The New Sudoku Players' Forum

[m_b_metcalf]

I'm posting this because it's a long slog to get to the solution, and the SE rating is somewhat different to my own estimate:

Code: Select all

 . 1 . . . . . . .
 2 . . . . . . . .
 3 4 . . 5 . . 2 6
 7 . . . . 8 . . 2
 . . . . . . . . .
 4 . . 2 . . . . 9
 8 3 . . 4 . . 6 1
 . . . . . . . . 4
 . . . . . . . 3 .   X-sudoku

.1.......2........34..5..267....8..2.........4..2....983..4..61........4.......3.

[Hajime]

If you admit Naked & Hidden Quads (SER=5.4) it is solvable with Pointing/Claiming and Generic Locked Singles.
No more methods needed. If Quads are out (high SER) then lots of other methods are needed.

Solving Path: Show

Code: Select all

[1,1] r9c3=4 Hidden Single in row 9
[1,2] r7c7=2 Hidden Single in sudokuX\
[1,3] r4c4=4 Hidden Single in sudokuX\
[1,4] r2c8=4 Hidden Single in sudokuX/
[2,5] r1c6=4 Hidden Single in row 1
[2,6] r5c7=4 Hidden Single in row 5
[2,7] r1c5=2 Hidden Single in box 2
[3,7] Naked/Hidden Pairs,Triplets,Quads  | NQuin (56789)\12389 => (-679)r5c5 (-567)r6c6
[4,7] Naked/Hidden Pairs,Triplets,Quads  | NPair (13)b5e59 => (-13)r4c5 (-13)r5c4 (-13)r5c6 (-13)r6c5
[5,7] Pointing, Claiming  | (5)b5,r5 => (-5)r5c1 (-5)r5c2 (-5)r5c3 (-5)r5c8 (-5)r5c9 | (1)b3,c7 => (-1)r4c7 (-1)r6c7 | (6)\,b1 => (-6)r1c3 (-6)r2c3 | (6)/,b7 => (-6)r8c1 (-6)r8c3 (-6)r9c2
[6,7] Naked/Hidden Pairs,Triplets,Quads  | NQuad (5789)c3r1237 => (-59)r4c3 (-89)r5c3 (-58)r6c3 (-579)r8c3
[7,7] Pointing, Claiming  | (5)b4,c2 => (-5)r2c2 (-5)r8c2 (-5)r9c2 | (8)b4,c2 => (-8)r2c2 | (6)c3,b4 => (-6)r4c2 (-6)r5c1 (-6)r5c2 (-6)r6c2
[8,7] Generalized Intersection  | (9)c8,r1,\ => (-9)r1c1 | (3)/,r5,c9 => (-3)r5c9 | (3)b6,c7 => (-3)r1c7 (-3)r2c7
[9,7] Naked/Hidden Pairs,Triplets,Quads  | NQuad (1578)b6e2568 => (-5)r4c7 (-578)r6c7
[10,7] Naked/Hidden Pairs,Triplets,Quads  | NQuad (1367)r6c3567 => (-17)r6c8 | NTriple (136)r6c367 => (-6)r6c5
[11,8] r6c5=7 Naked Single
[12,8] Pointing, Claiming  | (5)b6,c8 => (-5)r1c8 (-5)r8c8
[13,8] Generalized Intersection  | (5)\,r1,c9 => (-5)r1c9 | (5)/,r8,c1,b7 => (-5)r8c1 | (5)c1,r9,\ => (-5)r9c9 | (5)\,r9,c1 => (-5)r9c1 | (5)b7,c3 => (-5)r1c3 (-5)r2c3 | (5)b9,c7 => (-5)r1c7 (-5)r2c7
[14,9] r1c1=5 Hidden Single in row 1
[14,10] r1c4=6 Hidden Single in row 1
[14,11] r2c9=5 Hidden Single in row 2
[14,12] r2c2=6 Hidden Single in row 2
[14,13] r9c1=6 Hidden Single in col 1
[14,14] r7c3=5 Hidden Single in col 3
[14,15] r1c9=3 Hidden Single in col 9
[14,16] r6c6=3 Hidden Single in box 5
[14,17] r4c7=3 Hidden Single in box 6
[14,18] r6c7=6 Hidden Single in box 6
[14,19] r5c5=1 Hidden Single in sudokuX\
[15,20] r5c1=9 Naked Single
[15,21] r5c4=5 Naked Single
[15,22] r5c6=6 Naked Single
[15,23] r6c3=1 Naked Single
[15,24] r8c1=1 Naked Single
[15,25] r8c3=2 Naked Single
[16,26] r4c2=5 Naked Single
[16,27] r4c3=6 Naked Single
[16,28] r4c5=9 Naked Single
[16,29] r4c8=1 Naked Single
[16,30] r5c3=3 Naked Single
[16,31] r6c2=8 Naked Single
[16,32] r6c8=5 Naked Single
[16,33] r9c5=8 Naked Single
[16,34] r9c9=7 Naked Single
[17,35] r2c5=3 Naked Single
[17,36] r5c2=2 Naked Single
[17,37] r5c9=8 Naked Single
[17,38] r8c5=6 Naked Single
[17,39] r9c2=9 Naked Single
[17,40] r9c4=1 Naked Single
[17,41] r9c7=5 Naked Single
[18,42] r5c8=7 Naked Single
[18,43] r8c2=7 Naked Single
[18,44] r9c6=2 Naked Single
[19,45] r3c7=9 Naked Single
[19,46] r8c7=8 Naked Single
[19,47] r8c8=9 Naked Single
[20,48] r1c7=7 Naked Single
[20,49] r1c8=8 Naked Single
[20,50] r2c7=1 Naked Single
[20,51] r3c3=8 Naked Single
[20,52] r3c4=7 Naked Single
[20,53] r3c6=1 Naked Single
[20,54] r7c4=9 Naked Single
[20,55] r7c6=7 Naked Single
[20,56] r8c4=3 Naked Single
[20,57] r8c6=5 Naked Single
[21,58] r1c3=9 Naked Single
[21,59] r2c3=7 Naked Single
[21,60] r2c4=8 Naked Single
[21,61] r2c6=9 Naked Single


(Note NakedQuin=HiddenQuad)

[m_b_metcalf]

It can be solved with just an XY-wing (4.2) but SE uses a Unique rectangle (4.6). There are, indeed, many different paths.

Mike