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The following Classic Sudoku Puzzle (SER = 8.4) was generated in April, 2021
using HoDoKu for a training practice with als/ahs.
I solved it (manually) in two main steps
(i.e., apart from moves with scope in a single house - the "basics").
(image created using SudokuExplainer)
After performing the basics, find non-basic moves that solve this puzzle.
After performing all basic eliminations, write all condidates
.--------------------------------------------------------------.
| 126 1269 5 | 4 79 3 | 8 179 1279 |
| 123 8 234 | 159 579 6 | 12479 134579 123579 |
| 7 1349 34 | 1589 2 58 | 6 13459 1359 |
|---------------------+----------------+-----------------------|
| 28 24 1 | 59 48 7 | 3 6 59 |
| 68 5 678 | 3 89 1 | 79 2 4 |
| 9 347 347 | 6 45 2 | 17 157 8 |
|---------------------+----------------+-----------------------|
| 13568 1367 9 | 2 36 458 | 147 13478 137 |
| 2358 237 2378 | 578 1 458 | 2479 34789 6 |
| 4 12367 23678 | 78 36 9 | 5 1378 1237 |
'--------------------------------------------------------------'
and (a) look at the pattern of 2s to get some eliminations,
(b) Now, study carefully boxes 1 (top-left) and 4 (middle-left).
Final Update (Jun 14, 2025!)
.--------------------------------------------------------------.
| 126 1269 5 | 4 79 3 | 8 179 1279 | 9
| 123 8 234 | 159 579 6 | 12479 134579 123579 | 8
| 7 1349 34 | 1589 2 58 | 6 13459 1359 | 7
|---------------------+----------------+-----------------------|
| 28 24 1 | 59 48 7 | 3 6 59 | 6
| 68 5 678 | 3 89 1 | 79 2 4 | 5
| 9 347 347 | 6 45 2 | 17 157 8 | 4
|---------------------+----------------+-----------------------|
| 13568 1367 9 | 2 36 458 | 147 13478 137 | 3
| 358-2 37-2 2378 | 578 1 458 | 2479 34789 6 | 2
| 4 12367 23678 | 78 36 9 | 5 1378 1237 | 1
'--------------------------------------------------------------'
a b c d e f g h i
(a) can be seen as a grouped skyscraper eliminating (2) a2,b2.
.--------------------------------------------------------------.
| 16-2 1269 5 | 4 79 3 | 8 179 1279 | 9
| 13-2 8 234 | 159 579 6 | 12479 134579 123579 | 8
| 7 1349 34 | 1589 2 58 | 6 13459 1359 | 7
|---------------------+----------------+-----------------------|
| 28 24 1 | 59 48 7 | 3 6 59 | 6
| 68 5 678 | 3 89 1 | 79 2 4 | 5
| 9 347 347 | 6 45 2 | 17 157 8 | 4
|---------------------+----------------+-----------------------|
| 13568 1367 9 | 2 36 458 | 147 13478 137 | 3
| 358 37 2378 | 578 1 458 | 2479 34789 6 | 2
| 4 12367 23678 | 78 36 9 | 5 1378 1237 | 1
'--------------------------------------------------------------'
a b c d e f g h i
(b) can be seen as an ALS-xz move based on the almost naked pair (234)c78.
After basics, find a move that solves this Classic Sudoku puzzle ("three waves"):
(image created using SudokuExplainer)
This puzzle was found with Sudoku Architect when I was playing around with waves.
.-------------------------------------------------------.
| 3 19 5 | 169 4 7 | 2 169 8 |
| 2679 4 169 | 1369 8 2369 | 1379 5 167 |
| 2679 129 8 | 5 169 2369 | 1379 13679 4 |
|------------------+-----------------+------------------|
| 48 6 34 | 7 5 1 | 38 2 9 |
| 1 79 2 | 689 3 689 | 4 67 5 |
| 5 3789 39 | 2 69 4 | 1378 1367 167 |
|------------------+-----------------+------------------|
| 49 5 1349 | 139 7 39 | 6 8 2 |
| 2689 1289 7 | 1689 169 5 | 19 4 3 |
| 689 1389 1369 | 4 2 3689 | 5 179 17 |
'-------------------------------------------------------'
Look for a fish in the digit 6 !After basics, this Classic Sudoku puzzle can be solved in just two non-basic steps:
(image created using SudokuExplainer)
This puzzle was found with Sudoku Architect.
.------------------------------------------------------------.
| 1 4 59 | 67 2 8 | 56 79 3 |
| 2735 6 35 | 4 9 17 | 15 8 27 |
| 279 79 8 | 5 3 16 | 16 4 279 |
|--------------------+-------------------+-------------------|
| 356 8 1356 | 1367 1567 4 | 9 2 17 |
| 569 159 7 | 8 156 2 | 3 15 4 |
| 35 2 4 | 1379 157 579 | 8 157 6 |
|--------------------+-------------------+-------------------|
| 4 1379 169 | 1679 8 679 | 2 1369 5 |
| 5679 1579 1569 | 2 1567 3 | 4 169 8 |
| 8 1359 2 | 169 4 569 | 7 1369 19 |
'------------------------------------------------------------'
1) a nice UR (unique rectangle), 2) a symmetrical chain with 4 strong links.The following Classic Sudoku puzzle (found with Sudoku Architect)
is a tough puzzle! With careful analysis, it can be solved in a few steps,
revealing interesting structures forming its foundations.
There is a solution in 3 steps. The first step is complex and only boxes 1,7 do not take part.
,--------------------------------------------------------,
| 8 4 1279 | 6 17 157 | 239 125 2359|
| 127 5 127 | 3 9 178 | 4 128 6 |
| 3 169 169 | 158 2 4 | 89 7 59 |
|--------------------+-----------------+-----------------|
| 1279 12679 4 | 179 3 1679 | 5 26 8 |
| 1279 38 12679 | 1789 5 16789 | 2367 4 23 |
| 57 38 567 | 2 4 678 | 367 9 1 |
|--------------------+-----------------+-----------------|
| 4 1279 3 | 1579 8 (2)1579| 269 (25)6 (25)9|
| 259 29 8 | 4 6 (2)59 | 1 3 7 |
| 6 1279 12579 | 1579 17 3 | 289 258 4 |
'--------------------------------------------------------'
The key idea is to notice the strong link (2)r7c6 = (2)r8c6 and the almost naked pair(25)r7c89,
with spoilers (6)r7c8, (9)r7c9. After the resulting key elimination we get 4 placements.
Step 2 is easier and the key idea starts with (5)r9c5=(5)r9c8.
,------------------------------------------------------,
| 8 4 1279 | 6 17 157 | 239 125 2359|
| 12 5 127 | 3 9 178 | 4 128 6 |
| 3 169 169 | 158 2 4 | 89 7 59 |
|-----------------+------------------+-----------------|
| 129 126 4 | 179 3 1679 | 5 26 8 |
| 129 38 126 | 189 5 1689 | 7 4 23 |
| 7 38 5 | 2 4 68 | 36 9 1 |
|-----------------+------------------+-----------------|
| 4 1279 3 | 1579 8 12579 | 269 256 259 |
| 5 29 8 | 4 6 29 | 1 3 7 |
| 6 1279 129 | (5)179 17 3 | 289 (5)28 4 |
'------------------------------------------------------'
Boxes 1,4,5 and 7 are not used in this second step and the resulting elimination gives
7 placements, weakening severely the puzzle. A chain with 4 strong links finishes it.
Can you find it ?
,---------------------------------------------,
| 8 4 129 | 6 7 5 | 239 12 239 |
| 12 5 7 | 3 9 18 | 4 128 6 |
| 3 69 169 | 18 2 4 | 89 7 5 |
|--------------+--------------+---------------|
| 19 26 4 | 179 3 179 | 5 26 8 |
| 129 38 126 | 189 5 1689 | 7 4 23 |
| 7 38 5 | 2 4 68 | 36 9 1 |
|--------------+--------------+---------------|
| 4 1 3 | 579 8 279 | 269 256 29 |
| 5 29 8 | 4 6 29 | 1 3 7 |
| 6 7 29 | 59 1 3 | 289 258 4 |
'---------------------------------------------'
The following Classic Sudoku puzzle (found with Sudoku Architect)
is an interesting puzzle, with many patterns. How to solve it ?
After basics, the configuration is as follows.
.---------------------------------------------------.
| 6 249 1249 | 49 89 5 | 7 138 38 |
| 47 8 479 | 479 3 1 | 6 5 2 |
| 157 57 3 | 6 78 2 | 4 18 9 |
|---------------------+------------+----------------|
| 57 1 6 | 2 79 3 | 589 4 578 |
| 8 23579 279 | 579 6 4 | 2359 379 1 |
| 23457 234579 2479 | 579 1 8 | 2359 6 357 |
|---------------------+------------+----------------|
| 9 6 8 | 3 5 7 | 1 2 4 |
| 347 347 5 | 1 2 9 | 38 378 6 |
| 1237 237 127 | 8 4 6 | 359 379 357 |
'---------------------------------------------------'
I found a solution in 3 steps.
Step 1 is an ALS-xz move that eliminates (8)r1c9 [3 placements].
Step 2 is a wing that was not available before step 1.
The final step is a bit complex (wing-related, very pretty!)
and becomes possible by the key elimination made in step 2.
The following Classic Sudoku puzzle (found with Sudoku Architect)
has a slightly higher rating than #13, but in my view it is a lot easier to solve.
How ?
After basics, the configuration is as follows.
.------------------------------------------------------------.
| 1 4 6 | 5 3 2 | 8 9 7 |
| 9 2 5 | 7 8 14 | 6 134 13 |
| 3 8 7 | 46 9 146 | 124 5 12 |
|---------------+----------------------+---------------------|
| 4 19 8 | 3 7 5 | 129 6 129 |
| 7 3 12 | 2468 246 9 | 145 148 158 |
| 6 5 29 | 1 24 48 | 7 348 389 |
|---------------+----------------------+---------------------|
| 58 6 19 | 289 125 3 | 159 7 4 |
| 58 7 3 | 4689 1456 468 | 159 2 15689 |
| 2 19 4 | 689 156 7 | 3 18 15689 |
'------------------------------------------------------------'
I have found a solution in two steps. In the first step, I used an ALS
in column 6 within a chain (with 6 strong links) to show that 5 is false at r9c9.
After this, there are at least two wings that finish the puzzle.
The following tough Classic Sudoku puzzle (found with Sudoku Architect)
has a solution in two steps that requires considerable work analyzing the puzzle.
After basics, the configuration is as follows.
.--------------------------------------------------------------------.
| 23567 2367 2369 | 469 479 1 | 267 25679 8 |
| 1267 8 4 | 69 5 679 | 3 12679 279 |
| 1567 167 69 | 2 3 8 | 1467 15679 4579 |
|----------------------+----------------------+----------------------|
| 2367 2367 236 | 359 29 4 | 8 3569 1 |
| 48 5 1 | 389 6 79 | 247 2379 23479 |
| 48 9 236 | 1 278 57 | 467 3567 3457 |
|----------------------+----------------------+----------------------|
| 1269 1246 7 | 45689 1489 569 | 12 1238 23 |
| 126 1246 5 | 468 148 3 | 9 1278 27 |
| 139 13 8 | 7 19 2 | 5 4 6 |
'--------------------------------------------------------------------'
For the first move, search for a Sue de Coq!
(SDCs are elusive, so look carefully at boxes 5 and 6)
The second move is harder: only two boxes are not involved.
