## 2 X 4 sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### 2 X 4 sudoku

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

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

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.
urhegyi

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

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=41.2, Hidden Single: R3C8: 6 in block: r3c8=61.2, Hidden Single: R3C5: 5 in block: r3c5=51.2, Hidden Single: R5C8: 4 in block: r5c8=41.5, Hidden Single: R1C4: 6 in column: r1c4=61.2, Hidden Single: R2C7: 6 in block: r2c7=61.5, Hidden Single: R8C4: 5 in column: r8c4=51.2, Hidden Single: R8C1: 2 in block: r8c1=21.2, Hidden Single: R7C8: 5 in block: r7c8=51.2, Hidden Single: R1C7: 5 in block: r1c7=51.2, Hidden Single: R2C2: 5 in block: r2c2=51.2, Hidden Single: R2C1: 1 in block: r2c1=11.2, Hidden Single: R6C3: 5 in block: r6c3=51.2, Hidden Single: R6C1: 6 in block: r6c1=61.2, Hidden Single: R7C3: 6 in block: r7c3=61.2, Hidden Single: R7C5: 7 in block: r7c5=71.2, Hidden Single: R2C8: 7 in block: r2c8=71.5, Hidden Single: R6C7: 7 in row: r6c7=71.5, Hidden Single: R8C5: 4 in row: r8c5=41.2, Hidden Single: R8C7: 1 in block: r8c7=11.5, Hidden Single: R2C6: 4 in row: r2c6=41.0, Hidden Single: R2C5: 8 in row: r2c5=81.5, Hidden Single: R4C5: 1 in row: r4c5=11.2, Hidden Single: R6C6: 1 in block: r6c6=12.6, Pointing: Cells R3C1,R3C2,R3C3: 3 in block and row: r3c6<>32.6, Pointing: Cells R6C5,R6C8: 2 in block and row: r6c2<>23.4, Hidden Pair: Cells R3C2,R5C2: 1,2 in column: r5c2<>3,8, r3c2<>3,83.8, Swordfish: Cells R1C5,R1C6,R6C2,R6C5,R7C2,R7C6: 3 in 3 columns and 3 rows: r6c8<>3, r7c1<>36.6, Turbot Fish (w/4 nodes): R3C3.8 off: r3c3<>86.6, Turbot Fish (w/4 nodes): R5C3.8 off: r5c3<>86.6, Turbot Fish (w/4 nodes): R7C2.8 off: r7c2<>84.2, XY-Wing: Cells R7C2,R7C1,R6C2 on value 8: r5c1<>84.2, XY-Wing: Cells R7C2,R8C3,R1C2 on value 8: r1c3<>81.5, Hidden Single: R8C3: 8 in column: r8c3=81.0, Hidden Single: R8C8: 3 in row: r8c8=31.0, Hidden Single: R7C6: 8 in block: r7c6=81.2, Hidden Single: R4C7: 3 in block: r4c7=31.0, Hidden Single: R5C7: 8 in column: r5c7=81.2, Hidden Single: R4C8: 8 in block: r4c8=81.0, Hidden Single: R3C6: 2 in block: r3c6=21.0, Hidden Single: R1C6: 3 in column: r1c6=31.0, Hidden Single: R1C5: 2 in block: r1c5=21.0, Hidden Single: R6C5: 3 in column: r6c5=31.0, Hidden Single: R6C8: 2 in block: r6c8=21.0, Hidden Single: R4C4: 2 in row: r4c4=21.0, Hidden Single: R6C2: 8 in row: r6c2=81.2, Hidden Single: R1C1: 8 in block: r1c1=81.2, Hidden Single: R1C2: 4 in block: r1c2=41.0, Hidden Single: R1C3: 7 in block: r1c3=71.2, Hidden Single: R3C4: 8 in block: r3c4=81.0, Hidden Single: R5C4: 7 in column: r5c4=71.2, Hidden Single: R3C1: 7 in block: r3c1=71.2, Hidden Single: R3C3: 3 in block: r3c3=31.0, Hidden Single: R3C2: 1 in block: r3c2=11.0, Hidden Single: R5C3: 1 in column: r5c3=11.2, Hidden Single: R5C2: 2 in block: r5c2=21.0, Hidden Single: R5C1: 3 in block: r5c1=31.0, Hidden Single: R7C1: 4 in column: r7c1=41.0, Hidden Single: R7C2: 3 in block: r7c2=3ED=6.6/1.2/1.2`
1to9only

