The New Sudoku Players' Forum

by **m_b_metcalf** » Sun Feb 26, 2023 11:57 am

Code: Select all: . . 1 2 3 4 5 6 . . . . . 7 6 . . . . . . . 8 9 . . . . . . . 6 3 . . . . . . . 2 5 . . . . . . . 1 8 . . . . . . . 9 7 . . . . . . . 5 2 . . . . . 2 6 4 1 9 7 . quite hard . . 1 2 3 4 5 6 . . . . . 7 6 . . . . . . . 5 8 . . . . . . . 6 9 . . . . . . . 1 5 . . . . . . . 2 3 . . . . . . . 8 2 . . . . . . . 9 1 . . . . . 3 6 4 7 8 2 . moderate

by **Leren** » Sun Feb 26, 2023 7:51 pm

The moderate puzzle needed 8 non-basic moves to solve but nothing too special. I managed to solve the Quite Hard puzzle without forcing chains - just.

Hopefully Hajime will have a go and we may be able to compare solutions.

Leren

by **Hajime** » Sun Feb 26, 2023 8:04 pm

The moderate one, lots of X-chains (2-String-Kite,SkyScraper,TurbotCrane and even one with a diagonal)

Hidden Text: Show

Code: Select all: [1,1] r9c1=5 Naked Single [1,2] r9c9=9 Naked Single [2,3] r9c2=1 Naked Single [3,4] r1c2=9 Hidden Single in row 1 [3,5] r7c1=9 Hidden Single in row 7 [4,5] Naked/Hidden Pairs,Triplets,Quads | NTriple (467)r7c237 => (-47)r7c8 (-467)r7c9 [5,5] Pointing, Claiming | (2)\,b1 => (-2)r2c1 (-2)r2c3 (-2)r3c1 (-2)r3c2 | (3)/,b3 => (-3)r2c7 (-3)r2c9 (-3)r3c8 (-3)r3c9 | (6)/,b7 => (-6)r7c2 (-6)r8c1 (-6)r8c3 [6,5] Generalized Intersection | (6)r7,c3,\ => (-6)r3c3 | (6)\,r7,c3 => (-6)r7c3 | (6)r7,c7 => (-6)r5c7 (-6)r6c7 (-6)r8c7 | (6)r7,b9 => (-6)r8c9 | (6)r8,c2 => (-6)r3c2 (-6)r5c2 (-6)r6c2 | (6)b1,c1 => (-6)r5c1 (-6)r6c1 [7,6] r3c1=6 Hidden Single in row 3 [7,7] r7c7=6 Hidden Single in row 7 [7,8] r8c2=6 Hidden Single in row 8 [7,9] r3c7=2 Hidden Single in sudokuX/ [7,10] r2c8=3 Hidden Single in sudokuX/ [8,11] r2c2=2 Hidden Single in row 2 [8,12] r2c3=5 Hidden Single in row 2 [8,13] r3c2=3 Hidden Single in row 3 [8,14] r8c8=5 Hidden Single in sudokuX\ [9,15] r7c8=1 Naked Single [9,16] r7c9=3 Naked Single [9,17] r8c4=3 Naked Single [10,18] r7c4=5 Naked Single [11,18] Naked/Hidden Pairs,Triplets,Quads | NPair (47)c3r37 => (-47)r4c3 (-47)r5c3 (-47)r6c3 (-47)r8c3 | NPair (28)c3r48 => (-28)r5c3 (-8)r6c3 | NSext (134789)b6e124578 => (-1478)r4c9 (-478)r5c9 (-1478)r6c9 | NPair (47)b7e23 => (-47)r8c1 [12,18] Pointing, Claiming | (8)b1,c1 => (-8)r4c1 (-8)r5c1 (-8)r6c1 (-8)r8c1 | (8)c2,b4 => (-8)r4c3 | (1)b6,c7 => (-1)r2c7 | (7)b1,\ => (-7)r4c4 [13,19] r4c3=2 Naked Single [13,20] r4c9=5 Naked Single [13,21] r6c9=6 Naked Single [13,22] r8c1=2 Naked Single [13,23] r8c3=8 Naked Single [14,24] r5c9=2 Naked Single [14,25] r6c3=9 Naked Single [15,26] r5c3=6 Naked Single [16,27] r6c2=5 Hidden Single in row 6 [17,27] Naked/Hidden Pairs,Triplets,Quads | NTriple (478)r4c248 => (-47)r4c1 (-47)r4c7 [18,27] (STUVW)XYZ-Wing | XYZ Wing Type B on {479} (-4)b3r3 => (-4)r3c9 [19,27] 2-String-Kite,SkyScraper,TurbotCrane | X-Chain [4] (4)r2c1=r3c3-r7c3=r6c4 => (-4)r6c1 [20,27] 2-String-Kite,SkyScraper,TurbotCrane | Turbot Crane (4)r3c8=r3c3-r7c3=r6c4 => (-4)r6c8 [21,27] 2-String-Kite,SkyScraper,TurbotCrane | 2-String Kite (4)r3c8=r3c3-r2c1=r5c1 => (-4)r5c8 [22,27] 2-String-Kite,SkyScraper,TurbotCrane | Turbot Crane (4)r4c4=r3c3-r3c8=r4c8 => (-4)r4c2 [23,27] Pointing, Claiming | (4)b4,r5 => (-4)r5c4 (-4)r5c7 [24,27] 2-String-Kite,SkyScraper,TurbotCrane | 2-String Kite (7)r1c1=r1c9-r6c4=r5c4 => (-7)r5c1 [25,27] 2-String-Kite,SkyScraper,TurbotCrane | 2-String Kite (7)r1c9=r1c1-r3c3=r7c3 => (-7)r6c4 [26,28] r5c4=7 Hidden Single in col 4 [27,28] (X)Y-Wing | XY-wing [3] (4)(4=9)r2c7-(9=3)r5c7-(3=4)r5c1 => (-4)r2c1 [28,29] r2c1=8 Naked Single [29,30] r1c1=7 Naked Single [29,31] r1c9=8 Naked Single [29,32] r3c3=4 Naked Single [29,33] r4c4=8 Naked Single [29,34] r6c1=1 Naked Single [29,35] r6c4=4 Naked Single [29,36] r6c7=7 Naked Single [29,37] r6c8=8 Naked Single [29,38] r7c3=7 Naked Single [29,39] r8c7=4 Naked Single [29,40] r8c9=7 Naked Single [30,41] r2c7=9 Naked Single [30,42] r3c8=7 Naked Single [30,43] r3c9=1 Naked Single [30,44] r4c1=3 Naked Single [30,45] r4c2=7 Naked Single [30,46] r4c7=1 Naked Single [30,47] r4c8=4 Naked Single [30,48] r5c1=4 Naked Single [30,49] r5c2=8 Naked Single [30,50] r5c7=3 Naked Single [30,51] r5c8=9 Naked Single [30,52] r7c2=4 Naked Single [31,53] r2c4=1 Naked Single [31,54] r2c9=4 Naked Single [31,55] r3c4=9 Naked Single

