The New Sudoku Players' Forum

[tarek]

I've started a thread about 8 clue puzzles at the 8 clue (Regional constraints only) puzzles on the SudokuSolver forum.

I've already posted several examples including symmetrical ones to include the combo (Sudoku, X, Disjoint Groups (DG), Diamond diagonals (DD) & DG diagonals (DGD)) & Clover X Sudokus.

The latest were Anti-Kning Anti Knight puzzles.

the Anti-King Anti-Knight Sudoku is another example where the 8-clue barrier can be easily reached. Here are 4 symmetrical examples of variable difficulties:

This is an EASY

Code: Select all

.............................3.974.............281.5.............................
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 
-------+-------+------
 . . 3 | . 9 7 | 4 . . 
 . . . | . . . | . . . 
 . . 2 | 8 1 . | 5 . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . .

Code: Select all

+-------+-------+-------+
| 2 8 1 | 3 5 9 | 7 4 6 |
| 3 5 9 | 7 4 6 | 2 8 1 |
| 7 4 6 | 2 8 1 | 3 5 9 |
+-------+-------+-------+
| 8 1 3 | 5 9 7 | 4 6 2 |
| 5 9 7 | 4 6 2 | 8 1 3 |
| 4 6 2 | 8 1 3 | 5 9 7 |
+-------+-------+-------+
| 1 3 5 | 9 7 4 | 6 2 8 |
| 9 7 4 | 6 2 8 | 1 3 5 |
| 6 2 8 | 1 3 5 | 9 7 4 |
+-------+-------+-------+

This is a SUPERIOR

Code: Select all

.........................5.2...9.......8.7.......1...4.3.........................
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . 5 . 
-------+-------+------
 2 . . | . 9 . | . . . 
 . . . | 8 . 7 | . . . 
 . . . | . 1 . | . . 4 
-------+-------+------
 . 3 . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . .

Code: Select all

+-------+-------+-------+
| 7 2 1 | 3 5 9 | 4 8 6 |
| 3 5 9 | 4 8 6 | 7 2 1 |
| 4 8 6 | 7 2 1 | 3 5 9 |
+-------+-------+-------+
| 2 1 3 | 5 9 4 | 8 6 7 |
| 5 9 4 | 8 6 7 | 2 1 3 |
| 8 6 7 | 2 1 3 | 5 9 4 |
+-------+-------+-------+
| 1 3 5 | 9 4 8 | 6 7 2 |
| 9 4 8 | 6 7 2 | 1 3 5 |
| 6 7 2 | 1 3 5 | 9 4 8 |
+-------+-------+-------+

This is MILDLY ADVANCED

Code: Select all

.........................5.2...9.7.............8.1...4.3.........................
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . 5 . 
-------+-------+------
 2 . . | . 9 . | 7 . . 
 . . . | . . . | . . . 
 . . 8 | . 1 . | . . 4 
-------+-------+------
 . 3 . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . .

Code: Select all

+-------+-------+-------+
| 8 2 1 | 3 5 9 | 4 7 6 |
| 3 5 9 | 4 7 6 | 8 2 1 |
| 4 7 6 | 8 2 1 | 3 5 9 |
+-------+-------+-------+
| 2 1 3 | 5 9 4 | 7 6 8 |
| 5 9 4 | 7 6 8 | 2 1 3 |
| 7 6 8 | 2 1 3 | 5 9 4 |
+-------+-------+-------+
| 1 3 5 | 9 4 7 | 6 8 2 |
| 9 4 7 | 6 8 2 | 1 3 5 |
| 6 8 2 | 1 3 5 | 9 4 7 |
+-------+-------+-------+

And this is IMPOSSIBLE

Code: Select all

....97..4..................3.........................5..................2..81....
 . . . | . 9 7 | . . 4 
 . . . | . . . | . . . 
 . . . | . . . | . . . 
-------+-------+------
 3 . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . 5 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 2 . . | 8 1 . | . . .

Code: Select all

+-------+-------+-------+
| 6 5 3 | 2 9 7 | 8 1 4 |
| 4 8 1 | 6 5 3 | 2 9 7 |
| 7 2 9 | 4 8 1 | 6 5 3 |
+-------+-------+-------+
| 3 6 5 | 7 2 9 | 4 8 1 |
| 1 4 8 | 3 6 5 | 7 2 9 |
| 9 7 2 | 1 4 8 | 3 6 5 |
+-------+-------+-------+
| 5 3 6 | 9 7 2 | 1 4 8 |
| 8 1 4 | 5 3 6 | 9 7 2 |
| 2 9 7 | 8 1 4 | 5 3 6 |
+-------+-------+-------+

Enjoy,

tarek

[Red Ed]

I prefer the regional constraints to be simpler and clearly visible, like these: du-sum-oh.

