The New Sudoku Players' Forum

[urhegyi]

In March 2010 this 14 clues sudoku was discovered by a User called Afmob on the programmers forum.
Is this still the minimum for 2 X 4 and can this sudoku be rated and analyzed showing the different solving methods?

Code: Select all

.... ...1
..23 ....

.... ..4.
56.. .7..

.... 65..
...4 ....

...1 ..2.
.7.. .6..

brute force solution:

Hidden Text: Show

[urhegyi]

When trying to solve I get stuck here:

Edit:
What I found was if R7C6 = 3 then R1C6=2 and R3C6=8 and R4C7=3
In the other case as R7C6 = 8 then R8C8=3 and R4C8<>3 so R4C7 is also 3.

solved but is there a better technique?
I think I have found one a w-wing at R4C7 and R8C8 connected by 2 8ths at R3C6 and R7C6: R4C7=3 or R8C8=3 --> R4C8<>3 --> pair 2/8 at row 4 : conclusion is that R4C7=3; same result as with method above.

[1to9only]

SE Rating:

Code: Select all

.......1..23..........4.56...7......65.....4.......1..2..7...6.. 2Rx4C ED=6.6/1.2/1.2


Solution Path: Show

Code: Select all

1.2, Hidden Single: R4C3: 4 in block: r4c3=4
1.2, Hidden Single: R3C8: 6 in block: r3c8=6
1.2, Hidden Single: R3C5: 5 in block: r3c5=5
1.2, Hidden Single: R5C8: 4 in block: r5c8=4
1.5, Hidden Single: R1C4: 6 in column: r1c4=6
1.2, Hidden Single: R2C7: 6 in block: r2c7=6
1.5, Hidden Single: R8C4: 5 in column: r8c4=5
1.2, Hidden Single: R8C1: 2 in block: r8c1=2
1.2, Hidden Single: R7C8: 5 in block: r7c8=5
1.2, Hidden Single: R1C7: 5 in block: r1c7=5
1.2, Hidden Single: R2C2: 5 in block: r2c2=5
1.2, Hidden Single: R2C1: 1 in block: r2c1=1
1.2, Hidden Single: R6C3: 5 in block: r6c3=5
1.2, Hidden Single: R6C1: 6 in block: r6c1=6
1.2, Hidden Single: R7C3: 6 in block: r7c3=6
1.2, Hidden Single: R7C5: 7 in block: r7c5=7
1.2, Hidden Single: R2C8: 7 in block: r2c8=7
1.5, Hidden Single: R6C7: 7 in row: r6c7=7
1.5, Hidden Single: R8C5: 4 in row: r8c5=4
1.2, Hidden Single: R8C7: 1 in block: r8c7=1