The hard one is very hard with 2 backdoor cells: r7c4=8 and r7c3=5

Followed with lots of (TUVW)XYZ wings

Hidden Text: Show

Code: Select all: [1,1] r8c4=3 Naked Single [2,1] Pointing, Claiming | (8)b9,r8 => (-8)r8c1 (-8)r8c2 (-8)r8c3 | (5)/,b7 => (-5)r7c1 (-5)r7c2 (-5)r9c2 | (6)/,b7 => (-6)r7c1 (-6)r7c2 (-6)r8c1 (-6)r8c3 | (1)\,b9 => (-1)r7c8 (-1)r7c9 (-1)r8c7 (-1)r8c9 [3,1] Generalized Intersection | (6)\,r7,c3 => (-6)r7c3 | (6)r7,c7,b9 => (-6)r8c7 | (6)r7,b9 => (-6)r8c9 | (6)r8,c2 => (-6)r3c2 (-6)r5c2 (-6)r6c2 | (3)r9,c2,\ => (-3)r2c2 [4,2] r7c3=5 Naked Single [4,3] r9c1=8 Naked Single [4,4] r9c2=3 Naked Single [4,5] r9c9=5 Naked Single [5,6] r1c2=8 Hidden Single in row 1 [5,7] r8c2=6 Hidden Single in row 8 [6,7] Naked/Hidden Pairs,Triplets,Quads | NPair (14)r7c12 => (-14)r7c7 (-4)r7c8 (-4)r7c9 | NPair (14)b7e12 => (-14)r8c1 (-4)r8c3 | NQuad (4789)r8c1379 => (-4)r8c8 | 1 (1)c8r8 => (-1)r2c8 (-1)r3c8 (-1)r4c8 (-1)r5c8 | NTriple (479)\124 => (-47)r3c3 | NTriple (479)/126 => (-47)r3c7 [7,8] r3c7=1 Naked Single [7,9] r8c8=1 Naked Single [8,10] r3c4=5 Naked Single [9,11] r2c4=1 Naked Single [10,12] r2c1=5 Hidden Single in row 2 [11,12] Naked/Hidden Pairs,Triplets,Quads | NPair (79)c1r18 => (-7)r3c1 (-79)r4c1 (-79)r5c1 (-79)r6c1 | NTriple (349)r2c238 => (-34)r2c7 (-349)r2c9 | NQuad (2489)r2c2789 => (-49)r2c3 | 1 (3)c3r2 => (-3)r3c3 (-3)r5c3 (-3)r6c3 | NPair (36)c3r23 => (-6)r5c3 (-6)r6c3 | NPair (28)b3e46 => (-2)r3c8 (-2)r3c9 | NSept (1245789)b4e1235689 => (-14)r5c1 (-24)r6c1 | NQuad (4679)\1234 => (-6)r7c7 [12,13] r2c3=3 Naked Single [12,14] r3c3=6 Naked Single [12,15] r7c7=3 Naked Single [12,16] r7c8=2 Naked Single [12,17] r7c9=6 Naked Single [13,17] Pointing, Claiming | (4)c3,b4 => (-4)r4c1 (-4)r4c2 (-4)r5c2 (-4)r6c2 | (7)c7,b6 => (-7)r4c9 (-7)r5c9 (-7)r6c9 | (8)c8,b6 => (-8)r4c7 (-8)r4c9 (-8)r5c7 (-8)r5c9 | (9)b1,\ => (-9)r4c4 | (9)b3,/ => (-9)r6c4 [14,18] r5c4=9 Hidden Single in col 4 [15,18] Generalized Intersection | (4)/,r6,c8 => (-4)r6c8 [16,18] (STUVW)XYZ-Wing | WXYZ Wing Type B on {1479} (-7)b1c2 => (-7)r3c2 | WXYZ Wing Type B on {1247} (-4)b1c2 => (-4)r2c2 | YZ Wing Type A on {24} (9)b1r3 => (-9)r1c1 | YZ Wing Type A on {24} (34)b1r3 => (-34)r3c9 | YZ Wing Type A on {79} (49)b3r1 => (-4)r3c8 | VWXYZ Wing Type B on {23789} (-9)b3r2 => (-9)r2c8 | XYZ Wing Type A on {248} (7)b3r2 => (-7)r1c9 | YZ Wing Type A on {34} (348)b3c8 => (-48)r4c8 (-3)r6c8 | UVWXYZ Wing Type B on {124789} (-9)b4c2 => (-9)r4c2 | UVWXYZ Wing Type B on {124789} (-9)b4c2 => (-9)r6c2 | TUVWXYZ Wing Type B on {1245789} (-7)b4c3 => (-7)r6c3 | TUVWXYZ Wing Type B on {1245789} (-7)b4c3 => (-7)r5c3 | TUVWXYZ Wing Type B on {1245789} (-7)b4c3 => (-7)r4c3 | UVWXYZ Wing Type B on {123467} (-7)b4r4 => (-7)r4c2 | TUVWXYZ Wing Type B on {1245789} (-4)b4r4 => (-4)r4c3 | XYZ Wing Type B on {589} (-9)b6r4 => (-9)r4c9 | TUVWXYZ Wing Type B on {1234589} (-4)b6r5 => (-4)r5c7 | XYZ Wing Type B on {459} (-9)b6r6 => (-9)r6c9 | TUVWXYZ Wing Type B on {1245679} (-4)b6c8 => (-4)r5c8 | YZ Wing Type A on {14} (7)b7c1 => (-7)r8c1 [17,19] r1c1=7 Naked Single [17,20] r1c9=9 Naked Single [17,21] r2c2=9 Naked Single [17,22] r2c8=4 Naked Single [17,23] r3c8=3 Naked Single [17,24] r3c9=7 Naked Single [17,25] r4c4=4 Naked Single [17,26] r5c8=8 Naked Single [17,27] r6c4=7 Naked Single [17,28] r8c1=9 Naked Single [17,29] r8c3=7 Naked Single [18,30] r5c3=4 Naked Single [18,31] r6c3=9 Naked Single [18,32] r6c8=5 Naked Single [19,33] r4c3=8 Naked Single [19,34] r4c8=9 Naked Single [19,35] r6c2=2 Naked Single [20,36] r3c2=4 Naked Single [20,37] r4c1=1 Naked Single [20,38] r4c2=5 Naked Single [20,39] r4c9=2 Naked Single [20,40] r5c2=7 Naked Single [20,41] r5c7=6 Naked Single [20,42] r6c7=4 Naked Single [20,43] r6c9=3 Naked Single [20,44] r7c1=4 Naked Single [20,45] r7c2=1 Naked Single [20,46] r8c7=8 Naked Single [20,47] r8c9=4 Naked Single [21,48] r2c7=2 Naked Single [21,49] r2c9=8 Naked Single [21,50] r3c1=2 Naked Single [21,51] r4c7=7 Naked Single [21,52] r5c1=3 Naked Single [21,53] r5c9=1 Naked Single [21,54] r6c1=6 Naked Single