(ALS(193)r9c25 and ALS(2379)r5c678 take part in this powerful move)
The following Classic Sudoku puzzle (found with Sudoku Architect)
has a nice solution in one step.
After basics, the configuration is as follows.
.-----------------------------------------------------------.
| 1 238 238 | 6 7 9 | 4 23 5 |
| 45 29 7 | 45 3 8 | 6 29 1 |
| 459 369 3456 | 2 1 45 | 8 39 7 |
|-------------------+-------------------+-------------------|
| 7 4 9 |(35) 8 6 | 235 1 23 |
| 8 123 123 | 1359 (59) 7 | 359 6 4 |
| 6 5 13 | 1349 2 34 | 39 7 8 |
|-------------------+-------------------+-------------------|
| 2 689 68 | 379 4 1 | 37 5 369 |
| 459 19 145 | 3579 6 235 | 1237 8 239 |
| 3 7 156 | 8 59 25 | 12 4 269 |
'-----------------------------------------------------------'
ALS(359) (shown above) participates in a powerful move that essentially solves the puzzle.
The following Classic Sudoku puzzle (found with Sudoku Architect)
has an interesting solution in two steps.
After basics, the configuration is as follows.
,-----------------------------------------------------------,
| 19 69 8 | 2 5 7 | 4 3 16 |
| 25 27 4 | 6 3 1 | 9 8 57 |
| 15 67 3 | 4 8 9 | 15 2 67 |
|-------------------+-------------------+-------------------|
| 247 8 257 | 1357 6 245 | 15 9 135 |
| 479 3 579 | 1579 179 458 | 2 6 158 |
| 6 29 1 | 35 29 58 | 7 4 358 |
|-------------------+-------------------+-------------------|
| 3 1 79 | 79 4 6 | 8 5 2 |
| 8 4 6 | 15 12 25 | 3 7 9 |
| 279 5 279 | 8 79 3 | 6 1 4 |
'-----------------------------------------------------------'
My first solution had 2 steps:
(i) UR(27)r49c13 using externals to eliminate 7 from r7c4 and from r5c5,
(ii) a simple chain with 5 strong links using (5)r3c7 = (5)r4c7
(eliminates 9 from r1c2)
Then, I noticed a solution in just one step, using
,-----------------------------------------------------------,
| 19 69 8 | 2 5 7 | 4 3 16 |
| 25 27 4 | 6 3 1 | 9 8 57 |
| 15 67 3 | 4 8 9 | 1(5) 2 67 |
|-------------------+-------------------+-------------------|
| 247 8 257 | 1357 6 245 | 1(5) 9 135 |
| 479 3 579 | 1579 179 458 | 2 6 158 |
| 6 2-9 1 | 35 29 58 | 7 4 358 |
|-------------------+-------------------+-------------------|
| 3 1 (7)9 |(7)9 4 6 | 8 5 2 |
| 8 4 6 | 15 12 25 | 3 7 9 |
| 279 5 279 | 8 79 3 | 6 1 4 |
'-----------------------------------------------------------'
the strong links (5)r3c7 = (5)r4c7 and (7)r7c3 = (7)r7c4.
I have recently battled with the following tough Classic Sudoku puzzle
(found with Sudoku Architect)
Can you find a solution in about 8 non-basic steps ?
After basics, the configuration is as follows.
.--------------------------------------------------------------------.
| 9 7 234 | 5 13 8 | 124 146 1246 |
| 268 236 2368 | 4 7 13 | 128 5 9 |
| 1 45 458 | 9 6 2 | 3 47 478 |
|----------------------+----------------------+----------------------|
| 24 234 1 | 7 29 6 | 459 8 345 |
| 5 8 23467 | 1 29 34 | 479 467 3467 |
| 467 346 9 | 8 34 5 | 147 2 13467 |
|----------------------+----------------------+----------------------|
| 478 1 478 | 2 5 9 | 6 3 478 |
| 3 245 2457 | 6 8 14 | 12457 9 12457 |
| 268 9 2568 | 3 14 7 | 258 14 258 |
'--------------------------------------------------------------------'
After basics, x-wing(1), ALS-xz(column 8, box 3), Kite(4) and ER(3),
one gets the following key configuration:
.--------------------------------------------------------------------.
| 9 7 234 | 5 13 8 | 24 14 6 |
| 268 26 2368 | 4 7 13 | 128 5 9 |
| 1 45 458 | 9 6 2 | 3 7 48 |
|----------------------+----------------------+----------------------|
| 24 234 1 | 7 29 6 | 459 8 345 |
| 5 8 247 | 1 29 34 | 479 6 347 |
| 467 346 9 | 8 34 5 | 147 2 1347 |
|----------------------+----------------------+----------------------|
| 478 1 478 | 2 5 9 | 6 3 478 |
| 3 245 2457 | 6 8 14 | 1457 9 12457 |
| 268 9 2568 | 3 14 7 | 58 14 258 |
'--------------------------------------------------------------------'
Now there is something interesting (column 1 & box 4).
After the elimination from that step, there is an
x-chain on digit 4 that leads to
,--------------------------------------------------------------------,
| 9 7 23 | 5 13 8 | 24 14 6 | 9
| 268 26 2368 | 4 7 13 | 12 5 9 | 8
| 1 45 45 | 9 6 2 | 3 7 8 | 7
|----------------------+----------------------+----------------------|
| 24 23 1 | 7 29 6 | 459 8 345 | 6
| 5 8 247 | 1 29 34 | 479 6 347 | 5
| 467 36 9 | 8 34 5 | 147 2 1347 | 4
|----------------------+----------------------+----------------------|
| 478 1 478 | 2 5 9 | 6 3 47 | 3
| 3 45 2457 | 6 8 14 | 1457 9 12457 | 2
| 26 9 256 | 3 14 7 | 8 14 25 | 1
'--------------------------------------------------------------------'
a b c d e f g h i
(now rated SE = 7.1).
Update (Apr 26, 2025!)
A simple chain with 5 stong links and a BUG+1 solves it.
I have found an interesting tough Classic Sudoku puzzle
(found with Sudoku Architect)
This puzzle is solvable in two steps.
After basics, the configuration is as follows.
,--------------------------------------------------------------------,
| 267 2567 25 | 3 4 79 | 8 69 1 |
| 9 4 3 | 1 6 8 | 57 257 257 |
| 67 8 1 | 5 2 79 | 39 3469 46 |
|----------------------+----------------------+----------------------|
| 2478 27 248 | 267 9 3 | 4567 1 4567 |
| 5 2379 6 | 27 1 4 | 39 379 8 |
| 1 379 (49) | 67 8 5 | 2 34679 467 |
|----------------------+----------------------+----------------------|
| 468 56 7 | 48 3 2 | 1 456 9 |
| 248 1 24589 | 489 7 6 | 45 245 3 |
| 3 269 249 | 49 5 1 | 467 8 2467 |
'--------------------------------------------------------------------'
Hint for solution in two steps: for both steps, study the interaction
between (49)r6c3 and row 4.
This classic sudoku puzzle has a solution in just one step!
(found with Sudoku Architect)
After basics, the configuration is as follows.
,--------------------------------------------------------------------,
| 2 8 359 | 69 679 4 | 35 137 157 |
| 39 6 1 | 5 79 23 | 2348 23478 2478 |
| 35 7 4 | 13 8 123 | 235 6 9 |
|----------------------+----------------------+----------------------|
| 589 3 589 | 689 469 7 | 1 248 24568 |
| 4 2 5789 | 1689 369 16 | 3568 378 5678 |
| 6 1 78 | 2 34 5 | 9 3478 478 |
|----------------------+----------------------+----------------------|
| 138 4 2368 | 7 5 9 | 268 128 1268 |
| 18 9 (68) | 346 2 36 | 7 5 1468 |
| 7 5 26 | 46 1 8 | 246 9 3 |
'--------------------------------------------------------------------'
The idea is to find first a solution in two steps and then,
look if they can be combined in a single step.
My first move involves boxes 1,2,4,7,8; (68)r8c3 is a key part.
After that move,
,------------------------------------------------------,
| 2 8 35 | 69 69 4 | 35 17 17 |
| 9 6 1 | 5 7 23 | 2348 2348 248 |
| 35 7 4 | 1-3 8 123 | 235 6 9 |
|---------------+------------------+-------------------|
| 58 3 589 | 869 469 7 | 1 248 24568 |
| 4 2 5789| 1869 369 16 | 368 378 5678 |
| 6 1 78 | 2 34 5 | 9 3478 478 |
|---------------+------------------+-------------------|
| 138 4 2368| 7 5 9 | 268 128 1268 |
| 18 9 68 | 346 2 36 | 7 5 1468 |
| 7 5 26 | 46 1 8 | 246 9 3 |
'------------------------------------------------------'
there is an ALS-wing that solves the puzzle (boxes 1,2,4,5).
Regarding the solution in one main step, looking if move 2 is possible as the first
step, one notices a single spoiler. But the spoiler being true leads to the
same elimination of the ALS-wing of the previous 2-step solution.
(68)r8c3 (and box 7) does not take part in this second solution.
This classic sudoku puzzle has a solution in three steps!
(found with Sudoku Architect)
After basics, the configuration is as follows.
,-----------------------------------------------------------------------------,
| 9 8 6 | 5 247 237 | 1 37 347 |
| 457 3457 2 | 1 4679 367 | 8 35679 345679 |
| 1457 13457 1345 | 34679 4679 8 | 4579 35679 2 |
|-------------------------+-------------------------+-------------------------|
| 3 14 9 | 2467 5 267 | 247 1267 8 |
| 6 2 7 | 49 8 1 | 3 59 459 |
| 145 145 8 | 234679 24679 2367 | 2479 12679 14679 |
|-------------------------+-------------------------+-------------------------|
| 1247 9 134 | 267 1267 5 | 27 8 137 |
| 8 1357 135 | 27 127 4 | 6 123579 13579 |
| 1257 6 15 | 8 3 9 | 257 4 157 |
'-----------------------------------------------------------------------------'
For move 1, there is a beaultiful relashionship between column 7 and box 6.
This leads to four placements and a hidden triple.
For move 2,
,----------------------------------------------------------------------, | 9 8 6 | 5 247 237 | 1 37 34 | | 457 3457 2 | 1 4679 367 | 8 35679 34569 | | 1457 13457 435 | 34679 4679 8 | 479 35679 2 | |----------------------+-----------------------+-----------------------| | 3 14 9 | 2467 5 267 | 47 126 8 | | 6 2 7 | 49 8 1 | 3 59 459 | | 145 145 8 | 234679 24679 2367 | 479 126 16 | |----------------------+-----------------------+-----------------------| | 47 9 34 | 67 167 5 | 2 8 13 | | 8 357 35 | 27 127 4 | 6 139 139 | | 2 6 1 | 8 3 9 | 5 4 7 | '----------------------------------------------------------------------'
there is a nice wing, not available before those placements and eliminations.
For move 3,
,-----------------------------------------------------------,
| 9 8 6 | 5 427 27 | 1 37 34 |
| 457 3 2 | 1 9 67 | 8 567 456 |
| 4157 4157 45 | 3 467 8 | 9 567 2 |
|--------------------+------------------+-------------------|
| 3 14 9 | 267 5 267 | 47 126 8 |
| 6 2 7 | 4 8 1 | 3 59 59 |
| 145 145 8 | 9 267 3 | 47 126 16 |
|--------------------+------------------+-------------------|
| 47 9 34 | 67 167 5 | 2 8 13 |
| 8 57 35 | 27 127 4 | 6 139 139 |
| 2 6 1 | 8 3 9 | 5 4 7 |
'-----------------------------------------------------------'
there is an ALS-wing involving neighbour boxes.