1.5, Hidden Single: R2C6: 4 in row: r2c6=4
1.0, Hidden Single: R2C5: 8 in row: r2c5=8
1.5, Hidden Single: R4C5: 1 in row: r4c5=1
1.2, Hidden Single: R6C6: 1 in block: r6c6=1
2.6, Pointing: Cells R3C1,R3C2,R3C3: 3 in block and row: r3c6<>3
2.6, Pointing: Cells R6C5,R6C8: 2 in block and row: r6c2<>2
3.4, Hidden Pair: Cells R3C2,R5C2: 1,2 in column: r5c2<>3,8, r3c2<>3,8
3.8, Swordfish: Cells R1C5,R1C6,R6C2,R6C5,R7C2,R7C6: 3 in 3 columns and 3 rows: r6c8<>3, r7c1<>3
6.6, Turbot Fish (w/4 nodes): R3C3.8 off: r3c3<>8
6.6, Turbot Fish (w/4 nodes): R5C3.8 off: r5c3<>8
6.6, Turbot Fish (w/4 nodes): R7C2.8 off: r7c2<>8
4.2, XY-Wing: Cells R7C2,R7C1,R6C2 on value 8: r5c1<>8
4.2, XY-Wing: Cells R7C2,R8C3,R1C2 on value 8: r1c3<>8
1.5, Hidden Single: R8C3: 8 in column: r8c3=8
1.0, Hidden Single: R8C8: 3 in row: r8c8=3
1.0, Hidden Single: R7C6: 8 in block: r7c6=8
1.2, Hidden Single: R4C7: 3 in block: r4c7=3
1.0, Hidden Single: R5C7: 8 in column: r5c7=8
1.2, Hidden Single: R4C8: 8 in block: r4c8=8
1.0, Hidden Single: R3C6: 2 in block: r3c6=2
1.0, Hidden Single: R1C6: 3 in column: r1c6=3
1.0, Hidden Single: R1C5: 2 in block: r1c5=2
1.0, Hidden Single: R6C5: 3 in column: r6c5=3
1.0, Hidden Single: R6C8: 2 in block: r6c8=2
1.0, Hidden Single: R4C4: 2 in row: r4c4=2
1.0, Hidden Single: R6C2: 8 in row: r6c2=8
1.2, Hidden Single: R1C1: 8 in block: r1c1=8
1.2, Hidden Single: R1C2: 4 in block: r1c2=4
1.0, Hidden Single: R1C3: 7 in block: r1c3=7
1.2, Hidden Single: R3C4: 8 in block: r3c4=8
1.0, Hidden Single: R5C4: 7 in column: r5c4=7
1.2, Hidden Single: R3C1: 7 in block: r3c1=7
1.2, Hidden Single: R3C3: 3 in block: r3c3=3
1.0, Hidden Single: R3C2: 1 in block: r3c2=1
1.0, Hidden Single: R5C3: 1 in column: r5c3=1
1.2, Hidden Single: R5C2: 2 in block: r5c2=2
1.0, Hidden Single: R5C1: 3 in block: r5c1=3
1.0, Hidden Single: R7C1: 4 in column: r7c1=4
1.0, Hidden Single: R7C2: 3 in block: r7c2=3
ED=6.6/1.2/1.2



