.5..............8.8...4.1........2...386.2.9..961..........3.1..........92....3..
359781462147326985862945173715894236438652791296137548584273619673519824921468357
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13467 ```5 12479 | `379 1236789 `16789 | ``4679 `3467 `234679
13467 1467 12479 | 3579 1235679 ``5679 | `45679 ````8 2345679
````8 ``67 ``279 | 3579 ``````4 ``5679 | `````1 `3567 `235679
-----------------+---------------------+----------------------
`1457 `147 `1457 | ```8 ```3579 ``4579 | `````2 34567 `134567
`1457 ```3 ````8 | ```6 `````57 `````2 | ```457 ````9 ```1457
````2 ```9 ````6 | ```1 ````357 ```457 | ``4578 ``457 ``34578
-----------------+---------------------+----------------------
`4567 `478 ``457 | ```2 ``56789 `````3 | 456789 ````1 `456789
14567 `478 ````3 | `457 `156789 456789 | 456789 ````2 `456789
````9 ```2 `1457 | `457 ``15678 145678 | `````3 `4567 ``45678
I call the extra houses in the puzzle "windows" and number them w1, w2, w3 and w4
b2.14679 {-128}.235 // hidden triple in box2
c2 {1} w1.28 // claiming: column2 claims all the candidate {1} from the rest of window1
w1 {2} b1.3 c3.1 // window1 claims all the candidate {3} from box1 and column3
w1 {3} b2.1 c4.1
w2 {3} c8.1
b5 {4} c6.89
{4} r8c1 % w3 // r8c1 cannot have candidate {4} as then w3 is devoid of candidate {4}'s
{5} r7c5 % w3
{5} r8c1 % w3
b2 {6} c6.89 w2.269
b7 {6} c1.12
w4 {6} b9.3689 c7.1
{7} r8c1 % w3
c7 {8} w4.7
c4 {9} b2.69
{9} r8c9 % w4
--assert singles--
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1347 ```5 1479 | ``79 ``128 ``18 | ```479 ```6 `23479
1347 1467 2479 | 3579 ```12 `567 | ``4579 ```8 234579
```8 ``67 `279 | 3579 ````4 `567 | `````1 `357 `23579
---------------+-----------------+--------------------
1457 `147 `457 | ```8 `3579 4579 | `````2 3457 `````6
`457 ```3 ```8 | ```6 ```57 ```2 | ```457 ```9 `````1
```2 ```9 ```6 | ```1 ``357 `457 | ``4578 `457 `34578
---------------+-----------------+--------------------
4567 `478 `457 | ```2 ``789 ```3 | 456789 ```1 `45789
``16 `478 ```3 | `457 15789 `579 | 456789 ```2 ``4578
```9 ```2 1457 | `457 ````6 1578 | `````3 `457 ``4578
c6.23468 {-18}.(1)9
col 2f c36 {1} : r19 // x-wing (2-fish) in the columns 3 and 6 over rows 1 and 9
ff {4} r7c7 % c68 > r4 // finned fish: r7c7 cannot have candidate {4} because then columns 6 and 8 only has the candidate {4} in r4 [it needs to be in at least two places]
ff {4} r8c7 % c68 > r4
w4 {4} r6.9
r3.268 -3- r4.1238 {5} r4c6 // als-xz move, the restricted common is {3} between the sets r3 positions 2 6 and 8 and r4 positions 1 2 3 and 8. the {5} in r4c6 touches all the {5}'s in both sets
r4.123 -4- w2.1469 {7} r4c6
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`347 ```5 1479 | ``79 ```28 `18 | ``479 ```6 `23479
1347 1467 2479 | 3579 ```12 567 | `4579 ```8 234579
```8 ``67 `279 | 3579 ````4 567 | ````1 `357 `23579
---------------+----------------+-------------------
1457 `147 `457 | ```8 `3579 `49 | ````2 3457 `````6
`457 ```3 ```8 | ```6 ```57 ``2 | ``457 ```9 `````1
```2 ```9 ```6 | ```1 ``357 457 | `4578 `457 ``3578
---------------+----------------+-------------------
