The New Sudoku Players' Forum

[blue]

There are "four in one" puzzles, like this ...

Code: Select all

+------------------+------------------+--------------+
| 1     4     3579 | 3579  6     2    | 8    379  57 |
| 2     3579  6    | 8     3579  3579 | 359  4    1  |
| 3579  3579  8    | 4     1     3579 | 6    379  2  |
+------------------+------------------+--------------+
| 3579  8     4    | 3579  3579  6    | 2    1    57 |
| 6     3579  2    | 1     3579  8    | 359  379  4  |
| 3579  1     3579 | 2     4     3579 | 359  6    8  |
+------------------+------------------+--------------+
| 8     579   579  | 6     579   4    | 1    2    3  |
| 379   2     1    | 379   8     379  | 4    5    6  |
| 4     6     35   | 35    2     1    | 7    8    9  |
+------------------+------------------+--------------+

14..628..2.68...41..841.6.2.84..621.6.21.8..4.1.24..688..6.4123.21.8.45646..21789

[champagne]

Hi blue
14..628..2.68...41..841.6.2.84..621.6.21.8..4.1.24..688..6.4123.21.8.45646..21789

amazing skfr rating 9.2 !!!!!

My draft of code sees 2 possible TH, but this is a wonderful example to work on.

I was expecting a "best case" with all bands and stacks morphs of the band index 0, here we have six different indexes

106 147 17 105 259 220

[ghfick]

The puzzle of jovi has an interesting advance. After the TH, one gets r1c1=6. Then, YZF_Sudoku reveals two different impossible patterns:

Impossible Pattern(789{r2c358,r3c239,r7c157,r8c28,r9c39,r1c7})
Impossible Pattern(789{r3c239,r5c127,r7c17,r8c28,r9c39,r1c7,r2c8})

both with a single guardian and each with several exclusions.

[champagne]

The puzzle of jovi has an interesting advance. After the TH, one gets r1c1=6. Then, YZF_Sudoku reveals two different impossible patterns:

Impossible Pattern(789{r2c358,r3c239,r7c157,r8c28,r9c39,r1c7})
Impossible Pattern(789{r3c239,r5c127,r7c17,r8c28,r9c39,r1c7,r2c8})

both with a single guardian and each with several exclusions.

Hi gordon,
Could you remind us the puzzle you are working on.??

[ghfick]

Can do:

Code: Select all

+-------+-------+-------+
| . 1 2 | . . . | . 3 4 |
| 3 5 . | . . . | 6 . 2 |
| 4 . . | . . . | 1 5 . |
+-------+-------+-------+
| . . . | . 1 7 | . . . |
| . . . | 5 . 2 | . . . |
| . . . | 8 6 . | . . . |
+-------+-------+-------+
| . 4 3 | . . . | . 2 5 |
| 1 . 5 | . . . | 3 . 6 |
| 2 6 . | . . . | 4 1 . |
+-------+-------+-------+
.12....3435....6.24.....15.....17......5.2......86.....43....251.5...3.626....41.


marek stefanik posted the puzzle with a post TH path based on remote triples. I think the Impossible Patterns are using the same principles as the RTs but perhaps the IPs are more like the TH.

[ghfick]

Here is the first part of the path [edited]:

Hidden Pair: 16 in r7c4,r7c6 => r7c4<>79,r7c6<>89
Hidden Pair: 25 in r4c7,r6c7 => r4c7<>89,r6c7<>79
Triplet Oddagon Type 1: 789r17c17,r2c38,r3c29,r8c28,r9c39 => r1c1<>789
Naked Single: r1c1=6
Naked Triple: in r2c3,r3c3,r9c3 => r4c3<>89,r5c3<>789,r6c3<>79,
Naked Triple: in r3c2,r3c3,r3c9 => r3c4<>79,r3c5<>789,r3c6<>89,
ImpossiblePattern(789{r2c358,r3c239,r7c157,r8c28,r9c39,r1c7})r2c46,r58c5<>4,r2c5<>7,r2c5<>8,r2c5<>9
ImpossiblePattern(789{r3c239,r5c127,r7c17,r8c28,r9c39,r1c7,r2c8})r5c5<>3,r5c12789,r1789c5,r4c4,r6c6<>9

[eleven]

I think the Impossible Patterns are using the same principles as the RTs but perhaps the IPs are more like the TH.

As shye showed recently, if you have (easily) proved RT's, this also proves TH. Same works for other IP's.
And for manual solvers they often can be a quicker way for getting eliminations than to search for usefull IP's (see Marek's solution).

