The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |5..|...|..2|
 |63.|7..|.4.|
 |..9|...|8..|
 |---+---+---|
 |...|6..|93.|
 |...|.7.|...|
 |.6.|..4|...|
 |---+---+---|
 |..2|...|5..|
 |.4.|..3|.7.|
 |8..|...|..9|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 5      1      4      | 38     368    68     | 7      9      2      |
 | 6      3      8      | 7     d29    c29     | 1      4      5      |
 | 7      2      9      | 145    145  cd15     | 8      6      3      |
 *----------------------+----------------------+----------------------|
 | 4      58     157    | 6      1258   1258   | 9      3      17     |
 | 2     a589    135    | 13589  7     b1589   | 4     a58     6      |
 | 1-9    6      1357   | 13589  13589  4      | 2      58     17     |
 *----------------------+----------------------+----------------------|
 | 3      79     2      | 89     689    6789   | 5      1      4      |
 |f19     4     f15     | 2     e59     3      | 6      7      8      |
 | 8     e57     6      | 145    145  cd157    | 3      2      9      |
 *--------------------------------------------------------------------*


(9=58)r5c28 - (5|8=1|9)r5c6 - (1r39c6)&(9r2c6) = ((57)r39c6)|(9r2c5) - (79=5)r8c5,r9c2 - (5=19)r8c13 => -9 r6c1 ; stte

[Cenoman]

Code: Select all

 +--------------------+-------------------------+-----------------+
 |  5    1     4      | e38      368     68     |  7    9    2    |
 |  6    3     8      |  7       29      29     |  1    4    5    |
 |  7    2     9      |  145     145     15     |  8    6    3    |
 +--------------------+-------------------------+-----------------+
 |  4    58    157*   |  6       1258    1258   |  9    3    17*  |
 |  2    589  c135#   | d13589   7       1589   |  4    58   6    |
 |  19   6     1357*  |  13589   13589   4      |  2    58   17*  |
 +--------------------+-------------------------+-----------------+
 |  3    79    2      | f89      689     6789   |  5    1    4    |
 |  19   4    b15#    |  2      a5-9     3      |  6    7    8    |
 |  8    57    6      |  145     145     157    |  3    2    9    |
 +--------------------+-------------------------+-----------------+

UR(17)r46c39 using externals 1r5c3==1r8c3
(5)r8c5 = (5-1)r8c3==(1-3)r5c3 = r5c4 - (3=8)r1c4 - (8=9)r7c4 => -9 r8c5; ste

[Sudtyro2]

Major kudos for the solutions from Steve and Cenoman! Color me impressed!

SteveC

[SpAce]

Code: Select all

.------------------.---------------------------.-----------.
|  5     1    4    | 38      368       68      | 7  9   2  |
|  6     3    8    | 7      *29       *29      | 1  4   5  |
|  7     2    9    | 145     145       15      | 8  6   3  |
:------------------+---------------------------+-----------:
|  4     58   157% | 6       1258      1258    | 9  3   17%|
|  2    *589 b35€1 |a1358#9  7        *1589    | 4  58  6  |
|c*9€1   6    1357%| 13589   1358(#9)  4       | 2  58  17%|
:------------------+---------------------------+-----------:
|  3     79   2    | 89      68(#9)    678(#9) | 5  1   4  |
|d*1(9)  4    51   | 2      *5-9       3       | 6  7   8  |
|  8     57   6    | 145     145       157     | 3  2   9  |
'------------------'---------------------------'-----------'

7-link Oddagon(*9)+4 #; UR(17%)r46c39 externals €

(9)r6c5,r7c56 == (9-3)r5c4 = (3-1)r5c3 == (1-9)r6c1 = (9)r8c1 => -9 r8c5; stte

[Cenoman]

Major kudos for the solutions from Steve and Cenoman! Color me impressed!

SteveC

Thanks Steve !

A few minutes later, you could have associated SpAce to your congratulation message.
Using the UR inside the oddagon chains is very nice too !

[SpAce]

A few minutes later, you could have associated SpAce to your congratulation message.
Using the UR inside the oddagon chains is very nice too !