[1to9only]

Here is an alternative solution, using W-Wing.

SE Rating:

Code: Select all

.......1..23..........4.56...7......65.....4.......1..2..7...6.. 2Rx4C ED=4.1/1.2/1.2


Solution Path: Show

Code: Select all

1.2, Hidden Single: R4C3: 4 in block: r4c3=4
1.2, Hidden Single: R3C8: 6 in block: r3c8=6
1.2, Hidden Single: R3C5: 5 in block: r3c5=5
1.2, Hidden Single: R5C8: 4 in block: r5c8=4
1.5, Hidden Single: R1C4: 6 in column: r1c4=6
1.2, Hidden Single: R2C7: 6 in block: r2c7=6
1.5, Hidden Single: R8C4: 5 in column: r8c4=5
1.2, Hidden Single: R8C1: 2 in block: r8c1=2
1.2, Hidden Single: R7C8: 5 in block: r7c8=5
1.2, Hidden Single: R1C7: 5 in block: r1c7=5
1.2, Hidden Single: R2C2: 5 in block: r2c2=5
1.2, Hidden Single: R2C1: 1 in block: r2c1=1
1.2, Hidden Single: R6C3: 5 in block: r6c3=5
1.2, Hidden Single: R6C1: 6 in block: r6c1=6
1.2, Hidden Single: R7C3: 6 in block: r7c3=6
1.2, Hidden Single: R7C5: 7 in block: r7c5=7
1.2, Hidden Single: R2C8: 7 in block: r2c8=7
1.5, Hidden Single: R6C7: 7 in row: r6c7=7
1.5, Hidden Single: R8C5: 4 in row: r8c5=4
1.2, Hidden Single: R8C7: 1 in block: r8c7=1
1.5, Hidden Single: R2C6: 4 in row: r2c6=4
1.0, Hidden Single: R2C5: 8 in row: r2c5=8
1.5, Hidden Single: R4C5: 1 in row: r4c5=1
1.2, Hidden Single: R6C6: 1 in block: r6c6=1
2.6, Pointing: Cells R3C1,R3C2,R3C3: 3 in block and row: r3c6<>3
2.6, Pointing: Cells R6C5,R6C8: 2 in block and row: r6c2<>2
3.4, Hidden Pair: Cells R3C2,R5C2: 1,2 in column: r3c2<>3,8, r5c2<>3,8
3.8, Swordfish: Cells R1C5,R1C6,R6C2,R6C5,R7C2,R7C6: 3 in 3 columns and 3 rows: r7c1<>3, r6c8<>3
4.1, W-Wing: Cells R3C6,R4C7,R5C7,R6C8: 2 and 8: r4c8<>2
1.2, Hidden Single: R3C6: 2 in block: r3c6=2
1.2, Hidden Single: R1C5: 2 in block: r1c5=2
1.0, Hidden Single: R1C6: 3 in block: r1c6=3
1.0, Hidden Single: R6C5: 3 in column: r6c5=3
1.0, Hidden Single: R7C6: 8 in column: r7c6=8
1.0, Hidden Single: R8C8: 3 in block: r8c8=3
1.0, Hidden Single: R8C3: 8 in row: r8c3=8
1.2, Hidden Single: R4C4: 2 in block: r4c4=2
1.2, Hidden Single: R4C7: 3 in block: r4c7=3
1.0, Hidden Single: R4C8: 8 in block: r4c8=8
1.0, Hidden Single: R5C7: 8 in column: r5c7=8
1.0, Hidden Single: R6C8: 2 in block: r6c8=2
1.0, Hidden Single: R6C2: 8 in row: r6c2=8
1.2, Hidden Single: R1C1: 8 in block: r1c1=8
1.2, Hidden Single: R1C2: 4 in block: r1c2=4
1.0, Hidden Single: R1C3: 7 in block: r1c3=7
1.2, Hidden Single: R3C4: 8 in block: r3c4=8
1.0, Hidden Single: R5C4: 7 in column: r5c4=7
1.2, Hidden Single: R3C1: 7 in block: r3c1=7
1.2, Hidden Single: R3C3: 3 in block: r3c3=3
1.0, Hidden Single: R3C2: 1 in block: r3c2=1
1.0, Hidden Single: R5C3: 1 in column: r5c3=1
1.2, Hidden Single: R5C2: 2 in block: r5c2=2
1.0, Hidden Single: R5C1: 3 in block: r5c1=3
1.0, Hidden Single: R7C1: 4 in column: r7c1=4
1.0, Hidden Single: R7C2: 3 in block: r7c2=3
ED=4.1/1.2/1.2


[urhegyi]

I solved another one today, but needed an unorthodox way (Discontinuous nice loop), so I estimate it around SE 7.3.
Can sudokuexplainer find a better way?
.6...3.18.3.6...7.41.....865........154.....26.7...8.2.65.2...7. 2Rx4C

[1to9only]

Standard SE:

Code: Select all

.6...3.18.3.6...7.41.....865........154.....26.7...8.2.65.2...7. 2Rx4C ED=7.1/1.2/1.2

Analysis results
Difficulty rating: 7.1
This Sudoku can be solved using the following logical methods:
40 x Hidden Single (1.0-1.5)
5 x Pointing (2.6)
2 x Claiming (2.8)
1 x Naked Pair (3.0)
1 x BUG type 1 (5.6)
1 x Forcing X-Chain (6.7)
2 x Bidirectional Y-Cycle (6.8-7.0)
1 x Forcing Chain (7.1)


With W-Wing enabled:

Code: Select all

.6...3.18.3.6...7.41.....865........154.....26.7...8.2.65.2...7. 2Rx4C ED=6.8/1.2/1.2


