Got just this far...need ideas

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Got just this far...need ideas

Postby Jasper32 » Fri Sep 05, 2008 10:23 am

Code: Select all
 
 *-----------------------------------------------------------------------------*
 | 346     236     2346    | 1       8       9       | 45      47      257     |
 | 149     7       2489    | 45      246     2456    | 49      3       128     |
 | 149     1289    5       | 37      234     247     | 6       149     128     |
 |-------------------------+-------------------------+-------------------------|
 | 8       346     1       | 37      346     467     | 2       5       9       |
 | 2       469     7       | 89      5       46      | 1       68      3       |
 | 5       369     369     | 89      12      12      | 7       68      4       |
 |-------------------------+-------------------------+-------------------------|
 | 134679  12369   23469   | 45      149     15      | 8       1479    167     |
 | 1479    5       49      | 6       149     8       | 3       2       17      |
 | 1469    1689    468     | 2       7       3       | 459     149     156     |
 *-----------------------------------------------------------------------------*


This seems to be a tough puzzle....at least to me.
I got to this point on the puzzle and hit a brick wall. There is an unique rectangle on (8's) at r5c4, r5c8, r6c5 and r6c8 . I don't know if that can be used to crack the puzzle or not. Any help or ideas will be appreciated. I am stuck and without a clue as to where to go from here.

Thanks, Jasper32
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Postby DonM » Fri Sep 05, 2008 12:30 pm

Jasper, that isn't a unique rectangle; a UR requires 4 equal pairs, (above, 2 of the numbers are 8,9, the other 2 are 6,8). In any event, even if all 4 pairs were the same, say 8,9, the validity of the puzzle itself would be called into question because that would comprise the 'deadly pattern' which is impossible in a puzzle with one unique solution (ie. there would need to be at least one other digit, in addition to the pair, in at least one of the 4 cells to make the puzzle valid).
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Postby udosuk » Fri Sep 05, 2008 1:02 pm

This is a very diabolical puzzle... No elegant solution found yet, but you can try the following "forcing net" approach:

Firstly, notice there is a locked candidate for r6,b4 @ r6c23
Therefore r4c2 can't be 3.

Code: Select all
+-------------------------+-------------------------+-------------------------+
| 346     236     2346    | 1       8       9       | 45      47      257     |
| 149     7       2489    | 45      246     2456    | 49      3       128     |
| 149     1289    5       | 37      234     247     | 6       149     128     |
+-------------------------+-------------------------+-------------------------+
| 8       46      1       | 37      346     467     | 2       5       9       |
| 2       469     7       | 89      5       46      | 1       68      3       |
| 5       369     369     | 89      12      12      | 7       68      4       |
+-------------------------+-------------------------+-------------------------+
| 134679  12369   23469   | 45      149     15      | 8       1479    167     |
| 1479    5       49      | 6       149     8       | 3       2       17      |
| 1469    1689    468     | 2       7       3       | 459     149     156     |
+-------------------------+-------------------------+-------------------------+

Forcing net:

r8c9=1 => r2c1=r3c8=1 => r2c7=9, r9c2=1 => r3c2=8 => r3c9=2 => 2 @ r2,b2 locked @ r2c56
=> r2c3<>2 => r2c3=4 => r2c4=5, r8c3=9 => r7c4=4 => no candidate for r8c5 => contradiction

Therefore r8c9 can't be 1, must be 7.

Now we have:

Hidden single @ r7: r7c1=7
Hidden pair @ r7: r7c23={23}
Hidden single @ r7: r7c9=6
Hidden single @ c1: r1c1=3

Code: Select all
+-------------------+-------------------+-------------------+
| 3     26    246   | 1     8     9     | 45    47    25    |
|*149   7     2489  | 45    246   2456  | 49    3    *128   |
| 149  *1289  5     | 37    234   247   | 6     149   128   |
+-------------------+-------------------+-------------------+
| 8     46    1     | 37    346   467   | 2     5     9     |
| 2     469   7     | 89    5     46    | 1     68    3     |
| 5     369   369   | 89    12    12    | 7     68    4     |
+-------------------+-------------------+-------------------+
| 7     23    23    | 45    149   15    | 8     149   6     |
| 149   5     49    | 6     149   8     | 3     2     7     |
| 1469 *1689  468   | 2     7     3     | 459   149  -15    |
+-------------------+-------------------+-------------------+

Turbot fish:
1 @ r2 locked @ r2c19
1 @ c2 locked @ r39c2
Since r2c1 & r3c2 can't both be 1
=> one or both of r2c9+r9c2 must be 1
=> r9c9, seeing r2c9+r9c2, can't be 1, must be 5

All naked singles from here.:idea:
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Postby DonM » Fri Sep 05, 2008 1:44 pm

udosuk wrote:This is a very diabolical puzzle... No elegant solution found yet, but you can try the following "forcing net" approach:

Firstly, notice there is a locked candidate for r6,b4 @ r6c23
Therefore r4c2 can't be 3.