Thanks, Cenoman! I appreciate it. My first attempt was effectively a variant of yours, so I had to figure out something different -- and it wasn't easy with this puzzle! Still ended up using the same UR, because the alternative wasn't as pretty:

Code: Select all

.-------------------.----------------------------.-----------.
|  5     1     4    | 38      368        68      | 7  9   2  |
|  6     3     8    | 7      *29        *29      | 1  4   5  |
|  7     2     9    | 145     145       c15      | 8  6   3  |
:-------------------+----------------------------+-----------:
|  4     58    157  | 6       1258       1258    | 9  3   17 |
|  2    *589  b135  |a1358#9  7        b*1589    | 4  58  6  |
| *19    6     1357 | 13589   1358(#9)   4       | 2  58  17 |
:-------------------+----------------------------+-----------:
|  3     79    2    | 89      68(#9)     678(#9) | 5  1   4  |
|d*1(9)  4    d15   | 2      *5-9        3       | 6  7   8  |
|  8    d57    6    | 145     145       c157     | 3  2   9  |
'-------------------'----------------------------'-----------'

7-link Oddagon(*9) + 4 guardians #


(9)r6c5,r7c56 == (9-3|1)r5c4 = (31)r5c36 - (15=7)r39c6 - (715=9)b7p864 => -9 r8c5; stte

[pjb]

Code: Select all

 5       1       4      | 38     368    68     | 7      9      2     
 6       3       8      | 7      29     29     | 1      4      5     
 7       2       9      |*145   *145   *15     | 8      6      3     
------------------------+----------------------+---------------------
 4       58      157    | 6      1258   1258   | 9      3      17     
 2       589     135    | 13589  7      1589   | 4      58     6     
 19      6       1357   | 13589  13589  4      | 2      58     17     
------------------------+----------------------+---------------------
 3       79      2      | 89     689    6789   | 5      1      4     
 19      4       15     | 2      59     3      | 6      7      8     
 8       57      6      |*145   * 145   *7-15   | 3      2      9     


BUG-lite (type 1) of 145 at r39c456 => -15 r9c6; stte

Phil

[SpAce]

BUG-lite (type 1) of 145 at r39c456 => -15 r9c6; stte

Very impressive! Is it actually a MUG, though? I thought BUGs and BUG-lites only dealt with bivalue cells (as the name implies).

[SteveG48]

Code: Select all

 5       1       4      | 38     368    68     | 7      9      2     
 6       3       8      | 7      29     29     | 1      4      5     
 7       2       9      |*145   *145   *15     | 8      6      3     
------------------------+----------------------+---------------------
 4       58      157    | 6      1258   1258   | 9      3      17     
 2       589     135    | 13589  7      1589   | 4      58     6     
 19      6       1357   | 13589  13589  4      | 2      58     17     
------------------------+----------------------+---------------------
 3       79      2      | 89     689    6789   | 5      1      4     
 19      4       15     | 2      59     3      | 6      7      8     
 8       57      6      |*145   * 145   *7-15   | 3      2      9     


BUG-lite (type 1) of 145 at r39c456 => -15 r9c6; stte

Phil

I'm not very good with uniqueness patterns, so I'm having trouble seeing this one.

Suppose, for example, r9c6 is a 5, and r3c6 is a 1. Then r3c45 is a 45 pair, and r9c45 is a 14 pair. Why is that a deadly pattern?

[SpAce]

BUG-lite (type 1) of 145 at r39c456 => -15 r9c6; stte

I'm not very good with uniqueness patterns, so I'm having trouble seeing this one.

Suppose, for example, r9c6 is a 5, and r3c6 is a 1. Then r3c45 is a 45 pair, and r9c45 is a 14 pair. Why is that a deadly pattern?

It's not easy for me to see either. I found this possible explanation, though.

[Sudtyro2]

Hi Steve,
FWIW, here's my entire cheat sheet of MUGS, which includes the pattern in question...
Basic MUG patterns:
Deadly Test (aeb’s rule): “A pattern is deadly if every pattern that arises by discarding zero or more times all occurrences of a given digit from a given group [row,col,box] is a pattern without unique [or any] solution.”

Code: Select all

ab  .   .   | abc .   .   | bc  .   . 
ab  .   .   | abc .   .   | bc  .   . 
.   .   .   | .   .   .   | .   .   .

abc .   .   | abc .   .   | ab  .   . 
abc .   .   | abc .   .   | ab  .   . 
.   .   .   | .   .   .   | .   .   .
 
abc .   .   | abc .   .   | abc .   . 
abc .   .   | abc .   .   | abc .   . 
.   .   .   | .   .   .   | .   .   .