[ghfick]

I decided to try to create a puzzle with 2TH. I chose block 5 to be common to both patterns. I placed one of two TH in blocks 5, 6, 8 and 9 with givens to set it up and the second TH in blocks 1, 2, 4 and 5 without any additional givens set up. Each TH will have one guardian and that guardian will be the same digit for both. As a start, I have:

Code: Select all

+--------------------------------+--------------+--------------------+
| 123       123456789 123456789  | 123 59  46   | 12389 12356 12347  |
| 123456789 1234      123456789  | 78  123 46   | 12389 12356 12347  |
| 123456789 123456789 123        | 78  59  123  | 12389 12356 12347  |
+--------------------------------+--------------+--------------------+
| 123       49        49         | 5   6   123  | 123   7     8      |
| 78        123       78         | 4   123 9    | 5     123   6      |
| 56        56        123        | 123 8   7    | 4     9     123    |
+--------------------------------+--------------+--------------------+
| 123468    123468    123468     | 123 7   5    | 123   1234  9      |
| 12349     12349     12349      | 6   123 8    | 7     1234  5      |
| 12357     12357     12357      | 9   4   123  | 6     8     123    |
+--------------------------------+--------------+--------------------+


Then, I explored how the remaining candidates have exclusions:

Code: Select all

+--------------------+--------------+--------------------+
| 123    5678 56789  | 123 59  46   | 12389 12356 12347  |
| 56789  1234 56789  | 78  123 46   | 12389 12356 12347  |
| 56789  1234 123    | 78  59  123  | 12389 12356 12347  |
+--------------------+--------------+--------------------+
| 123    9    4      | 5   6   123  | 123   7     8      |
| 78     123  78     | 4   123 9    | 5     123   6      |
| 56     56   123    | 123 8   7    | 4     9     123    |
+--------------------+--------------+--------------------+
| 123468 68   12368  | 123 7   5    | 123   1234  9      |
| 12349  123  1239   | 6   123 8    | 7     1234  5      |
| 12357  57   12357  | 9   4   123  | 6     8     123    |
+--------------------+--------------+--------------------+


Then I set the 2 direct implications from the two TH and explored how these settings resulted in further exclusions and placements:

Code: Select all

 123     68      678    | 123    9      4      | 1238   5      1237   
 579     4       59     | 78     123    6      | 12389  123    1237   
 789     123     123    | 78     5      123    | 89     6      4     
------------------------+----------------------+---------------------
 123     9       4      | 5      6      123    | 123    7      8     
 78      123     78     | 4      123    9      | 5      123    6     
 6       5       123    | 123    8      7      | 4      9      123   
------------------------+----------------------+---------------------
 4       68      68     | 123    7      5      | 123    123    9     
 1239    123     1239   | 6      123    8      | 7      4      5     
 1235    7       1235   | 9      4      123    | 6      8      123


I cannot take the puzzle any further. This puzzle still has more than 300 solutions. I think, then, that the initial set up has at least possible puzzles (each with a unique solution).
I am unsure how to take this example further.

[champagne]

Hi ghfick,

This is more in the skills of "marek stefanik".
I'll look at you example when I have time, but one remark that can help:

When you have the "main TH" say in boxes 4589 in your case, then 2 of the 3 digits are assigned in box '1'
This is for the classical tridagon, but anyway, you can't have more than one unassigned digit

[coloin]

.....I cannot take the puzzle any further....

Adding 2 clues - gives 15 puzzles
removing superfluos clues gives 48013 minimal puzzles
expanding with gsf -E gives 120 non-minimal puzzles
36 of these are sfkr 9.0
the best one was

Code: Select all

.63.94.5.5418.69.7....5..64.9.5...78...4.95..6...8749.....75..9...6.874..7.94..8. ED=9.0/9.0/8.3 

[ghfick]

A solution path for coloin's puzzle could begin with 2 TH patterns:

Code: Select all

,-------------------,-------------------,------------------,
| 278    6     3    | b127   9     4   | 128   5    b12    |
| 5      4     1    | 8     b23    6   | 9     b23   7     |
| 2789   28    2789 | 1237  5     b123 | b1238  6    4     |
:-------------------+-------------------+------------------:
| 1234   9     24   | 5     1236  a123 | a1236  7    8     |
| 12378  1238  278  | 4     a1236  9   | 5     a123  1236  |
| 6      1235  25   | a123   8     7   | 4     9    a123   |
:-------------------+-------------------+------------------:
| 12348  1238  2468 | c123   7     5   | 1236  c123  9     |
| 1239   1235  259  | 6     c123   8   | 7     4    c1235  |
| 123    7     256  | 9     4     c123 | c1236  8    12356 |
'-------------------'-------------------'------------------'


Both TH (ac bc) have 4 guardians and the TH share blocks 8 and 9