Steps 1 and 2 can be replaced by a kraken-cell (almost M-wing).
This Classic Sudoku puzzle has a solution in 3 steps (2nd, 3rd are easy))!
(found with Sudoku Architect)
After basics
,-----------------------------------------------------------,
| 9 2 347 | 1 8 37 | 346 5 367 |
| 3678 468 3478 | 5 369 2 | 1 348 3789 |
| 3678 5 1 | 4 369 379 | 39 2 3789 |
|-------------------+-------------------+-------------------|
| 1 89 6 | 28 234 348 | 7 39 5 |
| 4 7 2 | 9 5 13 | 8 136 36 |
| 5 3 89 | 6 7 18 | 2 19 4 |
|-------------------+-------------------+-------------------|
| 36 469 349 | 28 249 489 | 5 7 1 |
| 2 489 5 | 7 1 6 | 349 348 389 |
| 78 1 4789 | 3 49 5 | 469 468 2 |
'-----------------------------------------------------------'
For move 1, look for interactions: blocks 2, 3 and 6.
In more detail: look for an almost Y-wing that almost solves the puzzle.
(needs something like two skyscrapers to finish)
This classic sudoku puzzle has a solution in just 2 steps.
(found with Sudoku Architect)
After basics
,------------------------------------------------------------------,
| 1 79 2 | 3 6 4 | 89 789 5 |
| 58 6 39 | 15789 2 1579 | 139 4 379 |
| 58 3479 349 | 15789 158 1579 | 6 1279 2379 |
|--------------------+------------------------+--------------------|
| 347 234 5 | 26789 348 23679 | 3489 289 1 |
| 347 8 134 | 12579 1345 123579 | 3459 6 2349 |
| 9 1234 6 | 1258 13458 1235 | 7 258 234 |
|--------------------+------------------------+--------------------|
| 34 1349 7 | 26 135 26 | 1459 159 8 |
| 2 5 19 | 4 7 8 | 19 3 6 |
| 6 134 8 | 15 9 135 | 2 157 47 |
'------------------------------------------------------------------'
(Jan 01, 2025)
Look carefully at Box 3 and Row 2.
(Why these two houses ? The three "39s" in Row 2 are a sort of clue.)
Happy New Year !!
I propose the following puzzle to be solved * without pencilmarks *
i.e., without writing candidates in the cells.
(found with Sudoku Architect)
Using the given digits, the following configuration should be obtained.
Digits marked with ** are derived digits (to distinguish from the given digits).
,---------+---------+---------,
| 6 3 8 | . 5 . | 4 *2* 9 |
| 7 1 9 |*2* 3 4 | . 5 . |
| . . *2*| . 8 . | 1 . . |
|---------+---------+---------|
| 2 9 . | . 6 . | 5 . 4 |
| . . 5 | 3 . *2*| 9 . . |
|*8* . . | . 9 . |*2* . *7*|
|---------+---------+---------|
| . . *4*| . . . |*7* 9 . |
| . 8 . | . . . | . *4* . |
| 9 . . | . . . | . . 1 |
'-----------------------------'
Update (Jan 6, 2025):
Step 1: a key digit can be placed as a consequence of
,---------+---------+---------,
| 6 3 8 | . 5 . | 4 *2* 9 | (17)r1c46
| 7 1 9 |*2* 3 4 | . 5 . | (68)r2c79
| . . *2*| . 8 . | 1 . . | (69)r3c46
|---------+---------+---------|
| 2 9 . | . 6 . | 5 . 4 |
| . x 5 | 3 x *2*| 9 . . | --.
|*8* . . | . 9 . |*2* . *7*| |
|---------+---------+---------| |----- 4 can only go here at column 5
| . . *4*| . . . |*7* 9 . | | 7 can only go here at column 2
| . 8 . | . . . | . *4* . | |
| 9 x . | . x . | . . 1 | --'
'-----------------------------'
^ ^
'---------'
2 can only go here at row 9
7 can only go here at row 5
Step 2: search for a unique rectangle.
I propose the following tough puzzle
(found with Sudoku Architect)
Study carefully boxes 3,6,9 of the configuration after basics.
,------------------------------------------------------------------------------,
| 13469 1347 34679 | 358 568 2 | 13459 1389 1345689 | 9
| 2369 5 8 | 7 1 4 | 39 239 2369 | 8
| 12346 1234 2346 | 358 9 356 | 1345 1238 7 | 7
|--------------------------+------------------------+--------------------------|
| 34568 3478 3467 | 1 45678 35679 | 2 379 349 | 6
| 123468 9 23467 | 348 4678 367 | 1347 5 134 | 5
| 1345 1347 347 | 3459 2 3579 | 8 6 1349 | 4
|--------------------------+------------------------+--------------------------|
| 239 23 5 | 249 47 8 | 6 12379 1239 | 3
| 7 248 249 | 6 3 1 | 59 289 2589 | 2
| 2389 6 1 | 259 57 579 | 379 4 2389 | 1
'------------------------------------------------------------------------------'
a b c d e f g h i
update (Jan 18, 2025)
This difficult puzzle is solvable in 4 steps. The first step is the hardest to see.
One good start is the bivalued cell (59)g2 and the observation that at box 3,
i89 has an AHS (6 is locked). There is a powerful Loop with cells in boxes 1 and 3.
This was my way to find a Sue de Coq in this puzzle.
Another way (no loop) involves only boxes 6 and 9: find two ALS connected to an AALS.
It is important to pay attention to all possible eliminations: -9 c2 is crucial!
After that important move, the configuration is the following
,------------------------------------------------------------------------------,
| 1346 7 9 | 358 568 2 | 1345 138 568 | 9
| 236 5 8 | 7 1 4 | 39 239 26 | 8
| 12346 1234 2346 | 358 9 356 | 1345 1238 7 | 7
|-------------------------+-------------------------+--------------------------|
| 34568 348 3467 | 1 45678 35679 | 2 37 349 | 6
| 123468 9 23467 | 348 4678 367 | 137 5 134 | 5
| 1345 134 347 | 3459 2 3579 | 8 6 1349 | 4
|-------------------------+-------------------------+--------------------------|
| 239 23 5 | 249 47 8 | 6 137 123 | 3
| 7 248 24 | 6 3 1 | 59 289 258 | 2
| 2389 6 1 | 259 57 579 | 37 4 238 | 1
'------------------------------------------------------------------------------'
a b c d e f g h i
Looking at the eliminations from move 1, there is a wing at boxes 6,9 (two wings, actually).
For move 3, study carefully the configuration of 3.
The final move involves boxes 2 and 3.
Update (Jul 19, 2025!)
,------------------------------------------------------------------------------,
| 1346 7 9 | 358 568 2 | 1345 138 568 | 9
| 236 5 8 | 7 1 4 | 39 239 26 | 8
| 12346 1234 2346 | 358 9 356 | 1345 1238 7 | 7
|-------------------------+-------------------------+--------------------------|
| 34568 348 3467 | 1 45678 35679 | 2 37 349 | 6
| 123468 9 23467 | 348 4678 367 | 13-7 5 134 | 5
| 1345 134 347 | 3459 2 3579 | 8 6 1349 | 4
|-------------------------+-------------------------+--------------------------|
| 239 23 5 | 249 47 8 | 6 13-7 123 | 3
| 7 248 24 | 6 3 1 | 59 289 258 | 2
| 2389 6 1 | 259 57 579 | 37 4 238 | 1
'------------------------------------------------------------------------------'
a b c d e f g h i
For move 2, we have a Grouped W-wing => -7 h3, g5 [10 placements and LC elimination]
(an alternative is a Grouped S-Wing => -3 h6 [10 placements and LC elimination])
The previous hint for move 3 is sufficient.
The scenario for the last move (move 4) is
,--------------------------------------------------------------,
| 1346 7 9 | 35 8 2 | 145-3 1-3 56 | 9
| 36 5 8 | 7 1 4 | 39 29 26 | 8
| 1234 1234 234 | 35 9 6 | 1345 8 7 | 7
|---------------------+------------------+---------------------|
| 3458 348 346 | 1 46 35 | 2 7 9 | 6
| 1234 9 23467 | 8 46 37 | 13 5 134 | 5
| 1345 134 347 | 9 2 357 | 8 6 134 | 4
|---------------------+------------------+---------------------|
| 9 23 5 | 4 7 8 | 6 13 123 | 3
| 7 248 24 | 6 3 1 | 59 29 258 | 2
| 38 6 1 | 2 5 9 | 7 4 38 | 1
'--------------------------------------------------------------'
a b c d e f g h i
and the previous hint is sufficient.
On the occasion of completing one year of this Website,
I propose the following Classic Sudoku puzzle.
(found with Sudoku Architect)
After basics moves, one should get the following configuration:
,--------------------------------------------------------------------,
| 2 6 9 | 7 13 13 | 4 8 5 |
| 5 1 3 | 8 4 26 | 267 9 27 |
| 4 7 8 | 29 69 5 | 126 12 3 |
|----------------------+----------------------+----------------------|
| 9 2 145 | 1345 8 147 | 37 6 47 |
| 7 8 45 | 3459 569 469 | 239 24 1 |
| 6 3 14 | 149 2 1479 | 79 5 8 |
|----------------------+----------------------+----------------------|
| 3 59 7 | 12459 159 8 | 125 124 6 |
| 8 4 6 | 1259 7 129 | 125 3 29 |
| 1 59 2 | 6 359 349 | 8 7 49 |
'--------------------------------------------------------------------'
Update (Feb 15/16, 2025):
There exists a solution in 3 steps.
For step 1, the strong links (1)r1c5=(1)r7c5, (3)r1c5=(3)r9c5
are important together with the almost X-wing on 1.
So, the first move was found by noticing that almost X-wing.
(but the final written move has no X-wing in it!).
That move eliminates (1)r7c5 and gives 7 placements.
After move 1 and its consequences, we get the following
,----------------------------------------------------,
| 2 6 9 | 7 1 3 | 4 8 5 |
| 5 1 3 | 8 4 26 | 267 9 27 |
| 4 7 8 | 29 69 5 | 126 12 3 |
|---------------+------------------+-----------------|
| 9 2 145 | 35 8 147 | 37 6 47 |
| 7 8 45 | 35 69 469 | 239 24 1 |
| 6 3 14 | 149 2 1479 | 79 5 8 |
|---------------+------------------+-----------------|
| 3 9 7 | 24 5 8 | 12 124 6 |
| 8 4 6 | 129 7 129 | 5 3 29 |
| 1 5 2 | 6 3 49 | 8 7 49 |
'----------------------------------------------------'
Here, the hint is to look carefully at the pattern of 2, since
it allows one to get more than the simple X-wing elimination.
After move 2, the puzzle is solved easily with an skyscraper.
I propose the following Classic Sudoku puzzle that can be solved in 4 steps.