4567 `478 `457 | ```2 ``789 ``3 | 56789 ```1 `45789
``16 `478 ```3 | `457 15789 579 | 56789 ```2 ``4578
```9 ```2 1457 | `457 ````6 `18 | ````3 `457 ``4578
at this point, I do not have a definite solution step; however I notice that speculating a {5} to r8c4 gives:
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``3 ```5 479 | `79 ``8 ``1 | `479 ``6 ````2
147 1467 479 | 379 ``2 567 | 4579 ``8 34579
``8 ``67 ``2 | 379 ``4 567 | ```1 357 `3579
-------------+-------------+----------------
147 `147 ``5 | ``8 379 `49 | ```2 347 ````6
`47 ```3 ``8 | ``6 `57 ``2 | `457 ``9 ````1
``2 ```9 ``6 | ``1 357 457 | 4578 457 `3578
-------------+-------------+----------------
``5 `478 `47 | ``2 `79 ``3 | ```6 ``1 `4789
``6 `478 ``3 | ``5 ``1 `79 | `789 ``2 ``478
``9 ```2 ``1 | ``4 ``6 ``8 | ```3 `57 ```57
b2.147 {-56}.69 // hidden pair {56} in box 2
b9.89 {57}.346 // naked pair {57} in box 9
c6.23 {56}.6 // naked pair {56] in column 6
w2.14 {56}.26 // hidden pair {56} in window 2
b9 {4} c9.2
c8 {4} b6.47
b3 {5} c9.69
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``3 ```5 479 | `79 ``8 `1 | 479 ``6 ```2
147 1467 479 | 379 ``2 56 | 479 ``8 3579
``8 ``67 ``2 | 379 ``4 56 | ``1 `37 3579
-------------+------------+--------------
147 `147 ``5 | ``8 379 49 | ``2 347 ```6
`47 ```3 ``8 | ``6 `57 `2 | `57 ``9 ```1
``2 ```9 ``6 | ``1 357 47 | 578 457 `378
-------------+------------+--------------
``5 `478 `47 | ``2 `79 `3 | ``6 ``1 `489
``6 `478 ``3 | ``5 ``1 79 | `89 ``2 ``48
``9 ```2 ``1 | ``4 ``6 `8 | ``3 `57 ```7
here singles solve.
There is one other position for a {5} in window 3, so trying that....
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`347 ```5 1479 | ``79 ```28 `18 | ``479 ```6 `23479
1347 1467 2479 | 3579 ```12 567 | `4579 ```8 234579
```8 ``67 `279 | 3579 ````4 567 | ````1 `357 `23579
---------------+----------------+-------------------
1457 `147 ``47 | ```8 `3579 `49 | ````2 3457 `````6
`457 ```3 ```8 | ```6 ```57 ``2 | ``457 ```9 `````1
```2 ```9 ```6 | ```1 ``357 457 | `4578 `457 ``3578
---------------+----------------+-------------------
`467 `478 ```5 | ```2 ``789 ``3 | `6789 ```1 ``4789
``16 `478 ```3 | ``47 15789 579 | 56789 ```2 ``4578
```9 ```2 `147 | `457 ````6 `18 | ````3 `457 ``4578
w1.1478 {1467}.2356
w1.124578 {-35}.36
r3.2468 {-29}.(3)9
b1.69 {29}.3
b2.47 {35}.69
b2.69 {67}.1
r3.26 {67}.8
b8.47 {47}.256
c6.23 {67}.6
w2.14 {67}.29
r9 {5} b9.46
c6 {5} w4.23
{5} r4c8 % c7
w2 {5} b3.6
{7} r7c7 % c8
{7} r8c7 % c8
w4 {7} r6.59 b6.49
r8.249 {478}.57
r1.7 -7- b6.2479 {4} r2c7
r2.6 =67= w2.24679 {4} r4c1
r2.6 =67= w2.24679 {4} r4c2
r2.6 =67= w2.24679 {4} r4c3
assert singles
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37 `5 1 | `9 `2 `8 | `47 `6 `347
37 `4 2 | 35 `1 `6 | ``9 `8 ``37
`8 `6 9 | 35 `4 `7 | ``1 `3 ```2
--------+----------+-------------
`5 `1 7 | `8 39 `4 | ``2 `3 ```6
`4 `3 8 | `6 `7 `2 | ``5 `9 ```1
`2 `9 6 | `1 35 `5 | 478 47 ``38
--------+----------+-------------
67 78 5 | `2 89 `3 | ``8 `1 4789
`1 78 3 | `4 59 59 | ``6 `2 ``78
`9 `2 4 | `7 `6 `1 | ``3 `5 ```8
box3 and column9 both lack placements for the {5} so r7c3 cannot have the {5} placed, thus the solution above is unique.
