Apr 19 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 is the only square in row 2 that can be <4>
R3C9 is the only square in row 3 that can be <2>
R1C6 is the only square in row 1 that can be <2>
R3C3 is the only square in row 3 that can be <5>
R1C8 is the only square in row 1 that can be <5>
R3C5 is the only square in row 3 that can be <6>
R5C5 can only be <7>
R4C9 is the only square in row 4 that can be <7>
R5C1 is the only square in row 5 that can be <2>
R5C9 is the only square in row 5 that can be <6>
R6C2 is the only square in row 6 that can be <5>
R7C9 is the only square in row 7 that can be <5>
R7C1 is the only square in row 7 that can be <7>
R8C6 is the only square in row 8 that can be <5>
Intersection of column 3 with block 7. The value <3> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C1 - removing <3> from <139> leaving <19>
Intersection of column 5 with block 8. The value <4> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C4 - removing <4> from <3467> leaving <367>
Intersection of column 7 with block 9. The value <4> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C8 - removing <4> from <23469> leaving <2369>
Squares R7C7<34>, R8C9<39> and R9C7<349> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <349>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <39> from <2369> leaving <26>
R9C8 - removing <39> from <2369> leaving <26>
Squares R1C3 and R7C3 in column 3 and R1C5 and R7C5 in column 5 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 1 and 7 can be removed.
R1C2 - removing <1> from <1789> leaving <789>
R1C4 - removing <1> from <1378> leaving <378>
R1C7 - removing <1> from <1389> leaving <389>
R3C7 is the only square in column 7 that can be <1>
R3C1 can only be <8>
Squares R7C3 and R9C3 in column 3, R1C5, R7C5 and R9C5 in column 5 and R1C7, R7C7 and R9C7 in column 7 form a Swordfish pattern on possibility <3>. All other instances of this possibility in rows 1, 7 and 9 can be removed.
R1C4 - removing <3> from <378> leaving <78>
R9C4 - removing <3> from <367> leaving <67>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C8 - removing <6> from <26> leaving <2>
R8C8 can only be <6>
R8C2 is the only square in row 8 that can be <2>
Squares R1C2, R1C3 and R1C7 in row 1, R5C3 and R5C7 in row 5 and R9C2, R9C3 and R9C7 in row 9 form a Swordfish pattern on possibility <9>. All other instances of this possibility in columns 2, 3 and 7 can be removed.
R2C2 - removing <9> from <179> leaving <17>
R4C2 - removing <9> from <189> leaving <18>
Squares R4C2 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C1 - removing <1> from <139> leaving <39>
R4C4 - removing <18> from <148> leaving <4>
R6C8 is the only square in row 6 that can be <4>
Intersection of row 2 with block 3. The value <9> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <9> from <389> leaving <38>
Squares R1C7 (XY), R2C8 (XZ) and R5C7 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R4C8 - removing <9> from <39> leaving <3>
R4C1 can only be <9>
R2C8 can only be <9>
R6C9 can only be <8>
R5C7 can only be <9>
R2C9 can only be <3>
R8C9 can only be <9>
R1C7 can only be <8>
R8C1 can only be <1>
R5C3 can only be <8>
R4C2 can only be <1>
R8C4 can only be <3>
R6C1 can only be <3>
R7C3 can only be <3>
R9C5 can only be <4>
R9C7 can only be <3>
R7C5 can only be <1>
R9C3 can only be <9>
R7C7 can only be <4>
R1C4 can only be <7>
R4C6 can only be <8>
R2C2 can only be <7>
R1C5 can only be <3>
R9C2 can only be <8>
R1C3 can only be <1>
R1C2 can only be <9>
R9C4 can only be <6>
R2C6 can only be <1>
R2C4 can only be <8>
R6C6 can only be <6>
R6C4 can only be <1>
R9C6 can only be <7>
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