W-Wing solution path: Show

Code: Select all

1.2, Hidden Single: R2C2: 1 in block: r2c2=1
1.2, Hidden Single: R1C3: 5 in block: r1c3=5
1.2, Hidden Single: R3C7: 6 in block: r3c7=6
1.2, Hidden Single: R6C2: 5 in block: r6c2=5
1.2, Hidden Single: R8C4: 6 in block: r8c4=6
1.2, Hidden Single: R5C1: 6 in block: r5c1=6
1.5, Hidden Single: R8C6: 1 in row: r8c6=1
1.2, Hidden Single: R4C7: 1 in block: r4c7=1
1.5, Hidden Single: R3C6: 8 in column: r3c6=8
2.6, Pointing: Cells R1C4,R2C4: 7 in block and column: r5c4<>7
2.6, Pointing: Cells R3C8,R4C8: 2 in block and column: r2c8<>2
2.8, Claiming: Cells R7C2,R8C2: 4 in column and block: r7c1<>4
2.8, Claiming: Cells R5C4,R6C4: 3 in column and block: r5c2<>3, r6c1<>3
6.8, Bidirectional Y-Cycle (w/12 nodes): R6C1,R6C4,R6C7,R1C7,R2C7,R7C7,R7C1: r7c5<>3, r7c2<>3
4.1, W-Wing: Cells R2C8,R2C7,R7C7,R7C5: 4 and 5: r8c8<>4, r1c5<>4
2.6, Pointing: Cells R7C5,R8C5: 4 in block and column: r4c5<>4
2.6, Pointing: Cells R2C6,R2C8: 4 in block and row: r2c4<>4
3.0, Naked Pair: Cells R5C8,R8C8: 3,8 in column: r3c8<>3, r4c8<>3
2.6, Pointing: Cells R3C5,R4C5: 3 in block and column: r8c5<>3
5.6, BUG type 1: R1C4: r1c4<>4,7
1.2, Hidden Single: R1C1: 4 in block: r1c1=4
1.2, Hidden Single: R2C4: 7 in block: r2c4=7
1.0, Hidden Single: R1C4: 2 in block: r1c4=2
1.2, Hidden Single: R2C7: 2 in block: r2c7=2
1.2, Hidden Single: R2C8: 5 in block: r2c8=5
1.0, Hidden Single: R2C6: 4 in row: r2c6=4
1.0, Hidden Single: R4C6: 7 in column: r4c6=7
1.2, Hidden Single: R1C5: 7 in block: r1c5=7
1.0, Hidden Single: R1C7: 8 in block: r1c7=8
1.2, Hidden Single: R4C8: 4 in block: r4c8=4
1.2, Hidden Single: R3C8: 2 in block: r3c8=2
1.2, Hidden Single: R4C1: 2 in block: r4c1=2
1.0, Hidden Single: R3C2: 3 in block: r3c2=3
1.0, Hidden Single: R3C5: 5 in row: r3c5=5
1.0, Hidden Single: R4C5: 3 in block: r4c5=3
1.2, Hidden Single: R5C2: 2 in block: r5c2=2
1.2, Hidden Single: R6C4: 4 in block: r6c4=4
1.0, Hidden Single: R5C4: 3 in column: r5c4=3
1.2, Hidden Single: R5C3: 7 in block: r5c3=7
1.0, Hidden Single: R5C8: 8 in row: r5c8=8
1.0, Hidden Single: R6C7: 3 in block: r6c7=3
1.0, Hidden Single: R7C7: 5 in column: r7c7=5
1.0, Hidden Single: R8C8: 3 in column: r8c8=3
1.2, Hidden Single: R6C3: 8 in block: r6c3=8
1.0, Hidden Single: R6C1: 1 in block: r6c1=1
1.0, Hidden Single: R7C1: 3 in column: r7c1=3
1.0, Hidden Single: R7C3: 1 in column: r7c3=1
1.2, Hidden Single: R7C2: 7 in block: r7c2=7
1.0, Hidden Single: R8C2: 4 in block: r8c2=4
1.0, Hidden Single: R7C5: 4 in row: r7c5=4
1.0, Hidden Single: R8C5: 8 in block: r8c5=8
ED=6.8/1.2/1.2



[urhegyi]

Diagonal 2x4 sudoku:
...2.3....6..7..38....6....73..57..41....2....74..3..5....1.7... 2R4C X-sudoku
Symmetrical design. Any idea how hard it will be to solve thisone by hand?

[1to9only]

It's very human solvable: ED=1.7/1.2/1.2.

Code: Select all

Analysis results
Difficulty rating: 1.7
This Sudoku can be solved using the following logical methods:
43 x Hidden Single (1.0-1.5)
1 x Direct Pointing (1.7)


If you dislike Direct Pointing (1.7) and Direct Hidden Pair (2.0), then the rating is: ED=2.6/1.2/1.2

Code: Select all

Analysis results
Difficulty rating: 2.6
This Sudoku can be solved using the following logical methods:
43 x Hidden Single (1.0-1.5)
1 x Naked Single (2.3)
2 x Pointing (2.6)


[urhegyi]

Yes it was very easy.
solution:

Hidden Text: Show

Code: Select all

54728316
83614752
38452167
61273845
76541283
12835674
47386521
25167438


[urhegyi]

qualified as medium
I solved it with a two string kite in 8's
R1C1;R4C1;R3C2;R3C8 --> R1C8<>8 and R3C8=8 and so R4C1=8.
I can't find any less difficult step then a kite, so for me it's a hard one and not a medium.

