Edit: Images added for easier reading.A few typos fixed

- Code: Select all
`*-----------*`

|...|.7.|5.8|

|.9.|..8|3..|

|51.|.2.|...|

|---+---+---|

|8..|...|...|

|.45|.6.|98.|

|...|...|..4|

|---+---+---|

|...|.9.|.56|

|..1|4..|.7.|

|4.7|.5.|...|

*-----------*

After basic logic and coloring:

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`*-----------------------------------------------------------------------------*`

| 236 23 2346 | 169 7 149 | 5 12469 8 |

| 7 9 246 | 5 14 8 | 3 1246 12 |

| 5 1 8 | 369 2 349 | 67 469 79 |

|-------------------------+-------------------------+-------------------------|

| 8 237 2369 | 12379 134 123479 | 1267 1236 5 |

| 123 4 5 | 1237 6 1237 | 9 8 1237 |

| 1236 237 2369 | 123789 138 5 | 1267 123 4 |

|-------------------------+-------------------------+-------------------------|

| 23 8 23 | 17 9 17 | 4 5 6 |

| 9 5 1 | 4 38 6 | 28 7 23 |

| 4 6 7 | 238 5 23 | 18 139 139 |

*-----------------------------------------------------------------------------*

Solution:

1.[r3c4](-9-[r1c6])(-9-[r3c6])-9-[r3c789]=9|3=[(r3c6)]-3-[r579c6]=3|4=[(r1c6)]-4-[r1c123]=4|1=[r1c4]=6=[r3c4] => [r3c4]<>9

Blue=weak link, Red=strong link, Green boxes=grouped nodes/ALS

2. [r1c8](-6-[r1c4]=6=[r3c4]=3=[r3c6](-3-[r5c6])-3-[r9c6]-2-[(r5c6)]-6-[r1c1]=6=[r6c1]=1=[r5c1]-1-[(r5c6)]-7-[r5c9]=7=[r3c9]-7-[r3c7]-6-[r1c8] => [r1c8]<>6

Blue=weak link, Red=strong link

Edit: The following loop is written inconsistently, although the deduction is true if it is interpreted as an implication network that eliminates all candidates from [r5c6]. A corrected loop notation is written a few posts down.

3. [r2c3]-6-[r1c1|r1c3](=6|19=[r1c8])(=6|19=[r1c6])=6=[r1c4]-6-[r3c4]-3-[r4569c4]-{ANL:[r8c9]-3-[r8c5]=3=[r9c6]-3-[r5c6]=3=[r5c9]-3-[r8c9]}-3-[r8c9](-2-[r8c7]-8-[r8c5]-3-[r9c6]-2-[r5c6])(-2-[r5c9])-2-[r2c9](-1-[(r5c9)])

-1-[(r1c8)](-9-[(r1c6)]-1-[r7c6]-7-[(r5c6)])-9-[r3c9]-7-[(r5c9)]-3-[(r5c6)]-1-[r5c1]=1=[r6c1]=6=[(r1c1)]-6-[r2c3] => [r2c3]<>6

Blue=weak link, Red=strong link, Black=weak link indicating elimination from almost nice loop in the middle(ANL), red dots on ends of weak links show the implicating end in the loop notation

And the puzzle is solved with singles after that.

Loop 3 separated by steps and color coded for multiple references:

3. [r2c3]-6-[r1c1|r1c3]

(=6|19=[r1c8])

(=6|19=[r1c6])

=6=[r1c4]-6-[r3c4]-3-[r4569c4]-{ANL:[r8c9]-3-[r8c5]=3=[r9c6]-3-[r5c6]=3=[r5c9]-3-[r8c9]}

-3-[r8c9]

(-2-[r8c7]-8-[r8c5]-3-[r9c6]-2-[r5c6])

(-2-[r5c9])

-2-[r2c9]

(-1-[(r5c9)])

-1-[(r1c8)]

(-9-[(r1c6)]-1-[r7c6]-7-[(r5c6)])

-9-[r3c9]-7-[(r5c9)]-3-[(r5c6)]-1-[r5c1]=1=[r6c1]=6=[(r1c1)]-6-[r2c3] => [r2c3]<>6

Is there anything wrong with such a complicated mess of multiple inferences?