(found with Sudoku Architect)
After basics moves, one should get the following configuration:
,--------------------------------------------------------------------,
| 246 38 246 | 239 5 239 | 678 678 1 | 9
| 7 9 13 | 13 8 6 | 2 5 4 | 8
| 26 18 5 | 7 4 12 | 68 3 9 | 7
|----------------------+----------------------+----------------------|
| 1348 6 1347 | 2348 27 23478 | 9 247 5 | 6
| 3489 2 3479 | 5 679 34789 | 1 467 37 | 5
| 349 5 3479 | 23469 1 23479 | 367 2467 8 | 4
|----------------------+----------------------+----------------------|
| 126 17 126 | 48 3 458 | 458 9 27 | 3
| 239 4 239 | 168 67 1578 | 3578 78 237 | 2
| 5 37 8 | 249 279 2479 | 347 1 6 | 1
'--------------------------------------------------------------------'
a b c d e f g h i
This puzzle is not so easily defeated!
The initial hint is to look carefully at box 8.
There is a solution in 4 steps (only chains - no krakens).
Update (Mar 4, 2025)
In box 8, if no seven is true at e1,f1, then then we must have 7 at e2 or f2.
However, in that box, digit 1 must be true at d2 or f2, and digit 6 must be
true at d2 or e2. So, if 7 is false at e1, f1, then (761) must occupy d2, e2, f2.
This observation is the key to show that 5 and 8 must be false at f2
[it gives 2 placements, 1 locked candidate and 1 hidden triple (or naked quad)].
[A more powerful observation exists for box 8, but it belongs to a more complex
and powerful move]
After this, step 2 is easy:
,--------------------------------------------------------------------,
| 246 38 246 | 239 5 239 | 678 678 1 |
| 7 9 13 | 13 8 6 | 2 5 4 |
| 26 18 5 | 7 4 12 | 68 3 9 |
|----------------------+----------------------+----------------------|
| 1348 6 1347 | 234 27 23478 | 9 247 5 |
| 3489 2 3479 | 5 679 34789 | 1 467 37 |
| 349 5 3479 | 23469 1 23479 | 367 2467 8 |
|----------------------+----------------------+----------------------|
| 126 17 126 | 48 3 5 | 48 9 27 |
| 239 4 239 | 168 67 17 | 5 78 23 |
| 5 37 8 | 249 279 2479 | 347 1 6 |
'--------------------------------------------------------------------'
xy-chain eliminates (8)g3 [3 placements and Naked Pair elimination].
Update (Mar 5, 2025):
Step 3:
,--------------------------------------------------------------------,
| 246 38 246 | 239 5 239 | 678 67 1 | 9
| 7 9 13 | 13 8 6 | 2 5 4 | 8
| 26 18 5 | 7 4 12 | 68 3 9 | 7
|----------------------+----------------------+----------------------|
| 1348 6 1347 | 234 27 23478 | 9 24-7 5 | 6
| 3489 2 3479 | 5 679 34789 | 1 46-7 37 | 5
| 349 5 3479 | 23469 1 23479 | 367 246-7 8 | 4
|----------------------+----------------------+----------------------|
| 126 17 126 | 8 3 5 | 4 9 27 | 3
| 239 4 239 | 16 67 17 | 5 8 23 | 2
| 5 37 8 | 249 29 249 | 37 1 6 | 1
'--------------------------------------------------------------------'
a b c d e f g h i
another simple chain involving 5 boxes removes (7) from h456.
Step 4 (last):
,--------------------------------------------------------------------,
| 246 38 246 | 239 5 239 | 68 7 1 | 9
| 7 9 13 | 13 8 6 | 2 5 4 | 8
| 26 18 5 | 7 4 12 | 68 3 9 | 7
|----------------------+----------------------+----------------------|
| 1348 6 1347 | 234 27 23478 | 9 24 5 | 6
| 3489 2 3479 | 5 679 34879 | 1 46 37 | 5
| 349 5 3479 | 23469 1 23479 | 37 246 8 | 4
|----------------------+----------------------+----------------------|
| 126 17 126 | 8 3 5 | 4 9 27 | 3
| 239 4 239 | 16 6-7 17 | 5 8 23 | 2
| 5 37 8 | 249 29 249 | 37 1 6 | 1
'--------------------------------------------------------------------'
a b c d e f g h i
another simple chain involving 3 boxes shows that 7 is false at e2, solving the puzzle.
Instead of Step 3, we can go after the elimination of Step 4. This gives a solution
in three steps, but I only found a way with an almost-chain in step 3
[equivalent to a Kraken Row(6)d4,g4,h4] with the same steps 1 and 2 above.
Later, after studying more this puzzle [mainly what is going on in box 8]
I found a solution in two steps, with two krakens: a kraken cell (458)g3 for step 1
and the kraken mentioned above for step 2 (eliminates (6)d2). If someone wants to
pursue that route, it started with the observation that (4)d3.f3 = (429)d1.e1.f1
and the whole move eliminates (7)e1, (7)f1 [giving 5 placements out of step 1].
I haven't found a solution in just one step.
I propose the following Classic Sudoku puzzle.
(the non-minimal version found a while ago with QQwing Sudoku)
After basics moves, one should get the following configuration:
,-----------------------------------------------------------,
| 1 48 2468 | 246 5 7 | 9 3 246 | 9
| 7 3 246 | 1246 9 1246 | 1246 5 8 | 8
| 26 5 9 | 3 8 1246 | 7 126 1246 | 7
|-------------------+-------------------+-------------------|
| 8 6 7 | 5 14 9 | 1234 12 1234 | 6
| 3 14 5 | 1246 7 1246 | 8 16 9 | 5
| 9 2 14 | 8 146 3 | 5 7 146 | 4
|-------------------+-------------------+-------------------|
| 5 17 3 | 9 2 8 | 16 4 167 | 3
| 4 178 1268 | 16 136 5 | 123 9 1237 | 2
| 26 9 126 | 7 1346 146 | 123 8 5 | 1
'-----------------------------------------------------------'
a b c d e f g h i
Update (Mar 12, 2025):
Step 1: a complex finned fish eliminates (4)e6 [2 placements and LC elimination].
,-----------------------------------------------------------, | 1 48 2468 | 246 5 7 | 9 3 24-6 | 8 | 7 3 246 | 1246 9 1246 | 1246 5 8 | 8 | 26 5 9 | 3 8 1246 | 7 16 124-6 | 7 |-------------------+-------------------+-------------------| | 8 6 7 | 5 1 9 | 34 2 34 | 6 | 3 14 5 | 246 7 246 | 8 16 9 | 5 | 9 2 14 | 8 46 3 | 5 7 16 | 4 |-------------------+-------------------+-------------------| | 5 17 3 | 9 2 8 | 16 4 167 | 3 | 4 178 1268 | 16 36 5 | 123 9 1237 | 2 | 26 9 126 | 7 346 146 | 123 8 5 | 1 '-----------------------------------------------------------' a b c d e f g h i For Step 2, there is an ALS chain that eliminates (6)i7, (6)i9.
,----------------------------------------------------, | 1 4-8 2468 | 246 5 7 | 9 3 24 | 9 | 7 3 246 | 1246 9 1246 | 1246 5 8 | 8 | 26 5 9 | 3 8 1246 | 7 16 124 | 7 |----------------+-----------------+-----------------| | 8 6 7 | 5 1 9 | 34 2 34 | 6 | 3 14 5 | 246 7 246 | 8 16 9 | 5 | 9 2 14 | 8 46 3 | 5 7 16 | 4 |----------------+-----------------+-----------------| | 5 17 3 | 9 2 8 | 16 4 176 | 3 | 4 178 1268 | 16 36 5 | 123 9 1723 | 2 | 26 9 126 | 7 346 146 | 123 8 5 | 1 '----------------------------------------------------' a b c d e f g h i Now, for Step 3, a neat almost UR move eliminates (8)b9. After this only singles remain!
I propose the following Classic Sudoku puzzle (SE = 7.1).
(found with Sudoku Architect)
After basics moves, one should get the following configuration:
,-----------------------------------------------------------------------------,
| 2 1467 16 | 147 8 4567 | 4567 3 9 |
| 46 5 3 | 279 46 279 | 8 1 27 |
| 9 1467 8 | 3 1456 24567 | 24567 2457 24567 |
|-------------------------+-------------------------+-------------------------|
| 46 246 7 | 5 16 269 | 3 289 128 |
| 5 8 269 | 1249 1346 23469 | 12479 2479 1247 |
| 1 3 29 | 249 7 8 | 2459 6 245 |
|-------------------------+-------------------------+-------------------------|
| 7 9 56 | 8 2 1 | 456 45 3 |
| 3 12 4 | 6 9 57 | 1257 2578 12578 |
| 8 126 1256 | 47 345 3457 | 125679 2579 12567 |
'-----------------------------------------------------------------------------'
Update (March 28, 2025)
,-----------------------------------------------------------------------------,
| 2 1467 16 | 147 8 4567 | 4567 3 9 | 9
| 46 5 3 | 279 46 279 | 8 1 27 | 8
| 9 1467 8 | 3 1456 24567 | 24567 2457 24567 | 7
|-------------------------+-------------------------+-------------------------|
| 46 246 7 | 5 16 269 | 3 289 128 | 6
| 5 8 269 | 1249 1346 23469 | 12479 2479 1247 | 5
| 1 3 29 | 249 7 8 | 2459 6 245 | 4
|-------------------------+-------------------------+-------------------------|
| 7 9 5-6 | 8 2 1 | 456 45 3 | 3
| 3 12 4 | 6 9 57 | 1257 2578 12578 | 2
| 8 126 125-6 | 47 345 3457 | 125679 2579 12567 | 1
'-----------------------------------------------------------------------------'
a b c d e f g h i
For Step 1, there is a W-wing with transport that eliminates (6)c1, (6)c3.
This move gives 5 placements and locked candidates eliminations.
The resulting board is displayed below.
,----------------------------------------------------------------------,
| 2 147 6-1 | 147 8 4567 | 457 3 9 | 9
| 46 5 3 | 279 46 279 | 8 1 27 | 8
| 9 147 8 | 3 145 2457 | 2457 257 6 | 7
|----------------------+-----------------------+-----------------------|
| 46 24 7 | 5 16 269 | 3 289 128 | 6
| 5 8 269 | 1249 1346 23469 | 1279 279 1247 | 5
| 1 3 29 | 249 7 8 | 259 6 245 | 4
|----------------------+-----------------------+-----------------------|
| 7 9 5 | 8 2 1 | 6 4 3 | 3
| 3 12 4 | 6 9 57 | 1257 2578 12578 | 2
| 8 6 12 | 47 345 3457 | 12579 2579 1257 | 1
'----------------------------------------------------------------------'
a b c d e f g h i
There is a powerful move that finishes this puzzle by eliminating (1)c9.
Can you find it ?
Update (Mar 30,2025): Only boxes 4,7,9 are not involved in move 2, that eliminates (1)c9
and solves the puzzle with singles. The ALS (457)d1.f2 participates in that move.
,----------------------------------------------------------------------,
| 2 147 6-1 | 147 8 4567 | 457 3 9 | 9
| 46 5 3 | 279 46 279 | 8 1 27 | 8
| 9 147 8 | 3 145 2457 | 2457 257 6 | 7
|----------------------+-----------------------+-----------------------|
| 46 24 7 | 5 16 269 | 3 289 128 | 6
| 5 8 269 | 1249 1346 23469 | 1279 279 1247 | 5
| 1 3 29 | 2(4)9 7 8 | 259 6 245 | 4
|----------------------+----|------------------+-----------------------|
| 7 9 5 | 8 | 2 1 | 6 4 3 | 3
| 3 12 4 | 6 | 9 .--(57) | 1257 2578 12578 | 2
| 8 6 12 | (47) 34(5) 3457 | 12579 2579 1257 | 1
'----------------------------------------------------------------------'
a b c d e f g h i
After basics,can you find a move that essentially solves (ste) the following Classic Sudoku puzzle ?