[1to9only]

Depends if you rate Skyscrapers lower/higher than TwoStringKites.

Code: Select all

after singles
Naked Pair: Cells R5C2,R6C2: 5,6 in block: r6c1<>6
Hidden Single: R3C1: 6 in column: r3c1=6
Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 1: r1c8<>1, r4c7<>1
Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 8: r1c8<>8, r4c7<>8
stte


[urhegyi]

Depends if you rate Skyscrapers lower/higher than TwoStringKites.

Code: Select all

after singles
Naked Pair: Cells R5C2,R6C2: 5,6 in block: r6c1<>6
Hidden Single: R3C1: 6 in column: r3c1=6
Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 1: r1c8<>1, r4c7<>1
Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 8: r1c8<>8, r4c7<>8
stte


Thank you for pointing out the two skyscrapers. Now I see they form a remote pair so that R1C8<>1/8=6 and R4C7<>1/8=5.

[urhegyi]

found another 2x4 sudoku-X here: https://www.reddit.com/r/sudoku/comments/gbtayb/tough_8x8_diagonal_sudoku/.
needed two turbots or a turbot fish and a remote pair.
Resulted in R3C7=6 and R5C8=6.

Code: Select all

..5326....213...........6...5..4..7.......6..5..7....13......7..

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2R4C X-sudoku

Now my question is when both 1's at R2C4 AND R7C6 are replaced by 2 8's, is the sudoku-X still unique and what is the rating and would it solve in the same way as the original?
variant:

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..5326....283...........6...5..4..7.......6..5..7....83......7..

Code: Select all

2R4C X-sudoku

[1to9only]

Code: Select all

..5326....213...........6...5..4..7.......6..5..7....13......7.. 2Rx4C-X

after basics:
+-------------------------+-------------------------+
| 4     7     5     3     | 2     6     18    18    |
| 8     6     2     1     | 3     4     7     5     |
+-------------------------+-------------------------+
| 5     4     18    2     | 1678  38    168   13678 |
| 6     138   138   7     | 5     28    128   4     |
+-------------------------+-------------------------+
| 13    5     7     4     | 18    238   1268  1368  |
| 2     13    6     8     | 17    5     4     137   |
+-------------------------+-------------------------+
| 7     2     48    5     | 468   1     3     68    |
| 13    138   1348  6     | 48    7     5     2     |
+-------------------------+-------------------------+

2.9, Generalized Intersection: Cells R1C8,R3C6: 8 in diagonal(/): r3c8<>8
2.9, Generalized Intersection: Cells R3C3,R5C5: 1 in antidiagonal(\): r3c5<>1
2.8, Claiming: Cells R5C5,R6C5: 1 in column and block: r5c8<>1, r6c8<>1, r5c7<>1
2.9, Generalized Intersection: Cells R3C3,R5C5: 8 in antidiagonal(\): r3c5<>8
3.7, Two-String Kite: Cells R3C6,R3C8,R5C1,R8C1: 3: r5c8<>3
2.0, Direct Hidden Pair: Cells R3C8,R6C8: 3,7 in column: r3c8<>1,6, r1c8=1
stte


The grid is rated ED=3.7/1.2/1.2.

Code: Select all

..5326....283...........6...5..4..7.......6..5..7....83......7.. 2Rx4C-X

is the sudoku-X still unique? Yes
what is the rating? ED=3.7/1.2/1.2
would it solve in the same way as the original? Yes


In both grids, the strings are R3 and C1, and the kite is the main diagonal (/).

[Afmob]

I am a bit late to the party, but just for your info: 14 is the minimum number of clues for a 2 x 4 sudoku, i.e. there is no uniquely solvable 2 x 4 sudoku with 13 clues.