Posts: 4084
Joined: 04 April 2018

### Re: 2 X 4 sudoku

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=41.2, Hidden Single: R3C8: 6 in block: r3c8=61.2, Hidden Single: R3C5: 5 in block: r3c5=51.2, Hidden Single: R5C8: 4 in block: r5c8=41.5, Hidden Single: R1C4: 6 in column: r1c4=61.2, Hidden Single: R2C7: 6 in block: r2c7=61.5, Hidden Single: R8C4: 5 in column: r8c4=51.2, Hidden Single: R8C1: 2 in block: r8c1=21.2, Hidden Single: R7C8: 5 in block: r7c8=51.2, Hidden Single: R1C7: 5 in block: r1c7=51.2, Hidden Single: R2C2: 5 in block: r2c2=51.2, Hidden Single: R2C1: 1 in block: r2c1=11.2, Hidden Single: R6C3: 5 in block: r6c3=51.2, Hidden Single: R6C1: 6 in block: r6c1=61.2, Hidden Single: R7C3: 6 in block: r7c3=61.2, Hidden Single: R7C5: 7 in block: r7c5=71.2, Hidden Single: R2C8: 7 in block: r2c8=71.5, Hidden Single: R6C7: 7 in row: r6c7=71.5, Hidden Single: R8C5: 4 in row: r8c5=41.2, Hidden Single: R8C7: 1 in block: r8c7=11.5, Hidden Single: R2C6: 4 in row: r2c6=41.0, Hidden Single: R2C5: 8 in row: r2c5=81.5, Hidden Single: R4C5: 1 in row: r4c5=11.2, Hidden Single: R6C6: 1 in block: r6c6=12.6, Pointing: Cells R3C1,R3C2,R3C3: 3 in block and row: r3c6<>32.6, Pointing: Cells R6C5,R6C8: 2 in block and row: r6c2<>23.4, Hidden Pair: Cells R3C2,R5C2: 1,2 in column: r3c2<>3,8, r5c2<>3,83.8, Swordfish: Cells R1C5,R1C6,R6C2,R6C5,R7C2,R7C6: 3 in 3 columns and 3 rows: r7c1<>3, r6c8<>34.1, W-Wing: Cells R3C6,R4C7,R5C7,R6C8: 2 and 8: r4c8<>21.2, Hidden Single: R3C6: 2 in block: r3c6=21.2, Hidden Single: R1C5: 2 in block: r1c5=21.0, Hidden Single: R1C6: 3 in block: r1c6=31.0, Hidden Single: R6C5: 3 in column: r6c5=31.0, Hidden Single: R7C6: 8 in column: r7c6=81.0, Hidden Single: R8C8: 3 in block: r8c8=31.0, Hidden Single: R8C3: 8 in row: r8c3=81.2, Hidden Single: R4C4: 2 in block: r4c4=21.2, Hidden Single: R4C7: 3 in block: r4c7=31.0, Hidden Single: R4C8: 8 in block: r4c8=81.0, Hidden Single: R5C7: 8 in column: r5c7=81.0, Hidden Single: R6C8: 2 in block: r6c8=21.0, Hidden Single: R6C2: 8 in row: r6c2=81.2, Hidden Single: R1C1: 8 in block: r1c1=81.2, Hidden Single: R1C2: 4 in block: r1c2=41.0, Hidden Single: R1C3: 7 in block: r1c3=71.2, Hidden Single: R3C4: 8 in block: r3c4=81.0, Hidden Single: R5C4: 7 in column: r5c4=71.2, Hidden Single: R3C1: 7 in block: r3c1=71.2, Hidden Single: R3C3: 3 in block: r3c3=31.0, Hidden Single: R3C2: 1 in block: r3c2=11.0, Hidden Single: R5C3: 1 in column: r5c3=11.2, Hidden Single: R5C2: 2 in block: r5c2=21.0, Hidden Single: R5C1: 3 in block: r5c1=31.0, Hidden Single: R7C1: 4 in column: r7c1=41.0, Hidden Single: R7C2: 3 in block: r7c2=3ED=4.1/1.2/1.2`
1to9only

