Welcome!
This is a place chosen to make available some ideas (on puzzles, patterns, etc)
that seemed unsuitable for posting in a Forum, but some people may find interesting.
For difficult puzzles, possible solutions will not be shown (only hints).
For other puzzles, the solution wil be hidden so that a serious attempt can be made
without direct access to a solution.
(hopefully this will make the puzzles more interesting for newcomers)
(useful to look up for the meaning of some unfamiliar concept)
I propose this Sudoku-X puzzle to be solved manually **without pencilmarks! **
I had a great time solving it (something unexpected appeared !)
(generated and displayed with Sudoku6Explainer)
+-------+-------+
| . . . | 3 . . |
| . . . | 4 . . |
+-------+-------+
| 3 . . | . . . |
| 5 . . | . . . |
+-------+-------+
| . . . | 2 . . |
| . . . | 6 . . |
+-------+-------+ Sudoku_X
Update 1 (Feb 17, 2026)
+---------+---------+
6 | . . . | 3 . . |
5 | . . *3 | 4 . . |
+---------+---------+
4 | 3 *1 . |*5 . . |
3 | 5 . . |*1 *3 . |
+---------+---------+
2 | . *3 . | 2 . . |
1 | . . . | 6 . *3 |
+---------+---------+ Sudoku_X
a b c d e f
Update 2 (Feb 18, 2026)
Due to (1)d3, digit 1 has only two possible places
at the bottom-right box: e1 or f2. Consider the
consequences of (1)f2, paying close attention to
the restrictions imposed by both diagonals. Some
cells will have only one possible digit, but it
is important to notice the ones that have only two
possible digits.
Update 3 (Feb 19, 2026)
So, the previous hint allows one
to spot a beautiful bivalued oddagon
(impossible pattern), so that we
must have 8.(1)e1! with 4 additional
placements. We arrive at the following
grid:
+-----------+-----------+
6 | . . . | 3 . *1 |
5 |*1 . *3 | 4 . . |
+-----------+-----------+
4 | 3 *1 . |*5 . . |
3 | 5 . . |*1 *3 . |
+-----------+-----------+
2 |*6 *3 *1 | 2 . . |
1 | . . . | 6 *1 *3 |
+-----------+-----------+ Sudoku_X
a b c d e f
Again, we search for a cell with
few possibilities to explore. A
good candidate is cell a1.
Update 4 (Feb 20, 2026)
+-----------+-----------+
6 | D . . | 3 . *1 |
5 |*1 . *3 | 4 . E |
+-----------+-----------+
4 | 3 *1 # |*5 . . |
3 | 5 # . |*1 *3 . |
+-----------+-----------+
2 |*6 *3 *1 | 2 E . |
1 | B . . | 6 *1 *3 |
+-----------+-----------+ Sudoku_X
a b c d e f
(B=2) a1 can't be true because it would
imply (D=4)a6 [& (E=5)e2] and (E=5)f5,
etc [not spoiling the fun !], so that
(2|6) at b3 and c4 [marked below], but
another consequence would be (2)b5
... impossible!
So: 13.(4)a1! 14.(2)a6 and we get
+-----------+-----------+
|*2 . . | 3 . *1 | 6
|*1 . *3 | 4 . . | 5
+-----------+-----------+
| 3 *1 . |*5 . . | 4
| 5 . . |*1 *3 . | 3
+-----------+-----------+
|*6 *3 *1 | 2 . . | 2
|*4 . . | 6 *1 *3 | 1
+-----------+-----------+ Sudoku_X
a b c d e f
How to finish this puzzle ?
I propose this challenging Classic Sudoku puzzle (solvable in 3 steps).
(found with Sudoku 9 Explainer)
,------------------------------------------------------------,
| 6 3 19 | 478 47 5 | 148 489 2 |
| 2 5 19 | 6 3 48 | 48 7 19 |
| 8 7 4 | 9 2 1 | 5 3 6 |
|--------------------+--------------------+------------------|
| 179 4 2678 | 3578 567 278 | 1368 289 19 |
| 5 268 3 | 48 1 9 | 468 248 7 |
| 179 1268 2678 | 3478 467 2478 | 13468 2489 5 |
|--------------------+--------------------+------------------|
| 4 89 58 | 2 59 6 | 7 1 3 |
| 3 169 67 | 147 479 47 | 2 5 8 |
| 17 12 257 | 157 8 3 | 9 6 4 |
'------------------------------------------------------------'
Update 1 (Feb 17, 2026)
Before the solving part, we need to list the important features
noticed in the grid.
,------------------------------------------------------------,
9 | 6 3 19 | 478 47 5 | 148 489 2 |
8 | 2 5 19 | 6 3 48 | 48 7 19 |
7 | 8 7 4 | 9 2 1 | 5 3 6 |
|--------------------+--------------------+------------------|
6 | 179 4 2678 | 3578 567 278 | 1368 289 19 |
5 | 5 268 3 | 48 1 9 | 468 248 7 |
4 | 179 1268 2678 | 3478 467 2478 | 13468 2489 5 |
|--------------------+--------------------+------------------|
3 | 4 89 58 | 2 59 6 | 7 1 3 |
2 | 3 169 67 | 147 479 47 | 2 5 8 |
1 | 17 12 257 | 157 8 3 | 9 6 4 |
'------------------------------------------------------------'
a b c d e f g h i
Some interesting features in the puzzle!
