The New Sudoku Players' Forum

[ArkieTech]

Due to a dating problem I skipped this one early in the month.

Code: Select all

 *-----------*
 |..9|7..|35.|
 |52.|...|..7|
 |...|35.|..4|
 |---+---+---|
 |..1|..3|.76|
 |...|.7.|...|
 |97.|4..|8..|
 |---+---+---|
 |7..|.26|...|
 |1..|...|.48|
 |.35|..9|7..|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 468     1468    9        | 7       168     128      | 3       5       12       |
| 5       2       3        |a69      1689    4        | 16      168     7        |
| 68      168     7        | 3       5       128      | 1269    12689   4        |
|--------------------------+--------------------------+--------------------------|
|c248    c458     1        |b29      89      3        | 2459    7       6        |
| 3      c4568   c48       | 29-6    7       158      | 12459   129     59       |
| 9       7       26       | 4       16      15       | 8       123     35       |
|--------------------------+--------------------------+--------------------------|
| 7       489     48       | 18      2       6        | 159     139     359      |
| 1       69      26       | 5       3       7        | 269     4       8        |
| 268     3       5        | 18      4       9        | 7       126     12       |
*--------------------------------------------------------------------------------*

als xy-wing: (6=9) r2c4 - (9=2) r4c4 - (2=6) r4c12,r5c23 => r5c6 <> 6; stte.

Leren

[eleven]

(2=6)r4c45,r5c6,r6c56-(6=2)r6c3 => r4c1<>2

[pjb]

Same beginning and end, same elimination as Eleven, but straight chain:

r4c4=2=(2-6)r5c4=6=r5c2-6-(6=2)r6c3: => r4c1 <> 2

Phil

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 468     1468    9        | 7       168     128      | 3       5       12       |
| 5       2       3        | 69      1689    4        | 16      168     7        |
| 68      168     7        | 3       5       128      | 1269    12689   4        |
|--------------------------+--------------------------+--------------------------|
|a248    a458     1        |b29     c89      3        | 2459    7       6        |
| 3      a4568   a48       | 29-6    7      c158      | 12459   129     59       |
| 9       7       2-6      | 4      c16     c15       | 8       123     35       |
|--------------------------+--------------------------+--------------------------|
| 7       489     48       | 18      2       6        | 159     139     359      |
| 1       69      26       | 5       3       7        | 269     4       8        |
| 268     3       5        | 18      4       9        | 7       126     12       |
*--------------------------------------------------------------------------------*

als xy-wing: (6=2) r4c12,r5c23 - (2=9) r4c4 - (9=6) r46c5,r56c6 => r5c4, r6c3 <> 6; stte

Leren

[tlanglet]

Same genera logic without an ALS......

6r6c5=6r5c4-(6=9)r2c4-(9=2)r4c4-r4c1=(2-6)r6c3=6r6c5 => r6c5=6

[tlanglet]

I looked for another solution based on a totally different logic path and found this long chain.....

8r9c4=8r9c1-r7c3=r5c3-r5c6=(8-9)r4c5=r45c4-(9=6)r2c4-(6=1)r2c7-r1c9=r9c9-(1=8)r9c4 => r9c4=8

Ted

[ArkieTech]

Code: Select all

 *--------------------------------------------------------------------*
 | 468    1468   9      | 7      168    128    | 3      5      12     |
 | 5      2      3      | 69     1689   4      | 16     168    7      |
 | 68     168    7      | 3      5      128    | 1269   12689  4      |
 |----------------------+----------------------+----------------------|
 |d248    458    1      |c29     89     3      | 2459   7      6      |
 | 3      4568   48     |b269    7      158    | 12459  129    59     |
 | 9      7     e2-6    | 4     a16     15     | 8      123    35     |
 |----------------------+----------------------+----------------------|
 | 7      489    48     | 18     2      6      | 159    139    359    |
 | 1      69     26     | 5      3      7      | 269    4      8      |
 | 268    3      5      | 18     4      9      | 7      126    12     |
 *--------------------------------------------------------------------*
L-wing
6r6c5=(6-2)r5c4=r4c4-r4c1=2r6c3 => -6r6c3; stte

[eleven]

Same beginning and end, same elimination as Eleven, but straight chain:

In this case i really spotted it that way.
r4c4=9->r4c5=8->r56c6=15->r6c5=6
Normally i would find it from the strong links with a common cell:
2r4c4=2r5c4 and 6r5c4=6r6c5 => either r4c4=2 or 6r6c5=6

[Marty R.]

