b2, -3e1, 3a1.

(7) ? 3e9, (SSTS) ?? -3e9, (SSTS) -3h8.

(8) ? 7a5, (SSTS), ( ? 5e7, (SSTS) ?? -5e7), (SSTS) ?? -7a5.
This is a net within a net. I could maybe get rid of this, but I don't see any reason to : this is a solution for advanced players, and I like this example of *real* bifurcation instead of misnamed bifurcation.

(9) ? 2e1, (SSTS), ?? -2e1, -2h2.

(10) ? 8h9, (SSTS) ?? -8h9, (SSTS) -5h1.

(11) ? 8e9, (SSTS) ?? -8e9.

(12) ? 8h8, (SSTS) ?? -8h8, -8f5.

(13) ? 8e7, (SSTS) ?? -8e7.

(14) ? -12k1, (SSTS) ?? 12k1. (-456k1 !!!) (GMET).

(15) ? 1e9, (SSTS) ?? -1e9.

(16) ? 1e7, (SSTS) ?? -1e7.

(17) ? 1f8, (SSTS) ?? -1f8, 3f8, 3e2, 2d2.

(18) ? 3g9, (SSTS) ?? -3g9, 3k9, 3g5, 3b6, -4k3.

(19) ? 7a6, (SSTS) ?? -7a6. It's all singles after that.
gurth
 
Posts: 358
Joined: 11 February 2006
Location: Cape Town, South Africa

Solutions to Unsolvables #26, #25, #24.

Postby gurth » Thu Sep 21, 2006 9:43 am

Unsolvable #26 solved by Forcing Nets

(1) SSTS.

(2) ? 9e6, SSTS, ?? -9e6, 9k6.

(3) ? 7e5, SSTS, ?? -7e5, 9e5, SSTS.

(4) ? 1c2, SSTS, ?? -1c2, SSTS.

(5) ? 5e4, SSTS, ?? -5e4, 7e4, SSTS.



Unsolvable #25 solved by Forcing Nets

(1) SSTS.

(2) ? 1f3, SSTS, ?? -1f3, SSTS.

(3) ? 1f9, SSTS, ?? -1f9.

(4) ? 1f8, SSTS, ?? -1f8, 1d9, SSTS.

(5) ? 2g9, SSTS, ?? -2g9, 6g9, all naked singles after that.


Unsolvable #24 : Letting it all hang out.

As I always maintain that the main interest is not the solution but How the solution came about, hiding nothing, I have decided to show all incorrect and unnecessary tries made, just as they happened.

(1) SSTS. (2) ? 3c3, SSTS, ?? -3c3, 3b3, SSTS

(3) ? 3f2 led nowhere. ?9f8, SSTS, ?? -9f8, 5f8.

(4) ? 5h2, SSTS, ?? -5h2, SSTS.

(5) ? 5c3 led nowhere. ? 9f1, SSTS, -9f1.

(6) ? 4f6, rapid SSTS, ?? -4f6.

(7) ? 4a6, SSTS, ?? -4a6.

(8) ? 4c6, SSTS, ?? -4c6, 4k6.

(9) ? 1d5, SSTS, ?? -1d5.

(10) ? 1d4 led nowhere. ? 1h5, SSTS, ?? -1h5, SSTS.

(11) ? -1e5, SSTS, ?? 1e5, SSTS.

(12) ? 2c1, SSTS, ?? -2c1, SSTS to end.
gurth
 
Posts: 358
Joined: 11 February 2006
Location: Cape Town, South Africa

Re: Challenge: New set of 11 'Unsolvables'

Postby ravel » Thu Sep 21, 2006 9:55 am

AndrewStuart wrote:A new set of eleven Michael Mepham 'unsolvable' sudokus has been released on http://www.sudoku.org.uk/bifurcation.htm.

Whats wrong here? I can only see 22 puzzles on this page.
ravel
 
Posts: 998
Joined: 21 February 2006

Postby StrmCkr » Thu Sep 21, 2006 10:08 am

they where published on a sub link... i dont see it either... werid..
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 842
Joined: 05 September 2006

PreviousNext

Return to Advanced solving techniques