(found with Sudoku Architect)
After basics, one gets the following:
,-------------------------------------------------------,
| 1 2357 235 | 35 257 6 | 4 8 9 |
| 37 49 6 | 49 27 8 | 5 237 1 |
| 8 234579 23459 | 3459 1 279 | 6 237 237 |
|-------------------+----------------+------------------|
| 6 89 7 | 59 3 4 | 289 1 258 |
| 4 1 89 | 6 257 279 | 3 579 578 |
| 2 35 35 | 1 8 79 | 79 4 6 |
|-------------------+----------------+------------------|
| 9 378 1 | 2 4 5 | 78 6 378 |
| 35 2348 2348 | 7 6 1 | 289 2359 23458 |
| 57 6 24 | 8 9 3 | 1 257 2457 | (SE = 7.3)
'-------------------------------------------------------'
Update (Mar 31, 2025)
,-------------------------------------------------------,
| 1 2357 235 | 35 257 6 | 4 8 9 | 9
| 37 49 6 | 49 27 8 | 5 237 1 | 8
| 8 234579 23459 | 3459 1 279 | 6 237 237 | 7
|-------------------+----------------+------------------|
| 6 89 7 | 5-9 3 4 | 289 1 258 | 6
| 4 1 89 | 6 257 279 | 3 579 578 | 5
| 2 35 35 | 1 8 79 | 79 4 6 | 4
|-------------------+----------------+------------------|
| 9 378 1 | 2 4 5 | 78 6 378 | 3
| 35 2348 2348 | 7 6 1 | 289 2359 23458 | 2
| 57 6 24 | 8 9 3 | 1 257 2457 | 1
'-------------------------------------------------------'
a b c d e f g h i
The strong link (7)r7c7 = (7)r7c7 and the pattern of (8) can be used
to show that (9)d6 is false, solving the puzzle with singles.
I propose the following tough Classic Sudoku puzzle (SE = 8.2)
(found with Sudoku Architect)
After basics, one gets the following:
,--------------------------------------------------------------------,
| 23 157 24 | 1347 13479 6 | 3579 345 8 | 9
| 8 17 9 | 5 1347 1347 | 237 6 234 | 8
| 36 57 46 | 3478 34789 2 | 1 345 3459 | 7
|----------------------+----------------------+----------------------|
| 4 8 67 | 9 5 137 | 236 123 1236 | 6
| 17 2 3 | 1478 6 1478 | 589 1458 1459 | 5
| 16 9 5 | 1348 2 1348 | 368 7 1346 | 4
|----------------------+----------------------+----------------------|
| 9 6 8 | 2 13 5 | 4 13 7 | 3
| 5 3 27 | 6 1478 1478 | 28 9 12 | 2
| 27 4 1 | 378 378 9 | 23568 2358 2356 | 1
'--------------------------------------------------------------------'
a b c d e f g h i
Update (Apr 8, 2025)
This puzzle is solvable in two steps.
As it often happens, I missed a nice Sue de Coq at the beginning.
Can you find it ?
I wasn't too upset, because that move does not seem to lead into
a solution in two steps (but can be used for a krakenless solution in
3 steps). My step 1 was stronger, based on an almost chain
(that can be written as a small kraken) that eliminates (2)g2.
After this move we get the following:
,-----------------------------------------------------------,
| 23 157 24 | 137 1379 6 | 3579 345 8 | 9
| 8 17 9 | 5 1347 143 | 237 6 23 | 8
| 36 57 46 | 378 3789 2 | 1 345 359 | 7
|-------------------+-------------------+-------------------|
| 4 8 67 | 9 5 h37 | 236 123 1236 | 6
| 17 2 3 | 4 6 17 | 59 8 59 | 5
| 16 9 5 |i13 2 8 | 36 7 4 | 4
|-------------------+-------------------+-------------------|
| 9 6 8 | 2 13 5 | 4 13 7 | 3
| 5 3 27 | 6 147 14 | 8 9 12 | 2
| 27 4 1 | 378 378 9 | 2356 235 2356 | 1
'-----------------------------------------------------------'
a b c d e f g h i
Now there is a way to finish the puzzle in one step. How ?
Update 2 (April 9, 2025)
,-----------------------------------------------------------,
| 23 157 24 | 137 1379 6 | 3579 345 8 | 9
| 8 17 9 | 5 1347 143 | 237 6 23 | 8
| 3-6 57 46 | 378 3789 2 | 1 345 359 | 7
|-------------------+-------------------+-------------------|
| 4 8 67 | 9 5 h37 | 236 123 1236 | 6
| 17 2 3 | 4 6 17 | 59 8 59 | 5
| 16 9 5 |i13 2 8 | 36 7 4 | 4
|-------------------+-------------------+-------------------|
| 9 6 8 | 2 13 5 | 4 13 7 | 3
| 5 3 27 | 6 147 14 | 8 9 12 | 2
| 27 4 1 | 378 378 9 | 2356 235 2356 | 1
'-----------------------------------------------------------'
a b c d e f g h i
The final move eliminates (6)a7 using a simple chain with 7 strong links using the patterns
of 2 and 3 inside that chain.
Regarding that Sue de Coq for move 1,
,---------------------------------------------------------------------,
| 23 157 24 | 1347 13479 6 | 3579 (345) 8 | 9
| 8 17 9 | 5 1347 1347 | 237 6 23-4 | 8
| 36 57 46 | 3478 34789 2 | 1 (345) 359-4 | 7
|----------------------+----------------------+-----------------------|
| 4 8 67 | 9 5 137 | 236 12-3 1236 | 6
| 17 2 3 | 1478 6 1478 | 589 18-45 1459 | 5
| 16 9 5 | 1348 2 1348 | 368 7 1346 | 4
|----------------------+----------------------+-----------------------|
| 9 6 8 | 2 13 5 | 4 [13] 7 | 3
| 5 3 27 | 6 1478 1478 |{28} 9 {12} | 2
| 27 4 1 | 378 378 9 | 356-28 [2358] 356-2 | 1
'---------------------------------------------------------------------'
a b c d e f g h i
it has the AAALS[12358]h1.h3 doubly linked to both ALSs: ALS1(345)h7.h9, ALS2{128}g2.i2.
The resulting eliminations are displayed above [resulting in two placements and basics].
After this move, how to finish the puzzle without resorting to krakens ?
Final Update (Apr 11, 2025)
My second step
,-----------------------------------------------------------,
| 23 157 24 | 137 1379 6 | 3579 345 8 | 9
| 8 17 9 | 5 1347 134 | 237 6 23 | 8
| 36 57 46 | 378 3789 2 | 1 345 359 | 7
|-------------------+-------------------+-------------------|
| 4 8 67 | 9 5 37-1 | 236 12 1236 | 6
| 17 2 3 | 4 6 178 | 59 18 59 | 5
| 16 9 5 | 138 2 138 | 368 7 4 | 4
|-------------------+-------------------+-------------------|
| 9 6 8 | 2 13 5 | 4 13 7 | 3
| 5 3 27 | 6 1478 148 | 28 9 12 | 2
| 27 4 1 | 378 378 9 | 356 2358 356 | 1
'-----------------------------------------------------------'
a b c d e f g h i
was a grouped S-wing (boxes 4,5,6) eliminating (1)f6 [with 3 placements]
---
The third and final move
,-----------------------------------------------------------,
| 23 157 24 | 137 1379 6 | 3579 345 8 | 9
| 8 17 9 | 5 1347 134 | 237 6 23 | 8
| 36 57 46 | 378 3789 2 | 1 345 359 | 7
|-------------------+-------------------+-------------------|
| 4 8 67 | 9 5 3-7 | 236 12 1236 | 6
| 17 2 3 | 4 6 17 | 59 8 59 | 5
| 16 9 5 | 13 2 8 | 36 7 4 | 4
|-------------------+-------------------+-------------------|
| 9 6 8 | 2 13 5 | 4 13 7 | 3
| 5 3 27 | 6 147 14 | 8 9 12 | 2
| 27 4 1 | 378 378 9 | 356 235 356 | 1
'-----------------------------------------------------------'
a b c d e f g h i
eliminates (7)f6 using a simple chain ("spiral") with 4 strong links.
I propose the following Classic Sudoku puzzle (SE = 7.2).
(found with Sudoku Architect)
After basics moves, one should get the following configuration:
.-----------------------------------------------------------.
| 456 7 9 | 8 15 24 | 3 156 1256 |
| 8 45 3 | 24 15 6 | 125 9 7 |
| 1 2 56 | 9 3 7 | 58 4 568 |
|-------------------+-------------------+-------------------|
| 456 145 2 | 3 9 8 | 7 156 156 |
| 9 8 7 | 5 6 1 | 4 2 3 |
| 56 3 156 | 24 7 24 | 159 8 1569 |
|-------------------+-------------------+-------------------|
| 2 9 15 | 7 8 3 | 6 15 4 |
| 7 6 4 | 1 2 5 | 89 3 89 |
| 3 15 8 | 6 4 9 | 125 7 125 |
'-----------------------------------------------------------'
Update 1 (May 18, 2025)
In this puzzle, the following Bivalue Oddagon(15) pattern
.-----------------------------------------------------------.
| 456 7 9 | 8 15 24 | 3 156 1256 | 9
| 8 45 3 | 24 15 6 | 125 9 7 | 8
| 1 2 56 | 9 3 7 | 58 4 568 | 7
|-------------------+-------------------+-------------------|
| 456 *145 2 | 3 9 8 | 7 *156 156 | 6
| 9 8 7 | 5 6 1 | 4 2 3 | 5
| 56 3 156 | 24 7 24 | 159 8 1569 | 4
|-------------------+-------------------+-------------------|
| 2 9 *15 | 7 8 3 | 6 *15 4 | 3
| 7 6 4 | 1 2 5 | 89 3 89 | 2
| 3 *15 8 | 6 4 9 | 125 7 125 | 1
'-----------------------------------------------------------'
a b c d e f g h i
(marked with *) implies that at least one of the guardians
(4)b6, (6)h6 must be true. However, I did not see a way to use it
directly. As a conseguence of my first step, one of the guardians
gets eliminated and, by placing the remaining guardian, the puzzle
is solved (only singles to the end). So, the challenge of this puzzle
is to find a "good" first step. The strong link (2)g1=(2)g8 is a good
place to start.
Update 2 (May 20, 2025)
Certainly there are other ways. My first step
.-----------------------------------------------------------.
| 456 7 9 | 8 15 24 | 3 156 1256 | 9
| 8 45 3 | 24 15 6 | 125 9 7 | 8
| 1 2 56 | 9 3 7 | 58 4 568 | 7
|-------------------+-------------------+-------------------|
| 456 145 2 | 3 9 8 | 7 156 156 | 6
| 9 8 7 | 5 6 1 | 4 2 3 | 5
| 56 3 156 | 24 7 24 | 159 8 1569 | 4
|-------------------+-------------------+-------------------|
| 2 9 15 | 7 8 3 | 6 15 4 | 3
| 7 6 4 | 1 2 5 | 89 3 89 | 2
| 3 15 8 | 6 4 9 | 2-15 7 125 | 1
'-----------------------------------------------------------'
a b c d e f g h i
can be described by first noticing that either (2)g1 is true, or (1)b1
is true, so -1 g1. This can be shown starting at the strong link already
mentioned: (2)g1=(2)g8 - (2=4)d8 - (4=5)b8 - (5=1)b1.