[tarek]

I prefer the regional constraints to be simpler and clearly visible, like these: du-sum-oh.

Obviously the simpler the better, The closest thing to simple can be A cloverX puzzle which I posted & a Jigsaw (Hands) by NikoliFreak & similar by Hatman. These can be found in that thread linked in the 1st post above.

tarek

[tarek]

I managed to find a symmetric example with an Anti-Knight top-down Rt-Lt Wrap constraint.

In this variant each cell has 8 cells which are a Knight's move away

here is a demo with cells r1c1(red), r5c2(green) & r6c6(blue) highlighted


The puzzle itself is very difficult so don't solve unaided

Text format

Code: Select all

.........................5.......7.4...1.9...2.8.......3.........................
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . 5 . 
-------+-------+------
 . . . | . . . | 7 . 4 
 . . . | 1 . 9 | . . . 
 2 . 8 | . . . | . . . 
-------+-------+------
 . 3 . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 

Solution

Code: Select all

 6 2 1 | 5 8 7 | 4 9 3 
 3 4 5 | 6 9 2 | 1 8 7 
 9 8 7 | 3 4 1 | 6 5 2 
-------+-------+------
 1 9 3 | 2 5 8 | 7 6 4 
 7 5 4 | 1 6 9 | 2 3 8 
 2 6 8 | 7 3 4 | 5 1 9 
-------+-------+------
 4 3 6 | 9 2 5 | 8 7 1 
 8 7 9 | 4 1 6 | 3 2 5 
 5 1 2 | 8 7 3 | 9 4 6 

[tarek]

The following is my previous posting on the same thread on the SudokuSolver forum

Another example of a constrained puzzle is the Clover X (Sudoku, Windoku, Asterisk & X diagonals), here is a very very difficult 8 clue example:



Text format

Code: Select all

.....9..........5..........2......7...........8......4..........3..........1.....
 . . . | . . 9 | . . . 
 . . . | . . . | . 5 . 
 . . . | . . . | . . . 
-------+-------+------
 2 . . | . . . | . 7 . 
 . . . | . . . | . . . 
 . 8 . | . . . | . . 4 
-------+-------+------
 . . . | . . . | . . . 
 . 3 . | . . . | . . . 
 . . . | 1 . . | . . .

Solution

Code: Select all

526349187497218356318576429263451978954867231781932564142683795635794812879125643
 5 2 6 | 3 4 9 | 1 8 7 
 4 9 7 | 2 1 8 | 3 5 6 
 3 1 8 | 5 7 6 | 4 2 9 
-------+-------+------
 2 6 3 | 4 5 1 | 9 7 8 
 9 5 4 | 8 6 7 | 2 3 1 
 7 8 1 | 9 3 2 | 5 6 4 
-------+-------+------
 1 4 2 | 6 8 3 | 7 9 5 
 6 3 5 | 7 9 4 | 8 1 2 
 8 7 9 | 1 2 5 | 6 4 3

[tarek]

And here is my Post from the similar thread on the SudokuSolver forum regarding the DD X DG DGD constraints

The follwing is a combo (Sudoku, X, Disjoint Groups (DG), Diamond diagonals (DD) & DG diagonals (DGD)) with 42 "Declared" regional constraints.

It is special because it starts with 68 consecutive empty cells & still achieves a single solution. It is beyond What many would consider humanly solvable so no need to attempt un-aided :naughty:

Here is the puzzle with the constraints explained:


Solutin:


& the above in text formats:

Code: Select all

....................................................................6..521.849..7
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . . 6 | . . 5 
 2 1 . | 8 4 9 | . . 7

124935876857261943693478521341687259572394618986152734768513492439726185215849367
 1 2 4 | 9 3 5 | 8 7 6 
 8 5 7 | 2 6 1 | 9 4 3 
 6 9 3 | 4 7 8 | 5 2 1 
-------+-------+------
 3 4 1 | 6 8 7 | 2 5 9 
 5 7 2 | 3 9 4 | 6 1 8 
 9 8 6 | 1 5 2 | 7 3 4 
-------+-------+------
 7 6 8 | 5 1 3 | 4 9 2 
 4 3 9 | 7 2 6 | 1 8 5 
 2 1 5 | 8 4 9 | 3 6 7

Finally with the some programming, I've landed some nice symmetric examples.