.   .   abc | abc .   .   | .   .   . 
.   .   abc | abc .   .   | .   .   . 
.   .   abc | abc .   .   | .   .   . 
   
.   .   abc | abc .   .   | .   .   . 
.   .   abc | abc .   .   | .   .   . 
.   .   ab  | ab  .   .   | .   .   . 
   

The full discussion is here:
http://forum.enjoysudoku.com/forming-mugs-from-bug-lite-composites-t3210.html#p21052

SteveC

[SteveG48]

Thanks, guys! Told you I wasn't good with these things.

[Sudtyro2]

Code: Select all

.-------------------.----------------------------.-----------.
|  5     1     4    | 38      368        68      | 7  9   2  |
|  6     3     8    | 7      *29        *29      | 1  4   5  |
|  7     2     9    | 145     145       c15      | 8  6   3  |
:-------------------+----------------------------+-----------:
|  4     58    157  | 6       1258       1258    | 9  3   17 |
|  2    *589  b135  |a1358#9  7        b*1589    | 4  58  6  |
| *19    6     1357 | 13589   1358(#9)   4       | 2  58  17 |
:-------------------+----------------------------+-----------:
|  3     79    2    | 89      68(#9)     678(#9) | 5  1   4  |
|d*1(9)  4    d15   | 2      *5-9        3       | 6  7   8  |
|  8    d57    6    | 145     145       c157     | 3  2   9  |
'-------------------'----------------------------'-----------'

7-link Oddagon(*9) + 4 guardians #

(9)r6c5,r7c56 == (9-3|1)r5c4 = (31)r5c36 - (15=7)r39c6 - (715=9)b7p864 => -9 r8c5; stte

Hi SpAce,
First, I must certainly add a "well done" to you as well!

BTW, I had worked up two different 5-link oddagons for the 9s grid, and one of them had 9r5c4 as the only "tough" guardian, for which I simply could not find a suitable chain. My only question on your chain is about the two nodes marked in red above. That particular notation is new to me, but it seems perfectly legitimate. However, I finally realized that your marked segment is probably equivalent to 9r5c4 - (9=581)r5c268, with which I'm much more comfortable. Would you agree?

SteveC

[SpAce]

7-link Oddagon(*9) + 4 guardians #

(9)r6c5,r7c56 == (9-3|1)r5c4 = (31)r5c36 - (15=7)r39c6 - (715=9)b7p864 => -9 r8c5; stte

Hi SpAce,
First, I must certainly add a "well done" to you as well!

Thanks, Steve!

BTW, I had worked up two different 5-link oddagons for the 9s grid, and one of them had 9r5c4 as the only "tough" guardian, for which I simply could not find a suitable chain. My only question on your chain is about the two nodes marked in red above. That particular notation is new to me, but it seems perfectly legitimate. However, I finally realized that your marked segment is probably equivalent to 9r5c4 - (9=581)r5c268, with which I'm much more comfortable. Would you agree?

Yes. Mine is just the hidden alternative to your naked one. I thought about changing it because most prefer naked sets to hidden sets and it would have made it similar to the rest of the chain, but I kept the other route because that's how I originally saw it. The other reason was that a hidden pair is smaller than a naked triple so from that POV it's slightly simpler. In this case it's perhaps less readable, though, so I might agree that this is better:

(9)r6c5,r7c56 == (9)r5c4 - (9=581)r5c286 - (15=7)r39c6 - (715=9)b7p864 => -9 r8c5; stte

Sometimes naked ALS nodes are so huge that I would definitely prefer a smaller hidden variant, but here the difference is minimal.

Another matter of style is the number and placement of the digits in the ALS nodes, and I'm never quite sure which is best. I guess this would have been the most standard:

(9)r6c5,r7c56 == (9)r5c4 - (9=581)r5c286 - (1=57)r39c6 - (7=159)b7p864 => -9 r8c5; stte

...while some would prefer this:

(9)r6c5,r7c56 == (9)r5c4 - (9=1)r5c286 - (1=7)r39c6 - (7=9)b7p864 => -9 r8c5; stte

...while this might be the most accurate (though least readable):

(9)r6c5,r7c56 == (9)r5c4 - (958=581)r5c286 - (15=57)r39c6 - (715=159)b7p864 => -9 r8c5; stte

(Not to even mention the various orderings of the digits.) A simple language, yet so many choices!