But we don't need to stop this chain here, to infer that
either (2)g1 is true, or (5)g4 is true, which gives the additional
elimination -5 g1. This completes move 1 (and the final move 2 was
already described). ////
I propose the following Classic Sudoku puzzle (SE = 6.6)
solvable in just one step (after basics) !
(found with Sudoku Architect)
After basics moves, one should get the following configuration:
.-----------------------------------------------------------.
| 578 9 38 | 2 56 4 | 1 378 3678 | 9
| 578 35 4 | 79 56 1 | 69 378 2 | 8
| 1 2 6 | 79 3 8 | 59 4 57 | 7
|-------------------+-------------------+-------------------|
| 58 35 7 | 1 89 6 | 4 2 389 | 6
| 9 6 38 | 5 4 2 | 37 1378 1378 | 5
| 4 1 2 | 3 89 7 | 56 89 56 | 4
|-------------------+-------------------+-------------------|
| 3 7 1 | 6 2 9 | 8 5 4 | 3
| 2 8 9 | 4 1 5 | 37 6 37 | 2
| 6 4 5 | 8 7 3 | 2 19 19 | 1
'-----------------------------------------------------------'
a b c d e f g h i
Update 1 (May 22, 2025
Look carefully at the pattern of 8 and at column i
(to find a beautiful hidden move).
Another finishing move is to look for an ALS-xz with transport !
Final Update (May 23, 2025
Looking carefully at the pattern of 8
.-----------------------------------------------------------.
| 578 9 *(8)3 | 2 56 4 | 1 378 *(8)367 | 9
| 578 35 4 | 79 56 1 | 69 378 2 | 8
| 1 2 6 | 79 3 8 | 59 4 57 | 7
|-------------------+-------------------+-------------------|
| 5-8 35 7 | 1 89 6 | 4 2 *(8)39 | 6
| 9 6 *(8)3 | 5 4 2 | 37 1378 [8]137 | 5
| 4 1 2 | 3 89 7 | 56 89 56 | 4
|-------------------+-------------------+-------------------|
| 3 7 1 | 6 2 9 | 8 5 4 | 3
| 2 8 9 | 4 1 5 | 37 6 37 | 2
| 6 4 5 | 8 7 3 | 2 19 19 | 1
'-----------------------------------------------------------'
a b c d e f g h i
Either we have an skyscraper(8)c5.c9.a6.a9, or (8)i5,
but (8)i5 -> (1)i1 -> (9)i6 -> (8)e6,
so in any case, we have -8 a6.
( Almost Skyscraper: SS(8) c5.c9.a6.a9 = (819)i5.i1.i6 - (9=8)e6 )
But there is a better way!
.-------------------------------------------------------------.
| 578 9 38 | 2 56 4 | 1 378 B(3678) |
|D(8)57 35 4 | 79 56 1 | 69 C(8)37 2 |
| 1 2 6 | 79 3 8 | 59 4 B(57) |
|--------------------+-------------------+--------------------|
| 5-8 35 7 | 1 A(89) 6 | 4 2 A(389) |
| 9 6 38 | 5 4 2 | 37 1378 1378 |
| 4 1 2 | 3 89 7 | 56 89 B(56) |
|--------------------+-------------------+--------------------|
| 3 7 1 | 6 2 9 | 8 5 4 |
| 2 8 9 | 4 1 5 | 37 6 B(37) |
| 6 4 5 | 8 7 3 | 2 19 19 |
'-------------------------------------------------------------'
a b c d e f g h i
(8=93)e6.i6 - (3=5678)i2.i4.i7.i9 - (8)h8 = (8)a8 => -8 a6; ste
I propose the following Classic Sudoku puzzle (SE = 7.2)
solvable in two steps (after basics) !
(found with Sudoku Architect)
After basics moves, one should get the following configuration:
,--------------------------------------------------------------,
| 258 3 28 | 7 9 25 | 1 4 6 | 9
| 24 6 9 | 23 234 1 | 8 5 7 | 8
| 45 7 1 | 68 4568 456 | 3 9 2 | 7
|---------------------+----------------------+-----------------|
| 1237 9 237 | 4 1238 23 | 6 28 5 | 6
| 23 4 5 | 23689 2368 2369 | 7 28 1 | 5
| 12 8 6 | 5 12 7 | 4 3 9 | 4
|---------------------+----------------------+-----------------|
| 6789 5 478 | 1 467 469 | 2 67 3 | 3
| 3679 1 37 | 2369 2367 8 | 5 67 4 | 2
| 367 2 347 | 36 34567 3456 | 9 1 8 | 1
'--------------------------------------------------------------'
a b c d e f g h i
Update 1 (May 25, 2025)
For the first move, there is an ALS XY-Wing move to
remove (2)a8, (2)f9. After this eliminations one gets the following grid
,--------------------------------------------,
| 8 3 2 | 7 9 5 | 1 4 6 | 9
| 4 6 9 | 23 23 1 | 8 5 7 | 8
| 5 7 1 | 68 468 46 | 3 9 2 | 7
|-------------+----------------+-------------|
| 1 9 7 | 4 38 23 | 6 28 5 | 6
| 3 4 5 | 689 68 269 | 7 28 1 | 5
| 2 8 6 | 5 1 7 | 4 3 9 | 4
|-------------+----------------+-------------|
| 69 5 8 | 1 47 49 | 2 67 3 | 3
| 69 1 3 | 29 27 8 | 5 67 4 | 2
| 7 2 4 | 36 5 36 | 9 1 8 | 1
'--------------------------------------------'
a b c d e f g h i
Now, stepping aside an easy way in two more moves,
how can one finish the puzzle in one move ?
Final Update (May 27, 2025)
There are many ways. For instance,
,--------------------------------------------------,
| 8 3 2 | 7 9 5 | 1 4 6 | 9
| 4 6 9 | 23 23 1 | 8 5 7 | 8
| 5 7 1 | 68 468 46 | 3 9 2 | 7
|----------------+----------------+----------------|
| 1 9 7 | 4 38 23 | 6 28 5 | 6
| 3 4 5 | 689 68 26-9 | 7 28 1 | 5
| 2 8 6 | 5 1 7 | 4 3 9 | 4
|----------------+----------------+----------------|
| 69 5 8 | 1 47 49 | 2 67 3 | 3
| 69 1 3 | 29 27 8 | 5 67 4 | 2
| 7 2 4 | 36 5 36 | 9 1 8 | 1
'--------------------------------------------------'
a b c d e f g h i
there exists an ALS-xz move that eliminates (9)f5, and
after this elimination, one only has to find singles to
the end.
I have battled with the following Classic Sudoku puzzle (SE = 7.3).
I hope you enjoy solving it as much as I did!
(found with Sudoku Architect)
This puzzle can be solved in 3 main steps.
After basics moves, one should get the following configuration:
,-----------------------------------------------------------------------,
| 138 1238 28 | 5 7 13 | 469 49 69 | 9
| 9 137 6 | 2 13 4 | 158 1358 357 | 8
| 137 4 5 | 69 69 8 | 12 123 237 | 7
|------------------------+----------------------+-----------------------|
| 468 2689 1 | 7 489 25 | 3 2589 2569 | 6
| 4678 26789 3 | 49 489 25 | 256789 2589 1 | 5
| 5 2789 2789 | 13 13 6 | 2789 289 4 | 4
|------------------------+----------------------+-----------------------|
| 1368 13568 48 | 13468 2 9 | 145 7 35 | 3
| 2 1389 489 | 1348 5 7 | 149 6 39 | 2
| 1367 135679 479 | 1346 46 13 | 12459 123459 8 | 1
'-----------------------------------------------------------------------'
a b c d e f g h i
Update 1 (Jun 23, 2025):
Step 1: Looking at boxes 3, 6, 9 there is a grouped M-ring (M-wing in a Loop)
giving one placement and two locked candidates eliminations. For me it all
started with the bivalued cell (12)g7. The resulting grid is
,----------------------------------------------------------------------,
| 138 1238 28 | 5 7 13 | 69 4 69 | 9
| 9 137 6 | 2 13 4 | 58 1358 57 | 8
| 137 4 5 | 69 69 8 | 12 123 27 | 7
|-------------------------+--------------------+-----------------------|
| 468 2689 1 | 7 489 25 | 3 2589 256 | 6
| 4678 26789 3 | 49 489 25 | 5678 2589 1 | 5
| 5 2789 2789 | 13 13 6 | 78 289 4 | 4
|-------------------------+--------------------+-----------------------|
| 1368 13568 48 | 13468 2 9 | 145 7 35 | 3
| 2 1389 489 | 1348 5 7 | 149 6 39 | 2
| 1367 135679 479 | 1346 46 13 | 12459 12 8 | 1
'----------------------------------------------------------------------'
a b c d e f g h i
How to continue ?
Update 2 (Jun 24, 2025)
For Step 2, there is a nice AHS M-wing available to eliminate (7)a7.
This gives 31 placements (!) and one LC elimination. The grid changes to
,----------------------------------------------------------,
| 8 13 2 | 5 7 13 | 9 4 6 | 9
| 9 7 6 | 2 13 4 | 8 13 5 | 8
| 13 4 5 | 69 69 8 | 2 13 7 | 7
|-------------------+-------------------+-----------------|
| 4 6 1 | 7 8 5 | 3 9 2 | 6
| 7 8 3 | 49 49 2 | 6 5 1 | 5
| 5 2 9 | 13 13 6 | 7 8 4 | 4
|-------------------+-------------------+-----------------|
| 16 5 48 | 168 2 9 | 14 7 3 | 3
| 2 13 48 | 138 5 7 | 14 6 9 | 2
| 136 9 7 | 1346 46 13 | 5 2 8 | 1
'---------------------------------------------------------'
a b c d e f g h i
Now the puzzle is essentially solved in many ways.
I propose the following Classic Sudoku puzzle.
(found with Sudoku Architect)
After basics moves, one should get the following:
,-------------------------------------------------------------------------------,
| 124 1278 2478 | 126 5 9 | 14678 3 124678 | 9
| 1234 6 24578 | 123 2348 238 | 145789 2457 1245789 | 8
| 1234 12358 9 | 7 23468 238 | 14568 2456 124568 | 7
|-------------------------+-------------------------+---------------------------|
| 5 279 6 | 8 1 4 | 3 27 279 | 6
| 8 2379 1 | 2359 2379 2357 | 45679 24567 245679 | 5
| 239 4 27 | 2359 2379 6 | 1579 8 12579 | 4
|-------------------------+-------------------------+---------------------------|
| 46 58 3 | 56 678 1 | 2 9 45678 | 3
| 7 2589 2458 | 23569 23689 2358 | 4568 1 34568 | 2
| 1269 12589 258 | 4 236789 23578 | 5678 567 35678 | 1
'-------------------------------------------------------------------------------'
a b c d e f g h i
Update (Jun 29, 2025): This puzzle has a severe weakness! It is solvable in one step.