Posts: 4084
Joined: 04 April 2018

### Re: 2 X 4 sudoku

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
urhegyi

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

Standard SE:
Code: Select all
`.6...3.18.3.6...7.41.....865........154.....26.7...8.2.65.2...7. 2Rx4C ED=7.1/1.2/1.2Analysis resultsDifficulty rating: 7.1This 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=11.2, Hidden Single: R1C3: 5 in block: r1c3=51.2, Hidden Single: R3C7: 6 in block: r3c7=61.2, Hidden Single: R6C2: 5 in block: r6c2=51.2, Hidden Single: R8C4: 6 in block: r8c4=61.2, Hidden Single: R5C1: 6 in block: r5c1=61.5, Hidden Single: R8C6: 1 in row: r8c6=11.2, Hidden Single: R4C7: 1 in block: r4c7=11.5, Hidden Single: R3C6: 8 in column: r3c6=82.6, Pointing: Cells R1C4,R2C4: 7 in block and column: r5c4<>72.6, Pointing: Cells R3C8,R4C8: 2 in block and column: r2c8<>22.8, Claiming: Cells R7C2,R8C2: 4 in column and block: r7c1<>42.8, Claiming: Cells R5C4,R6C4: 3 in column and block: r5c2<>3, r6c1<>36.8, Bidirectional Y-Cycle (w/12 nodes): R6C1,R6C4,R6C7,R1C7,R2C7,R7C7,R7C1: r7c5<>3, r7c2<>34.1, W-Wing: Cells R2C8,R2C7,R7C7,R7C5: 4 and 5: r8c8<>4, r1c5<>42.6, Pointing: Cells R7C5,R8C5: 4 in block and column: r4c5<>42.6, Pointing: Cells R2C6,R2C8: 4 in block and row: r2c4<>43.0, Naked Pair: Cells R5C8,R8C8: 3,8 in column: r3c8<>3, r4c8<>32.6, Pointing: Cells R3C5,R4C5: 3 in block and column: r8c5<>35.6, BUG type 1: R1C4: r1c4<>4,71.2, Hidden Single: R1C1: 4 in block: r1c1=41.2, Hidden Single: R2C4: 7 in block: r2c4=71.0, Hidden Single: R1C4: 2 in block: r1c4=21.2, Hidden Single: R2C7: 2 in block: r2c7=21.2, Hidden Single: R2C8: 5 in block: r2c8=51.0, Hidden Single: R2C6: 4 in row: r2c6=41.0, Hidden Single: R4C6: 7 in column: r4c6=71.2, Hidden Single: R1C5: 7 in block: r1c5=71.0, Hidden Single: R1C7: 8 in block: r1c7=81.2, Hidden Single: R4C8: 4 in block: r4c8=41.2, Hidden Single: R3C8: 2 in block: r3c8=21.2, Hidden Single: R4C1: 2 in block: r4c1=21.0, Hidden Single: R3C2: 3 in block: r3c2=31.0, Hidden Single: R3C5: 5 in row: r3c5=51.0, Hidden Single: R4C5: 3 in block: r4c5=31.2, Hidden Single: R5C2: 2 in block: r5c2=21.2, Hidden Single: R6C4: 4 in block: r6c4=41.0, Hidden Single: R5C4: 3 in column: r5c4=31.2, Hidden Single: R5C3: 7 in block: r5c3=71.0, Hidden Single: R5C8: 8 in row: r5c8=81.0, Hidden Single: R6C7: 3 in block: r6c7=31.0, Hidden Single: R7C7: 5 in column: r7c7=51.0, Hidden Single: R8C8: 3 in column: r8c8=31.2, Hidden Single: R6C3: 8 in block: r6c3=81.0, Hidden Single: R6C1: 1 in block: r6c1=11.0, Hidden Single: R7C1: 3 in column: r7c1=31.0, Hidden Single: R7C3: 1 in column: r7c3=11.2, Hidden Single: R7C2: 7 in block: r7c2=71.0, Hidden Single: R8C2: 4 in block: r8c2=41.0, Hidden Single: R7C5: 4 in row: r7c5=41.0, Hidden Single: R8C5: 8 in block: r8c5=8ED=6.8/1.2/1.2`
1to9only