A. W-wing
B. Bivalued Oddagon
C. Some important SLs (different locations): (1)b2 = (1)d2,
(3)d6|(3)g6, (5)d6|(5)e6, (6)c6|(6)e6|(6)g6, (5)c1|(5)d1, (6)b5|(6)g5, (6)b2|(6)b4.b5
D. (2)h5 == (6)g5 [ALS(2468) d5.g5.h5]
E. AHS (356)d6.e6.g6 (due to C)
F. Almost Y-wing (78-84-47)d9.f8.f2
G. (2)b1 == (5)d1, (2)b1 == (6)c2
H. Some key BVCs: a1, b1, c2, d5, f2, g8
I. URs (do not seem useful, at least for now)
J. Single digit patterns: no.
Update 2 (Feb 18, 2026)
One of the easiest path [i.e., simpler moves in 4 steps] takes the
already available W-wing as one of the move, say, move 1.
For move 2, we create more bivalued cells by exploiting itens
C, E above, noticing that EITHER we have the hidden triple (356)d6.e6.g6,
OR (6)c6. This idea allows one to show that -(78)d6 and -(18) g6.
,------------------------------------------------------------,
9 | 6 3 19 | 478 47 5 | 148 489 2 |
8 | 2 5 19 | 6 3 48 | 48 7 19 |
7 | 8 7 4 | 9 2 1 | 5 3 6 |
|--------------------+--------------------+------------------|
6 | 179 4 2678 | 35-78 567 278 | 36-18 289 19 |
5 | 5 268 3 | 48 1 9 | 68 248 7 |
4 | 179 1268 2678 | 3478 467 2478 | 13468 2489 5 |
|--------------------+--------------------+------------------|
3 | 4 89 58 | 2 59 6 | 7 1 3 |
2 | 3 169 67 | 147 479 47 | 2 5 8 |
1 | 17 12 257 | 157 8 3 | 9 6 4 |
'------------------------------------------------------------'
a b c d e f g h i
How ?
Update 3 (Feb 19, 2026)
,------------------------------------------------------------,
9 | 6 3 19 | 478 47 5 | 148 489 2 |
8 | 2 5 19 | 6 3 48 | 48 7 19 |
7 | 8 7 4 | 9 2 1 | 5 3 6 |
|--------------------+--------------------+------------------|
6 | 179 4 2678 | 35-78 567 278 | 36-18 289 19 |
5 | 5 68-2 3 | 48 1 9 | 68 248 7 |
4 | 179 1268 2678 | 3478 467 2478 | 13468 2489 5 |
|--------------------+--------------------+------------------|
3 | 4 89 58 | 2 59 6 | 7 1 3 |
2 | 3 169 67 | 147 479 47 | 2 5 8 |
1 | 17 12 257 | 157 8 3 | 9 6 4 |
'------------------------------------------------------------'
a b c d e f g h i
For move 3, we use the recently created BVCs to show that
2 is false at b5, and this activate the last easy final move.
Next time, alternative [less steps, more complex] will be
mentiioned.
Update 4 (Feb 20, 2026)
After move 3 eliminating (2)b5, we place (2)h5 and (4)d5, releasing
a Y-wing to finish the puzzle.
My actual solution path started eliminating (2)b5 right from the beginning.
,------------------------------------------------------------,
9 | 6 3 19 | 478 47 5 | 148 489 2 |
8 | 2 5 19 | 6 3 48 | 48 7 19 |
7 | 8 7 4 | 9 2 1 | 5 3 6 |
|--------------------+--------------------+------------------|
6 | 179 4 [6]278| 3578 [6]57 278 |[6]138 289 19 |
5 | 5 68-2 3 | 48 1 9 |(6)48 (2)48 7 |
4 | 179 1268 2678 | 3478 467 2478 | 13468 2489 5 |
|--------------------+--------------------+------------------|
3 | 4 89 58 | 2 59 6 | 7 1 3 |
2 | 3 169 67 | 147 479 47 | 2 5 8 |
1 | 17 12 257 | 157 8 3 | 9 6 4 |
'------------------------------------------------------------'
a b c d e f g h i
I started with the observation of item (D) [in the previous list],
reasoning in the following way: if (2)h5 is not true, then (6)h5
(by (D)), so (6)g5 is not true, implying (6)c6|(6)e6. However,
looking at the consequences of either possibility also implies
the elimination of (2)b5, and so +2 h5. This can be written as
Kraken Row (6)c6.e6.g6 => -2 b5 [details omitted: not spoiling
the fun of finding it].
After this move, the W-wing eliminates (4)g5, placing (4)d5, and
allowing the Y-wing to be used to finish the puzzle.
Looking back at that initial list, only the UR and the BVOddagon
did not show up in the solution paths. I invite you to find a way
to eliminate (7) d1.d2 right from the beginning !
This is possible, but the move is complex. It starts a solution
path in three steps. Step 2 removes (2)b5 with the previouly hinted
ALS chain, and the last step is the W-wing available at the start.
All that preliminary observations (A)-(J) helped a lot in solving
the puzzle and realizing other possibilities.
Just the URs do seem to have any effect here.
I really enjoyed studying this (very instructive!) puzzle! /////
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com