Update (Jun 30, 2025)
,-------------------------------------------------------------------------------,
| 124 1278 2478 | 126 5 9 | 14678 3 124678 | 9
| 1234 6 24578 | 123 2348 238 | 145789 2457 1245789 | 8
| 1234 12358 9 | 7 23468 238 | 14568 2456 124568 | 7
|-------------------------+-------------------------+---------------------------|
| 5 279 6 | 8 1 4 | 3 27 279 | 6
| 8 2379 1 | 2359 2379 2357 | 45679 24567 245679 | 5
| 239 4 27 | 2359 2379 6 | 1579 8 12579 | 4
|-------------------------+-------------------------+---------------------------|
|(46) 58 3 |(56) 6(7)8 1 | 2 9 (7)568-4 | 3
| 7 2589 2458 | 23569 23689 2358 | 4568 1 34568 | 2
| 1269 12589 258 | 4 236789 23578 | 5678 567 35678 | 1
'-------------------------------------------------------------------------------'
a b c d e f g h i
The two bivalued cells (46)a3, (56)d3 form an almost locked set that is part of
a chain (with 3 additional strong links) that eliminates (4)i3. After this move,
the puzzle is solved with lclste.
The complete move is:
,-------------------------------------------------------------------------------,
| 124 1278 2478 | 126 5 9 | 14678 3 124678 | 9
| 1234 6 24578 | 123 2348 238 | 145789 2457 1245789 | 8
| 1234 12358 9 | 7 23468 238 | 14568 2456 124568 | 7
|-------------------------+-------------------------+---------------------------|
| 5 279 6 | 8 1 4 | 3 27 279 | 6
| 8 2379 1 |(5)239 2379 (57)23 | 45679 24567 245679 | 5
| 239 4 27 |(5)239 2379 6 | 1579 8 12579 | 4
|-------------------------+-------------------------+---------------------------|
|(46) 58 3 |(56) 6(7)8 1 | 2 9 (7)568-4 | 3
| 7 2589 2458 | 23569 23689 2358 | 4568 1 34568 | 2
| 1269 12589 258 | 4 236789 (7)2358| 5678 567 35678 | 1
'-------------------------------------------------------------------------------'
a b c d e f g h i
(4=65)r7c14 - (5)r56c4 = (5-7)r5c6 = (7)r9c5 - (7)r7c5 = (7)r7c9 => -4 r7c9; lclste
I propose the following Classic Sudoku puzzle.
(found with Sudoku Architect)
After basics moves, one should get the following:
,----------------------------------------------------------------,
| 1489 6 7 | 2 49 189 | 1349 5 1349 |
| 5 3 14 | 7 6 19 | 149 2 8 |
| 1489 1489 2 | 3489 459 13589 | 7 19 6 |
|--------------------+---------------------+---------------------|
| 1349 1459 1345 | 3469 2 3569 | 1359 8 7 |
| 1349 14579 8 | 349 459 3579 | 6 19 2 |
| 2 579 6 | 389 1 35789 | 359 4 359 |
|--------------------+---------------------+---------------------|
| 346 45 345 | 1 8 69 | 2 7 459 |
| 7 148 9 | 5 3 2 | 148 6 14 |
| 168 2 15 | 69 7 4 | 1589 3 159 |
'----------------------------------------------------------------'
Update (Jul 04, 2025): this puzzle is solvable in one step.
,----------------------------------------------------------------,
| 1489 6 7 | 2 49 189 | 1349 5 1349 | 9
| 5 3 14 | 7 6 19 | 149 2 8 | 8
| 1489 1489 2 | 3489 459 13589 | 7 19 6 | 7
|--------------------+---------------------+---------------------|
| 1349 1459 1345 | 3469 2 3569 | 1359 8 7 | 6
| 1349 14579 8 | 349 459 3579 | 6 19 2 | 5
| 2 579 6 | 389 1 35789 | 359 4 359 | 4
|--------------------+---------------------+---------------------|
| 346 45 345 | 1 8 69 | 2 7 459 | 3
| 7 148 9 | 5 3 2 | 148 6 14 | 2
| 168 2 15 | 69 7 4 | 1589 3 159 | 1
'----------------------------------------------------------------'
a b c d e f g h i
Two Y-wings, one Grouped M-wing are available (where ?), but they aren't the one-stepper move.
A small hint is to look the pattern of 4 and the key bivalued cell (14)c8.
Update 2 (Jul 5, 2025)
,----------------------------------------------------------------,
| 1489 6 7 | 2 49 189 | 1349 5 1349 | 9
| 5 3 14 | 7 6 19 | 149 2 8 | 8
| 1489 1489 2 | 3489 459 13589 | 7 19 6 | 7
|--------------------+---------------------+---------------------|
| 1349 1459 1345 | 3469 2 3569 | 1359 8 7 | 6
| 1349 14579 8 | 349 459 3579 | 6 19 2 | 5
| 2 579 6 | 389 1 35789 | 359 4 359 | 4
|--------------------+---------------------+---------------------|
| 346 45 345 | 1 8 69 | 2 7 459 | 3
| 7 148 9 | 5 3 2 | 148 6 14 | 2
| 168 2 15 | 69 7 4 | 1589 3 159 | 1
'----------------------------------------------------------------'
a b c d e f g h i
Y-wing (49-91-14)c8.f8.e9 => -4 a9
Y-wing (45-51-14)b3.c1.c8 => -4 b7, -4 c3
M-wing (9)f8 = (9-4)g8 = (4)gi9 - (4=9)e9 => -9 def7, -9 f9
Update 3 (Jul 6, 2025)
,----------------------------------------------------------------,
| 1489 6 7 | 2 49 18-9 | 1349 5 1349 | 9
| 5 3 (14) | 7 6 1-9 | 149 2 8 | 8
| 1489 1489 2 | 3489 459 1358-9| 7 19 6 | 7
|--------------------+---------------------+---------------------|
| 1349 1459 1345 | 3469 2 3569 | 1359 8 7 | 6
| 1349 14579 8 | 349 459 3579 | 6 19 2 | 5
| 2 579 6 | 389 1 35789 | 359 4 359 | 4
|--------------------+---------------------+---------------------|
| 346 45 345 | 1 8 (69) | 2 7 459 | 3
| 7 148 9 | 5 3 2 | 148 6 14 | 2
| 168 2 15 | 69 7 4 | 1589 3 159 | 1
'----------------------------------------------------------------'
a b c d e f g h i
How to eliminate (9) from f7, f8, f9 in a single move ? After this
elimination the puzzle is solved with only singles. The bivalued
cells (14)c8 and (69)f3 are involved, but we need an almost locked set.
I propose the following Classic Sudoku puzzle.
(found with Sudoku Architect)
After basics moves, one should get the following:
,-------------------------------------------------------,
| 1 2 9 | 4 3 68 | 68 7 5 | 9
| 7 3 68 | 56 1 568 | 9 4 2 | 8
| 4 68 5 | 2 7 9 | 368 38 1 | 7
|-----------------+--------------------+----------------|
| 5 1469 7 | 36 469 2346 | 234 123 8 | 6
| 29 1469 1246 | 8 4569 234567 | 2345 1235 79 | 5
| 289 489 3 | 1 459 2457 | 245 6 79 | 4
|-----------------+--------------------+----------------|
| 6 5 248 | 9 48 1 | 7 28 3 | 3
| 238 1478 1248 | 3567 4568 3456 | 258 9 46 | 2
| 389 4789 48 | 3567 2 3456 | 1 58 46 | 1
'-------------------------------------------------------'
a b c d e f g h i
Update (July 28, 2025)
The pair of (68) at b7, c8 can help eliminating (8)h7,
giving one placement and NP elimination.
,-------------------------------------------------------,
| 1 2 9 | 4 3 68 | 68 7 5 | 9
| 7 3 68 | 56 1 568 | 9 4 2 | 8
| 4 68 5 | 2 7 9 | 68 *3 1 | 7
|-----------------+--------------------+----------------|
| 5 1469 7 | 36 469 2346 | 234 123 8 | 6
| 29 1469 1246 | 8 4569 234567 | 2345 1235 79 | 5
| 289 489 3 | 1 459 2457 | 245 6 79 | 4
|-----------------+--------------------+----------------|
| 6 5 248 | 9 48 1 | 7 28 3 | 3
| 238 1478 1248 | 3567 4568 3456 | 25 9 46 | 2
| 389 4789 48 | 3567 2 3456 | 1 58 46 | 1
'-------------------------------------------------------'
a b c d e f g h i
There is also a wing already available after basics.
Update (July 30, 2025)
. (48)c1 and (48)r3 are the pincers of a W-wing that removes (4)c3, (4)f1
giving 5 placements and basic moves.
,-----------------------------------------------,
| 1 2 9 | 4 3 68 | 68 7 5 | 9
| 7 3 68 | 56 1 568 | 9 4 2 | 8
| 4 68 5 | 2 7 9 | 68 3 1 | 7
|-----------------+---------------+-------------|
| 5 69 7 | 3 69 24 | 24 1 8 | 6
| 29 1469 1246 | 8 569 247 | 3 25 79 | 5
| 289 489 3 | 1 59 247 | 245 6 79 | 4
|-----------------+---------------+-------------|
| 6 5 28 | 9 4 1 | 7 28 3 | 3
| 23 147 124 | 567 8 356 | 25 9 46 | 2
| 389 4789 48 | 567 2 356 | 1 58 46 | 1
'-----------------------------------------------'
a b c d e f g h i
The newly formed bivalued cell c3 can be used for a final move
that solves this puzzle with lclste.
Update (Jul 31, 2025)
,-----------------------------------------------,
| 1 2 9 | 4 3 68 | 68 7 5 | 9
| 7 3 6-8 | 56 1 568 | 9 4 2 | 8
| 4 68* 5 | 2 7 9 | 68 3 1 | 7
|-----------------+---------------+-------------|
| 5 69* 7 | 3 69 24 | 24 1 8 | 6
| 29* 1469 1246 | 8 569 247 | 3 25* 79 | 5
| 289 489 3 | 1 59 247 | 245 6 79 | 4
|-----------------+---------------+-------------|
| 6 5 28* | 9 4 1 | 7 28* 3 | 3
| 23 147 124 | 567 8 356 | 25 9 46 | 2
| 389 4789 48 | 567 2 356 | 1 58 46 | 1
'-----------------------------------------------'
a b c d e f g h i
=> -8 c8 lclste
I propose the following (interesting!) tough Classic Sudoku puzzle.
(found with Sudoku Architect)
After basics moves, one should get the following:
,---------------------------------------------------------------,
| 34 6 9 | 17 5 1237 | 2347 8 2347 | 9
| 358 2 38 | 4 3679 36789 | 1 359 3679 | 8
| 3458 7 1 | 69 369 23689 | 23469 23459 23469 | 7
|-----------------+----------------------+----------------------|
| 2689 1 48 | 569 3469 3569 | 2589 7 29 | 6
| 67 89 5 | 2 1 67 | 3489 349 349 | 5
| 279 3 47 | 8 479 579 | 259 6 1 | 4
|-----------------+----------------------+----------------------|
| 379 459 2 | 15679 8 15679 | 34679 349 34679 | 3
| 1 59 37 | 5679 679 4 | 23679 239 8 | 2
| 789 489 6 | 3 2 79 | 479 1 5 | 1
'---------------------------------------------------------------'
a b c d e f g h i
Update (Aug 3, 2025)
This puzzle is rated 8.4, but it is solvable (manually!) in three krakenless steps.
The first step removes (9)g5, (9)h5, (9)i5 [it gives 6 placements and
additional eliminations with basic moves].
Can you find it ?