Posts: 4084
Joined: 04 April 2018

### Re: 2 X 4 sudoku

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?
urhegyi

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

It's very human solvable: ED=1.7/1.2/1.2.
Code: Select all
`Analysis resultsDifficulty rating: 1.7This 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 resultsDifficulty rating: 2.6This 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)`
1to9only

Posts: 4084
Joined: 04 April 2018

### Re: 2 X 4 sudoku

Yes it was very easy.
solution:
Hidden Text: Show
Code: Select all
`5472831683614752384521676127384576541283128356744738652125167438`
urhegyi

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

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.
urhegyi

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

Depends if you rate Skyscrapers lower/higher than TwoStringKites.
Code: Select all
`after singlesNaked Pair: Cells R5C2,R6C2: 5,6 in block: r6c1<>6Hidden Single: R3C1: 6 in column: r3c1=6Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 1: r1c8<>1, r4c7<>1Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 8: r1c8<>8, r4c7<>8stte`
1to9only

Posts: 4084
Joined: 04 April 2018

### Re: 2 X 4 sudoku

1to9only wrote:Depends if you rate Skyscrapers lower/higher than TwoStringKites.
Code: Select all
`after singlesNaked Pair: Cells R5C2,R6C2: 5,6 in block: r6c1<>6Hidden Single: R3C1: 6 in column: r3c1=6Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 1: r1c8<>1, r4c7<>1Skyscraper: Cells R2C2,R2C7,R3C2,R3C8: 8: r1c8<>8, r4c7<>8stte`

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

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

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..`

Code: Select all
`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:
Code: Select all
`..5326....283...........6...5..4..7.......6..5..7....83......7..`

Code: Select all
`2R4C X-sudoku`
urhegyi

Posts: 618
Joined: 13 April 2020

### Re: 2 X 4 sudoku

Code: Select all
`..5326....213...........6...5..4..7.......6..5..7....13......7.. 2Rx4C-Xafter 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<>82.9, Generalized Intersection: Cells R3C3,R5C5: 1 in antidiagonal(\): r3c5<>12.8, Claiming: Cells R5C5,R6C5: 1 in column and block: r5c8<>1, r6c8<>1, r5c7<>12.9, Generalized Intersection: Cells R3C3,R5C5: 8 in antidiagonal(\): r3c5<>83.7, Two-String Kite: Cells R3C6,R3C8,R5C1,R8C1: 3: r5c8<>32.0, Direct Hidden Pair: Cells R3C8,R6C8: 3,7 in column: r3c8<>1,6, r1c8=1stte`

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-Xis the sudoku-X still unique? Yeswhat is the rating? ED=3.7/1.2/1.2would 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 (/).
1to9only

Posts: 4084
Joined: 04 April 2018

### Re: 2 X 4 sudoku

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.
Afmob

Posts: 132
Joined: 28 June 2011

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