Just for interest sake, if the locked candidate didn't eliminate the 3, the swordfish on 3 at r1c123, r6c23, r7c123 or the x-wing at r3c45, r4c45 would.:)
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Postby ronk » Fri Sep 05, 2008 3:37 pm

Jasper32, as DonM noted r56c48 is not a UR. However, those cells are a "marker" for a BUG-Lite.

Code: Select all
 346    236    2346   | 1      8      9      | 45     47     257
 149    7      2489   | 45     246    2456   | 49     3      128
 149    1289   5      | 37     234    247    | 6      149    128
----------------------+----------------------+-------------------
 8      46     1      | 37     346    467    | 2      5      9
 2     *69+4   7      |*89     5     %46     | 1     *68     3
 5     *69+3   369    |*89     12     12     | 7     *68     4
----------------------+----------------------+-------------------
 134679 12369  23469  | 45     149    15     | 8      1479   167
 1479   5      49     | 6      149    8      | 3      2      17
 1469   1689   468    | 2      7      3      | 459    149    156

To avoid multiple solutions, at least one of r5c2=4 and r6c2=3 must ultimately be true. Combined with three bivalued cells, there exists a nice loop for r6c2<>6. This deduction seems to lead nowhere, but it does salvage something from your observation.:)

r6c2 -6- r6c8 -8- r5c8 -6- r5c6 -4- BUG-Lite(689)r56c248:(r5c2 =4|3= r6c2) ==> r6c2<>6
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Postby udosuk » Fri Sep 05, 2008 10:22 pm

There does exist a UR (type-?) in the puzzle:
Code: Select all
+-------------------------+-------------------------+-------------------------+
| 346     236     2346    | 1       8       9       | 45      47      257     |
| 149     7       2489    | 45      246     2456    | 49      3       128     |
| 149     1289    5       | 37      234     247     | 6       149     128     |
+-------------------------+-------------------------+-------------------------+
| 8      *46      1       | 37      346    -467     | 2       5       9       |
| 2      *469     7       | 89      5      *46      | 1       68      3       |
| 5       369     369     | 89      12      12      | 7       68      4       |
+-------------------------+-------------------------+-------------------------+
| 134679  12369   23469   | 45      149     15      | 8       1479    167     |
| 1479    5       49      | 6       149     8       | 3       2       17      |
| 1469    1689    468     | 2       7       3       | 459     149     156     |
+-------------------------+-------------------------+-------------------------+

r45c26 can't form the deadly pattern {46}
There is a strong link of 4 @ r45c2
=> r4c6 can't be 4

Not that it is much useful for the solving either.
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Postby daj95376 » Sat Sep 06, 2008 12:58 pm

An alternate solution. Nothing outstanding. Some steps could probably be skipped.

Code: Select all
 r4  b5  Locked Candidate 1              <> 3    [r4c2]

 finned Franken Jellyfish c347b9\r1279   <> 4    [r9c1]

 SIN:  1r7c6  5r2c6  4r2c4  9r2c7  1r2c1  1r9c2  8r3c2  2r2c3  2r1c9  1r3c9  [b9]~1

 r9  b9  Locked Candidate 1              <> 4    [r9c3]

         XYZ-Wing [r7c8]/[r7c5]+[r8c9]   <> 1    [r7c9]

 -1r2c1  1r2c9  8r2c3  6r9c3  6r1c1  3r7c1  7r8c1  1r8c9  [chain] <> 1 [r2c9],[r8c1]

  6r9c3  9r9c1  9r7c8  1r7c5  1r9c2  8r9c3                [chain] <> 6 [r9c3]

 finned Swordfish r378\c157              <> 9    [r9c1]

  9r3c8  9r2c3  2r2c6  2r3c9  1r3c8                       [chain] <> 9 [r3c8]

         XY-Wing  [r1c1]/[r1c8]+[r7c1]   <> 7    [r7c8]
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