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Missing next step on this truly diabolical puzzle

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Missing next step on this truly diabolical puzzle

Postby McCoach » Sat Feb 04, 2006 5:15 pm

please tell me next clue for this puzzle...
+----------------------+---------------------------+---------------------------+
l-----2------9----1-----l---56----36-----35-------l---47-------47------8-----l
l-----4------3----8-----l----1-----7-------9-------l----2--------5-------6-----l
l----67-----5----67----l----4-----8-------2-------l----3--------9-------1-----l
+-----------------------+---------------------------+---------------------------+
l 15679---46------3---l---8----1249---1457----l--45679---2467---4579--l
l 15679----2----4679-l--57----1349---13457---l--45679----8-----34579-l
l 579-------8-----479-l--257---2349------6-----l-----1------247---34579-l
+-----------------------+----------------------------+---------------------------+
l-----8-----7------2---l---9------146------14-----l--456-------3-----45-----l
l----69-----1----469--l---3-------5-------478----l--4678----467-----2-----l
l-----3-----46-----5---l--267----246-----478----l--46789----1-----479----l
+-----------------------+-----------------------------+--------------------------+
PS: sorry for all the lines. not sure how to format in columns.
[/list]
      McCoach
       
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      Postby CathyW » Sat Feb 04, 2006 6:17 pm

      Your grid:
      Code: Select all
       
       *-----------*
       |291|...|..8|
       |438|179|256|
       |.5.|482|391|
       |---+---+---|
       |..3|8..|...|
       |.2.|...|.8.|
       |.8.|..6|1..|
       |---+---+---|
       |872|9..|.3.|
       |.1.|35.|..2|
       |3.5|...|.1.|
       *-----------*


      {2}     {9}     {1}     {56A}   {36A}   {35}    {47}    {47}    {8}     
      {4}     {3}     {8}     {1}     {7}     {9}     {2}     {5}     {6}     
      {67}    {5}     {67}    {4}     {8}     {2}     {3}     {9}     {1}     
      {15679} {46D}   {3}     {8}     {1249}  {1457}  {45679} {246B7} {4579} 
      {15679} {2}     {4679}  {57}    {1349}  {13457} {45679} {8}     {34579}
      {579}   {8}     {479}   {257}   {2349}  {6}     {1}     {247}   {34579}
      {8}     {7}     {2}     {9}     {146C}  {14}    {456C}  {3}     {45}   
      {69}    {1}     {469}   {3}     {5}     {478}   {46*78} {46B7}  {2}     
      {3}     {46D}   {5}     {26A7}  {246*}  {478}   {46*789}{1}     {479}   


      Colouring conjugate pairs of 6s (marked with A, B and C (and D)) allows some eliminations in r9c5, r9c7 and r8c7 (marked *). Having included the conjugate pair in column 2 as well, you can also eliminate 6 in r4c7 but have left that for now.

      Recolouring conjugate 6s with alternating colours (A, B) means you end up with the following situation:

      Code: Select all
       
      {2}     {9}     {1}     {56A}   {36B}   {35}    {47}    {47}    {8}     
      {4}     {3}     {8}     {1}     {7}     {9}     {2}     {5}     {6}     
      {67}    {5}     {67}    {4}     {8}     {2}     {3}     {9}     {1}     
      {15679} {46B}   {3}     {8}     {1249}  {1457}  {45679} {246B7} {4579} 
      {15679} {2}     {46A79} {57}    {1349}  {13457} {45679} {8}     {34579}
      {579}   {8}     {479}   {257}   {2349}  {6}     {1}     {247}   {34579}
      {8}     {7}     {2}     {9}     {146A}  {14}    {456B}  {3}     {45}   
      {69}    {1}     {46B9}  {3}     {5}     {478}   {478}   {46A7}  {2}     
      {3}     {46A}   {5}     {26B7}  {24}    {478}   {4789}  {1}     {479}   

      Note the two Bs in row 4 which is not possible therefore all cells marked with A must be 6. The rest solves with singles.