The bended TUVWXYZ Wings Type A and Type B are implemented according to the theory
http://www.sudokuwiki.org/sudoku/Generalizing_Sudoku_Strategies.pdf

by **Leren** » Mon Feb 27, 2023 12:31 am

Added this one of Hajime's 4 cell X chains : X-Chain [4] (4)r2c1=r3c3-r7c3=r6c4 => (-4)r6c1 and got the same solution for the moderate puzzle.

It also helped a bit for the Quite hard puzzle. Many thanks, Leren

by **Leren** » Mon Feb 27, 2023 3:06 am

Hi Hajime

I've just had a look at your Hard puzzle solution, where you appear to have used the 2 extra hints. This is where I get to after basics, which appears to agree with your detailed printout.

Code: Select all: *--------------------------------------------------------------------------------* | 79 8 1 | 2 3 4 | 5 6 79 | | 5 49 3 | 1 7 6 | 28 49 28 | | 24 247 6 | 5 8 9 | 1 34 347 | |--------------------------+--------------------------+--------------------------| | 12 12579 4789 | 47 6 3 | 247 4589 1249 | | 36 17 478 | 9 2 5 | 467 348 134 | | 36 2579 479 | 47 1 8 | 2467 359 2349 | |--------------------------+--------------------------+--------------------------| | 14 14 5 | 8 9 7 | 3 2 6 | | 79 6 79 | 3 5 2 | 48 1 48 | | 8 3 2 | 6 4 1 | 9 7 5 | *--------------------------------------------------------------------------------*

All that is required from here is 2 skyscrapers and and a WXYZ wing.

Leren

by **Hajime** » Mon Feb 27, 2023 8:42 am

Leren wrote:All that is required from here is 2 skyscrapers and and a WXYZ wing.

Hi Leren, you are rigth. I should have limited the search to 4 cells in a ~~TUV~~WXYZ wing.

by **m_b_metcalf** » Mon Feb 27, 2023 11:14 am

By their very nature, many of these letter puzzles cannot be minimal. I looked for minimal puzzles on the outlines of the letters, and the smallest I came up with was this 14-clue puzzle based on I:

Code: Select all: . . 0 1 0 0 2 3 . . . . . 4 0. . . . . . . . 0 5 . . . . . . . 0 6 . . . . . . . 7 8 . . . . . . . 0 0 . . . . . . . 0 0 . . . . . . . 6 7 . . . . . 2 3 0 0 8 9 . very easy, 14 clues

by **urhegyi** » Mon Feb 27, 2023 1:31 pm

Your 14 clues variant and a harder one:

Code: Select all: ...1..23.....4.........5........6.......78.........................67.....23..89. ED=3.0/1.5/1.5 ...7..34.....5.........1........4.......19.........................86.....34..79. ED=8.2/1.2/1.2

by **m_b_metcalf** » Mon Feb 27, 2023 2:44 pm

and its cousin:

Code: Select all: ...7..34.....5.........8........9.......17.........................86.....34..79. ED=4.4/1.2/1.2

by **urhegyi** » Mon Feb 27, 2023 3:24 pm

and another even higher one:

Code: Select all: ...1..23.....4.........5........6.......78.........................67.....23..89. ED=3.0/1.5/1.5 ...7..34.....5.........1........4.......19.........................86.....34..79. ED=8.2/1.2/1.2 ...2..97.....4.........5........1.......57.........................16.....39..42. ED=8.4/1.5/1.5 ...1..98.....6.........4........3.......52.........................45.....28..19. ED=9.0/1.5/1.5 ...9..81.....3.........4........9.......56.........................47.....61..98. ED=9.1/1.2/1.2

by **m_b_metcalf** » Mon Feb 27, 2023 3:29 pm

urhegyi wrote:and another even higher one:

Code: Select all: . . . 1 . . 2 3 . . . . . 4 . . . . . . . . . 5 . . . . . . . . 1 . . . . . . . 6 7 . . . . . . . . . . . . . . . . . . . . . . . . . 5 8 . . . . . 7 3 . . 1 2 . ED=9.1/1.2/1.2

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