Here is an image to explain the constraints

From top Left Clockwise: X diagonals (X), Disjoint Groups (DG), Diamond Diagonals (DD) & Disjoint Groups Diagonals (DGD)

The 1st is an 8 clue puzzle that requires advanced fish

Code: Select all

........438...9...................................................1...752........
 . . . | . . . | . . 4 
 3 8 . | . . 9 | . . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | 1 . . | . 7 5 
 2 . . | . . . | . . . 
162873594387459216945621738439215687521768943876394152758946321694132875213587469

The 2nd is a 9 clue puzzle that requires only "SUPERIOR" level techniques

Code: Select all

................6...1....4........5.....9.....8........3....7...2................
 . . . | . . . | . . . 
 . . . | . . . | . 6 . 
 . . 1 | . . . | . 4 . 
-------+-------+------
 . . . | . . . | . 5 . 
 . . . | . 9 . | . . . 
 . 8 . | . . . | . . . 
-------+-------+------
 . 3 . | . . . | 7 . . 
 . 2 . | . . . | . . . 
 . . . | . . . | . . .
674589123358412967291736845912367458746895231583124679835241796129673584467958312

................6...1....4........5.....9.....8........3....7...2................
d/: x diagonal /
d\: x diagonal \
dG: disjoint group
DGD: disjoint group diagonal
D: diamond
b: box
r: row
c: column
6 is a given clue in r2c8
[r1c789][r2c12345679][r3c79][r4c6][r5c28][r6c48][r7c38][r8c58][r9c18]<>6
1 is a given clue in r3c3
[r1c1239][r2c1236][r3c1245679][r4c34][r5c37][r6c369][r7c35][r8c348][r9c1369]<>1
4 is a given clue in r3c8
[r1c789][r2c79][r3c1245679][r56789c8][r69c5][r9c2]<>4
5 is a given clue in r4c8
[r1c2589][r24c6][r4c1234579][r56c789][r7c58][r8c48][r9c18]<>5
9 is a given clue in r5c5
[r19c159][r24c2456][r3c57][r5c12346789][r68c4568][r7c35]<>9
8 is a given clue in r6c2
[r1c29][r2c26][r3c25][r45c123][r6c13456789][r8c4][r9c1258]<>8
3 is a given clue in r7c2
[r1c258][r23459c2][r47c5][r7c134689][r89c13]<>3
7 is a given clue in r7c7
[r1c1479][r2c267][r3c57][r4c147][r5c37][r6c67][r7c1345689][r8c4789][r9c1789]<>7
2 is a given clue in r8c2
[r1c29][r2c25][r3c27][r4c26][r5c28][r68c4][r7c13][r8c1356789][r9c123]<>2
2 in r2c6 is a hidden single for D2
[r13c456][r2c13479][r5c369][r679c6]<>2
6 in r8c4 is a hidden single for D2
[r134579c4][r5c17][r79c56][r8c13679]<>6
3 in r1c9 is a hidden and naked single
[r1c13467][r23c79][r4c369][r5c19][r6c49][r89c9][r9c5]<>3
4 in r9c1 is the last digit to fill the sector
[r1c15][r245678c1][r49c6][r59c9][r69c47][r789c3]<>4
1 forms a intersection in d/ & b5
[r46c5][r5c46]<>1
7 forms a intersection in d/ & b5
[r46c5][r5c46]<>7
17 is a hidden double in b5
[r4c6]<>8 [r6c4]<>5
5 forms a intersection in d/ & D1
[r1c1][r2c4][r8c6][r9c9]<>5
8 forms a intersection in d/ & D1
[r1c1][r2c4][r8c6][r9c9]<>8
5 forms a intersection in d/ & DGD2
[r3c5][r5c3]<>5
8 forms a intersection in d/ & DGD2
[r5c7][r7c5]<>8
26 is a naked double in d\
[r1c5]<>6 [r4c2]<>6 [r4c4]<>2 [r5c1]<>2 [r5c9]<>6 [r6c6]<>6 [r6c8]<>2 [r9c5]<>2
2 forms a x-wing in b3d\ & r1c9
[r1c3][r467c9]<>2
2 in r4c3 is a hidden single for dG3
[r4c157][r6c13]<>2
2 forms a intersection in b6 & c7
[r19c7]<>2
6 forms a x-wing in b7d\ & r9c1
[r346c1][r9c7]<>6
6 in r6c7 is a hidden single for dG7
[r4c79][r6c359]<>6
2 in r5c7 is a hidden single in more than one sector
[r5c4][r7c5]<>2
2 in r6c5 is a hidden single in more than one sector
[r9c8]<>2
6 in r5c3 is a hidden single for b4
[r19c3][r3c5][r5c6]<>6
3 in r3c5 is a hidden and naked single
[r2c45][r3c146][r69c8][r8c5]<>3
4 in r7c5 is a hidden and naked single
[r14c2][r248c5][r7c469][r8c6]<>4
6 in r4c5 is a hidden single in more than one sector
[r1c2]<>6
4 in r2c4 is a hidden single for D1
[r1c46][r2c23][r45c4][r8c7]<>4
4 in r1c3 is a hidden single in more than one sector
[r4c9][r6c3]<>4
4 in r4c7 is a hidden single in more than one sector
[r6c9]<>4
4 in r5c2 is a hidden single in more than one sector
[r5c6]<>4
4 in r6c6 is a hidden single in more than one sector
r8c9 has the last 4 uncovered