      I find colouring can often be a useful technique on harder puzzles. Hope that helps.:)
      Last edited by CathyW on Sat Feb 04, 2006 8:25 pm, edited 1 time in total.
      CathyW
       
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      Postby FRANKH » Sat Feb 04, 2006 8:18 pm

      CathyW

      Why were you able to eliminate the 6 in r9c5?
      FRANKH
       
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      Postby CathyW » Sun Feb 05, 2006 12:27 am

      I thought for a moment it was another one of my "happy coincidences" but I think another conjugate pair - marked D in edited post above - allows the elimination at r9c5.
      CathyW
       
      Posts: 316
      Joined: 20 June 2005
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      Postby tso » Sun Feb 05, 2006 2:22 am

      The situation isn't nearly so complicated:

      Code: Select all
        .    .    .  |  6    6    .  |  .    .    . 
        .    .    .  |  .    .    .  |  .    .    . 
        6    .    6  |  .    .    .  |  .    .    . 
       --------------+---------------+-------------- 
        6   [6]   .  |  .    .    .  |  6   [6]   . 
        6    .    6  |  .    .    .  |  6    .    . 
        .    .    .  |  .    .    .  |  .    .    . 
       --------------+---------------+-------------- 
        .    .    .  |  .    6    .  |  6    .    . 
       x6    .   x6  |  .    .    .  |  6   [6]   . 
        .   [6]   .  |  6    6    .  |  6    .    . 

      Filtering for 6s -- the 4 cells marked with [brackets] exclude 6s r8c1 and r8c3, marked with 'x'. Any value placed in any of the bracketed cells will force force r8c13<>6. (This is also refered to as "turbo fish", "coloring", "mulitple colors" or "advanced coloring", depending on who is speaking.)

      Nothing but singles is required after this.



      Some of the exclusions CathyW suggests are not logically supported.

      Code: Select all
        .    .    .  |  6A   6A   .  |  .    .    . 
        .    .    .  |  .    .    .  |  .    .    . 
        6    .    6  |  .    .    .  |  .    .    . 
       --------------+---------------+-------------- 
        6    6D   .  |  .    .    .  |  6*   6B   . 
        6    .    6  |  .    .    .  |  6    .    . 
        .    .    .  |  .    .    .  |  .    .    . 
       --------------+---------------+-------------- 
        .    .    .  |  .    6C   .  |  6C   .    . 
        6    .    6  |  .    .    .  |  6*   6B   . 
        .    6D   .  |  6A   6*   .  |  6*   .    . 

      If r8c8 =6, then r9c7<>6.
      If r8c8<>6, then r4c8=6, then r4c2<>6, then r9c2=6, then r9c7<>6.
      Therefore, r9c7<>6.

      However, none of the other exclusions follow from this coloring.
      For example,
      If r8c8 =6, then r8c7<>6.
      If r8c8<>6, then r4c8=6, then r4c2<>6, then r9c2=6, then r9c7<>6 ... dead end.
      tso
       
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      Postby tarek » Sun Feb 05, 2006 2:32 am

      tso wrote:(This is also refered to as "turbo fish", "coloring", "mulitple colors" or "advanced coloring", depending on who is speaking.)


      How about "Sashimi" or "Almost finned x-wing":D
      User avatar
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      Postby CathyW » Sun Feb 05, 2006 2:54 pm

      tso wrote:Some of the exclusions CathyW suggests are not logically supported.

      Thanks for pointing this out Tso - after several "happy coincidences" with exclusions from colouring I can see I shall have to study this more to ensure the exclusions are genuinely logical.
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      Re: Missing next step on this truly diabolical puzzle

      Postby QBasicMac » Sun Feb 05, 2006 4:29 pm

      McCoach wrote:Not sure how to format


      Code: Select all
      +-----------------+------------------+--------------------+
      | 2      9   1    | 56   36    35    | 47     47    8     |
      | 4      3   8    | 1    7     9     | 2      5     6     |
      | 67     5   67   | 4    8     2     | 3      9     1     |
      +-----------------+------------------+--------------------+
      | 15679  46  3    | 8    1249  1457  | 45679  2467  4579  |
      | 15679  2   4679 | 57   1349  13457 | 45679  8     34579 |
      | 579    8   479  | 257  2349  6     | 1      247   34579 |
      +-----------------+------------------+--------------------+
      | 8      7   2    | 9    146   14    | 456    3     45    |
      | 69     1   469  | 3    5     478   | 4678   467   2     |
      | 3      46  5    | 267  246   478   | 46789  1     479   |
      +-----------------+------------------+--------------------+


      In other words, format in your editor using fixed-length characters (font=ariel new, etc.). Then post, surrounding your post with [code] and [/code].

      There is a CODE button on the page which on most machines automatically puts those code/code markers in one's post.
      Mac
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