Code: Select all

+-------------+--------------+-----------------+
| 468 1468 9  | 7   168  128 | 3     5     12  |
| 5   2    3  | 69  1689 4   | 16    168   7   |
| 68  168  7  | 3   5    128 | 1269  12689 4   |
+-------------+--------------+-----------------+
| 248 458  1  | 29  89   3   | 2459  7     6   |
| 3   4568 48 | 269 7    158 | 12459 129   59  |
| 9   7    26 | 4   16   15  | 8     123   35  |
+-------------+--------------+-----------------+
| 7   489  48 | 18  2    6   | 159   139   359 |
| 1   69   26 | 5   3    7   | 269   4     8   |
| 268 3    5  | 18  4    9   | 7     126   12  |
+-------------+--------------+-----------------+


Play this puzzle online at the Daily Sudoku site

I hope I learned the last ALS lesson that Don gave me.

(2=6)r6c3-(61589=2)r6c5r56c6r4c54=>r4c1<>2

[tlanglet]

Code: Select all

+-------------+--------------+-----------------+
| 468 1468 9  | 7   168  128 | 3     5     12  |
| 5   2    3  | 69  1689 4   | 16    168   7   |
| 68  168  7  | 3   5    128 | 1269  12689 4   |
+-------------+--------------+-----------------+
| 248 458  1  | 29  89   3   | 2459  7     6   |
| 3   4568 48 | 269 7    158 | 12459 129   59  |
| 9   7    26 | 4   16   15  | 8     123   35  |
+-------------+--------------+-----------------+
| 7   489  48 | 18  2    6   | 159   139   359 |
| 1   69   26 | 5   3    7   | 269   4     8   |
| 268 3    5  | 18  4    9   | 7     126   12  |
+-------------+--------------+-----------------+


Play this puzzle online at the Daily Sudoku site

I hope I learned the last ALS lesson that Don gave me.

(2=6)r6c3-(61589=2)r6c5r56c6r4c54=>r4c1<>2

Give the man a cigar, he hit the target

[Marty R.]

Give the man a cigar, he hit the target

Mmm, you're tempting me to become a former ex-smoker.

[DonM]

Here's something a little different using a Broken Wing pattern:

Code: Select all

+-------------+--------------+-----------------+
| 468 1468 9  | 7   168  128 | 3     5     12  |
| 5   2    3  | 69  1689 4   | 16    168   7   |
| 68  168  7  | 3   5    128 | 1269 G12689 4   |
+-------------+--------------+-----------------+
| 248 458  1  | 29  89   3   | 2459  7     6   |
| 3   4568 48 | 269 7    158 | 12459G129   59  |
| 9   7   *26 | 4   16   15  | 8    *123   35  |
+-------------+--------------+-----------------+
| 7   489  48 | 18  2    6   | 159   139   359 |
| 1   69  *26 | 5   3    7   | 269   4     8   |
|*268 3    5  | 18  4    9   | 7    *126  G12  |
+-------------+--------------+-----------------+

The * indicates cells comprising the Broken Wing. Cells containing Guardian 2s are indicated by G.

There is a potential 5-sided loop of conjugate links of 2s (the Broken Wing) at r9c1,r8c3,r6c3,r6c8,r9c8 which would be impossible if it existed by itelf. There are three 2s at r35c8, r9c9 called 'Guardians' that prevent that pattern. If (2)r1c9 were true then it would eliminate 2 of the guardians at r3c8,r9c9 leaving only (2)r5c8. Thus, if (2)r5c8 were to be removed then (2)r1c9 couldn't be true because it would eliminate the remaining 2 guardians at (2)r3c8, (2)r9c9 thus exposing the pure 5-sided loop of conjugate 2s.

Broken Wing (BW): (2)r9c1,r8c3,r6c3,r6c8,r9c8

(2)r5c8=BW-(2)r1c9=r9c9-r9c1=(2-6)r8c3=r6c3-r6c5=(6)r5c4 => -2r5c4 stte

(note: I'm not sure that this notation best expresses the logic).

[eleven]

Nice.

What i find interesting is, that without the 2 in r9c8 (which is eliminated by the kite inside the broken wing) the link between 2r5c8=r9c9 is no pattern anymore
Then you'd e.g. have to say, that both 2r3c8 and 2r6c8 (over the broken broken wing) imply 2r9c9, before you can use it.

[David P Bird]

Other names for "Broken Wings" are "Oddagons" and "Impossible Loops".

They derive a strong inference that one of the guardians must be true and so can be notated in much the same way as other deadly patterns.

I would therefore write:

(2)r5c8 =[(2)BW:r69c8,r9c1,r68c3]= (2)3c8,r9c9 - (2)r1c9 etc.

Note the guardians are considered to be external to the pattern and the strong link between them is justified by identifying the pattern.