5 in r2c2 is a hidden and naked single
[r2c13579][r3c12][r8c5][r9c2]<>5
5 in r9c5 is a hidden single in more than one sector
[r5c1][r7c46][r9c3467]<>5
3 in r5c8 is a hidden single for b6
[r5c46][r8c8]<>3
3 in r4c4 is a hidden single in more than one sector
[r4c1][r9c4]<>3
8 in r8c8 is a hidden and naked single
[r17c8][r28c5][r7c9][r8c137][r9c7]<>8
8 in r1c5 is a hidden single in more than one sector
[r1c467][r3c46][r5c9]<>8
8 in r4c9 is a hidden single in more than one sector
[r23c9][r7c36]<>8
8 in r3c7 is a hidden single in more than one sector
[r2c7][r3c1][r9c4]<>8
5 in r7c3 is the last digit to fill the sector
[r1c6][r68c3][r7c19][r8c1]<>5
5 in r6c1 is a hidden single in more than one sector
[r3c4]<>5
3 in r6c3 is a hidden single in more than one sector
[r2c3][r9c6]<>3
3 in r2c1 is a hidden single in more than one sector
[r8c7]<>3
8 in r2c3 is a hidden single in more than one sector
[r5c6][r9c3]<>8
5 in r5c6 is a hidden and naked single
[r3c6][r5c4]<>5
8 in r5c4 is a hidden and naked single
[r7c4]<>8
5 in r1c4 is a hidden single in more than one sector
[r1c7]<>5
5 in r3c9 is a hidden single in more than one sector
r8c7 has the last 5 uncovered
9 in r4c1 is a hidden single in more than one sector
[r1c7][r378c1][r7c4]<>9
9 in r6c9 is a hidden single in more than one sector
[r27c9][r39c6][r9c3]<>9
9 in r2c7 is a hidden single in more than one sector
[r1c8][r9c7]<>9
8 in r7c1 is a hidden single in more than one sector
r9c6 has the last 8 uncovered
6 in r1c1 is a hidden single in more than one sector
[r1c6][r3c2][r9c9]<>6
2 in r9c9 is the last digit to fill the sector
[r7c8][r9c4]<>2
2 in r1c8 is a hidden single in more than one sector
2 in r3c1 is a hidden single in more than one sector
r7c4 has the last 2 uncovered
1 in r1c7 is the last digit to fill the sector
[r1c6][r2c9][r9c7]<>1
7 in r2c9 is the last digit to fill the sector
[r2c5][r5c9][r8c36]<>7
1 in r2c5 is the last digit to fill the sector
[r8c5]<>1
7 in r8c5 is the last digit to fill the sector
[r8c1][r9c4]<>7
3 in r9c7 is the last digit to fill the sector
r8c6 has the last 3 uncovered
1 in r5c9 is a hidden and naked single
[r5c1][r6c8][r7c9]<>1
7 in r5c1 is the last digit to fill the sector
[r4c2]<>7
1 in r4c2 is the last digit to fill the sector
[r4c6][r7c8][r9c2]<>1
7 in r4c6 is the last digit to fill the sector
[r13c6][r6c4]<>7
1 in r6c4 is the last digit to fill the sector
[r9c4]<>1
7 in r6c8 is the last digit to fill the sector
[r39c2]<>7
6 in r7c9 is the last digit to fill the sector
1 in r8c1 is the last digit to fill the sector
9 in r8c3 is the last digit to fill the sector
[r9c2]<>9
7 in r9c3 is the last digit to fill the sector
6 in r3c6 is the last digit to fill the sector
6 in r9c2 is the last digit to fill the sector
7 in r1c2 is a hidden single in more than one sector
9 in r1c6 is the last digit to fill the sector
[r3c4][r7c6]<>9
9 in r3c2 is the last digit to fill the sector
[r9c8]<>9
7 in r3c4 is the last digit to fill the sector
1 in r7c6 is the last digit to fill the sector
9 in r7c8 is the last digit to fill the sector
9 in r9c4 is the last digit to fill the sector
1 in r9c8 is the last digit to fill the sector
Puzzle Solved
674589123358412967291736845912367458746895231583124679835241796129673584467958312

[tarek]

The Hands variant (introduced by Nikoli_Freak according to HATMAN) is another Sudoku variant where an 8 clue puzzle is possible ... On the face of it, only 9 extra regions are declared , however ....

From my experiments ... It seems that the irregular groups force the formation of X diagonals & an old lace group which partly explaines the restrained nature of the solution grid. Here are a few symmetric examples

This one should be easy


another easy


This one is solvable


This is a solvable diamond


This is very difficult even with the diagonals, only when the old lace group is used that the difficulty goes down


enjoy,

tarek