Update (Aug 4, 2025)
,---------------------------------------------------------------,
| 34 6 9 | 17 5 1237 | 2347 8 2347 | 9
| 358 2 38 | 4 3679 36789 | 1 359 3679 | 8
| 3458 7 1 | 69 369 23689 | 23469 23459 23469 | 7
|-----------------+----------------------+----------------------|
| 2689 1 48 | 569 3469 3569 | 2589 7 (29) | 6
| 67 8(9) 5 | 2 1 67 | 348-9 34-9 34-9 | 5
| 279 3 47 | 8 479 579 |(259) 6 1 | 4
|-----------------+----------------------+----------------------|
| 379 459 2 | 15679 8 15679 | 34679 349 34679 | 3
| 1 59 37 | 5679 679 4 | 23679 239 8 | 2
| 789 489 6 | 3 2 79 | 479 1 5 | 1
'---------------------------------------------------------------'
a b c d e f g h i
For move 1, the "hub" ALS (259)g4.i6 was noticed as a potential "pincer"
together with (9)b5. Indeed, they can be linked into an als/ahs chain.
For Step 2, one can go fishing!
,----------------------------------------------------------,
| 34 6 9 | 17 5 1237 | 237 8 2347 | 9
| 358 2 38 | 4 3679 36879 | 1 359 3679 | 8
| 3458 7 1 | 69 369 23689 | 2369 23459 23469 | 7
|--------------+----------------------+--------------------|
| 268 1 48 | 569 3469 3569 | 259 7 29 | 6
| 67 9 5 | 2 1 67 | 8 34 34 | 5
| 27 3 47 | 8 479 579 | 259 6 1 | 4
|--------------+----------------------+--------------------|
| 379 4 2 | 15 8 15 | 3679 39 3679 | 3
| 1 5 37 | 679 679 4 | 2379 239 8 | 2
| 79 8 6 | 3 2 79 | 4 1 5 | 1
'----------------------------------------------------------'
a b c d e f g h i
Update (Aug 6, 2025)
After that X-wing (7) in move 2, we have one placement
and naked pairs eliminations, producing the following
,----------------------------------------------------------,
| 34 6 9 | 17 5 123 | 237 8 2347 | 9
| 358 2 38 | 4 3679 3689 | 1 359 3679 | 8
| 3458 7 1 | 69 369 23689 | 2369 23459 23469 | 7
|--------------+----------------------+--------------------|
| 68 1 48 | 569 3469 3569 | 259 7 29 | 6
| 67 9 5 | 2 1 67 | 8 34 34 | 5
| 2 3 47 | 8 47 59 | 59 6 1 | 4
|--------------+----------------------+--------------------|
| 39 4 2 | 15 8 15 | 67 39 67 | 3
| 1 5 37 | 679 679 4 | 239 239 8 | 2
| 79 8 6 | 3 2 79 | 4 1 5 | 1
'----------------------------------------------------------'
a b c d e f g h i
Now, there is an easy move (can be seen as a fish) to solve the
puzzle with singles after finding a naked triple. It is a move
that does not seem promissing unless its consequences are noticed.
In my solving, I dismissed that move. That naked triple turns out
to be the almost locked set used in an als/ahs chain that
eliminates (9)a1. Only two boxes do not take part in that chain.
Afterwards, I realized the simple way [that second fish !].
(Added: Aug 8, 2025)
,------------------------------------------------------,
| 34 6 9 |(17) 5 (12)3 | 237 8 2347 |
|(358) 2 (38)| 4 (7)369 (8)369 | 1 (935) 3679 |
| 3458 7 1 | 69 369 (28)369| 2369 23459 23469 |
|-------------+-------------------+--------------------|
| 68 1 48 | 569 3469 3569 | 259 7 29 |
| 67 9 5 | 2 1 (7)6 | 8 34 34 |
| 2 3 47 | 8 (7)4 59 | 59 6 1 |
|-------------+-------------------+--------------------|
|(9)3 4 2 | 15 8 15 | 67 (9)3 67 |
| 1 5 37 | 679 679 4 | 2379 239 8 |
| 7-9 8 6 | 3 2 (79) | 4 1 5 |
'------------------------------------------------------'
After basics, the following Classic Sudoku puzzle is solvable in just one move !
(found with Sudoku Architect)
After basics moves:
,--------------------------------------------------------------,
| 16 248 2479 | 1268 26789 1279 | 1257 157 3 |
| 16 5 27 | 126 4 3 | 127 8 9 |
| 3 28 79 | 128 79 5 | 6 4 12 |
|--------------------+--------------------+--------------------|
| 5 23 23 | 7 1 49 | 49 6 8 |
| 48 7 6 | 2348 2389 249 | 13459 1359 15 |
| 48 9 1 | 5 38 6 | 34 2 7 |
|--------------------+--------------------+--------------------|
| 2 36 35 | 136 3567 8 | 13579 13579 4 |
| 7 346 8 | 9 356 14 | 1235 135 125 |
| 9 1 345 | 234 2357 247 | 8 357 6 |
'--------------------------------------------------------------'
Update (Aug 11, 2025)
One finishing move has an almost locked set at row 7 ("hubs" available there)
Update (Aug 12, 2025)
I should have written row "3" instead of "7" (see below)
,--------------------------------------------------------------,
| 16 248 2479 | 1268 26789 1279 | 1257 157 3 | 9
| 16 5 (27) | 126 4 3 | 127 8 9 | 8
| 3 8-2 (7)9 | 128 (7)9 5 | 6 4 12 | 7
|--------------------+--------------------+--------------------|
| 5 [23] 23 | 7 1 49 | 49 6 8 | 6
| 48 7 6 | 2348 2389 249 | 13459 1359 15 | 5
| 48 9 1 | 5 38 6 | 34 2 7 | 4
|--------------------+--------------------+--------------------|
| 2 [(36)] (35) |(136) (3567) 8 | 13579 13579 4 | 3
| 7 [346] 8 | 9 356 {14} | 1235 135 125 | 2
| 9 1 345 | 234 2357 247 | 8 357 6 | 1
'--------------------------------------------------------------'
a b c d e f g h
I propose the following puzzle.
(found with Sudoku Architect)
After basics moves:
,---------------------------------------------------------,
| 2369 3679 2679 | 379 59 1 | 56 4 8 | 9
| 4 168 16 | 79 58 2 | 56 3 79 | 8
| 5 38 79 | 34 6 348 | 1 2 79 | 7
|-------------------+------------------+------------------|
| 169 1469 5 | 249 7 489 | 248 16 3 | 6
| 139 2 1479 | 6 489 3489 | 48 157 15 | 5
| 36 3467 8 | 234 1 5 | 9 67 24 | 4
|-------------------+------------------+------------------|
| 1289 149 3 | 5 249 49 | 7 189 6 | 3
| 7 1459 1249 | 8 3 6 | 24 159 1245 | 2
| 2689 4569 2469 | 1 249 7 | 3 589 245 | 1
'---------------------------------------------------------'
a b c d e f g h i
(Update: Sept 4, 2025)
This puzzle is solvable quickly (one move), exploring strong
links in boxes boxes 2, 5 and 6 to eliminate (9)e9 (solves with lclste).
(Update: Sept 5, 2025)
,---------------------------------------------------------,
| 2369 3679 2679 |(9)37 (5)-9 1 | 56 4 8 | 9
| 4 168 16 |(9)7 (58) 2 | 56 3 79 | 8
| 5 38 79 | 34 6 348 | 1 2 79 | 7
|-------------------+------------------+------------------|
| 169 1469 5 |(92)4 7 489 |(28)4 16 3 | 6
| 139 2 1479 | 6 (8)49 3489 |(8)4 157 15 | 5
| 36 3467 8 | 234 1 5 | 9 67 24 | 4
|-------------------+------------------+------------------|
| 1289 149 3 | 5 249 49 | 7 189 6 | 3
| 7 1459 1249 | 8 3 6 | 24 159 1245 | 2
| 2689 4569 2469 | 1 249 7 | 3 589 245 | 1
'---------------------------------------------------------'
a b c d e f g h i
OR
,---------------------------------------------------------,
| 2369 3679 2679 |(9)37 (59) 1 | 56 4 8 | 9
| 4 168 16 |(9)7 (58) 2 | 56 3 79 | 8
| 5 38 79 | 34 6 34-8 | 1 2 79 | 7
|-------------------+------------------+------------------|
| 169 1469 5 |(29)4 7 (8)49 |(28)4 16 3 | 6
| 139 2 1479 | 6 489 3489 | 48 157 15 | 5
| 36 3467 8 | 234 1 5 | 9 67 24 | 4
|-------------------+------------------+------------------|
| 1289 149 3 | 5 249 49 | 7 189 6 | 3
| 7 1459 1249 | 8 3 6 | 24 159 1245 | 2
| 2689 4569 2469 | 1 249 7 | 3 589 245 | 1
'---------------------------------------------------------'
a b c d e f g h i
I propose the following interesting 9x9 Classic Sudoku puzzle.
(found with Sudoku Architect)
After basics moves:
,-----------------------------------------------------------,
| 458 3 58 | 2 9 147 | 157 6 1478 |
| 4568 1 2 | 3678 34 3467 | 579 459 4789 |
| 68 7 9 | 68 14 5 | 12 24 3 |
|-------------------+-------------------+-------------------|
| 7 8 3 | 1 245 24 | 6 2459 249 |
| 9 45 1 | 36 2345 2346 | 8 7 24 |
| 2 45 6 | 9 7 8 | 15 3 14 |
|-------------------+-------------------+-------------------|
| 158 9 578 | 4 12 127 | 3 28 6 |
| 3 6 4 | 5 8 29 | 279 1 279 |
| 18 2 78 | 37 6 1379 | 4 89 5 |
'-----------------------------------------------------------'
Update (Sept 7, 2025)
Search for a y-wing giving 5 placements.
Update (Sept 8, 2025)
The position after elimination of (2)h3 and 5 placements:
,-----------------------------------------------------------,
| 458 3 58 | 2 9 147 | 157 6 1478 | 9
| 4568 1 2 | 3678 34 3467 | 9 45 478 | 8
| 68 7 9 | 68 14 5 | 12 24 3 | 7
|-------------------+-------------------+-------------------|
| 7 8 3 | 1 245 24 | 6 245 9 | 6
| 9 45 1 | 36 2345 2346 | 8 7 24 | 5
| 2 45 6 | 9 7 8 | 15 3 14 | 4
|-------------------+-------------------+-------------------|
| 15 9 57 | 4 12 127 | 3 8 6 | 3
| 3 6 4 | 5 8 9 | 27 1 27 | 2
| 18 2 78 | 37 6 137 | 4 9 5 | 1
'-----------------------------------------------------------'
a b c d e f g h i
Now, an XY-chain with 4 strong links is available.
Update (Sept 10, 2025)
After move 2, we get the following configuration
,-----------------------------------------------------------,
| 458 3 58 | 2 9 147 | 17 6 478 | 9
| 468 1 2 | 3678 34 3467 | 9 5 478 | 8
| 68 7 9 | 68 14 5 | 12 24 3 | 7
|-------------------+-------------------+-------------------|
| 7 8 3 | 1 5 24 | 6 24 9 | 6
| 9 5 1 | 36 234 2346 | 8 7 24 | 5
| 2 4 6 | 9 7 8 | 5 3 1 | 4
|-------------------+-------------------+-------------------|
| 15 9 57 | 4 12 127 | 3 8 6 | 3
| 3 6 4 | 5 8 9 | 27 1 27 | 2
| 18 2 78 | 37 6 137 | 4 9 5 | 1
'-----------------------------------------------------------'
a b c d e f g h i
Now there is at least a M-wing with transport removing (2)i5 to finish the puzzle.