Sep 21 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 can only be <2>
R5C1 can only be <4>
R2C6 can only be <9>
R8C1 can only be <5>
R8C6 can only be <2>
R3C6 can only be <5>
R7C6 can only be <6>
R5C6 can only be <3>
R2C9 is the only square in row 2 that can be <6>
R5C9 can only be <8>
R8C9 can only be <3>
R4C7 can only be <9>
R5C7 can only be <7>
R6C7 can only be <5>
R3C5 is the only square in row 3 that can be <2>
R4C2 is the only square in row 4 that can be <2>
R4C5 is the only square in row 4 that can be <8>
R7C7 is the only square in row 7 that can be <2>
R7C5 is the only square in row 7 that can be <5>
R5C4 is the only square in column 4 that can be <9>
Squares R1C5 and R1C8 in row 1 and R9C5 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 5 and 8 can be removed.
R3C8 - removing <4> from <1489> leaving <189>
R7C8 - removing <4> from <148> leaving <18>
Squares R1C2 and R1C5 in row 1 and R9C2 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 5 can be removed.
R7C2 - removing <7> from <178> leaving <18>
Squares R7C2 and R7C8 in row 7 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.
R7C3 - removing <18> from <1478> leaving <47>
R7C4 - removing <8> from <478> leaving <47>
R8C4 is the only square in column 4 that can be <8>
Intersection of column 3 with block 1. The value <8> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <8> from <389> leaving <39>
Intersection of column 7 with block 3. The value <8> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <8> from <189> leaving <19>
Squares R4C3, R4C8, R6C3 and R6C8 form a Type-1 Unique Rectangle on <36>.
R6C3 - removing <36> from <1369> leaving <19>
Squares R3C8 (XY), R3C4 (XZ) and R1C8 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R1C5 - removing <4> from <47> leaving <7>
R3C7 - removing <4> from <148> leaving <18>
R1C2 can only be <9>
R9C5 can only be <4>
R2C4 can only be <1>
R2C7 can only be <8>
R3C4 can only be <4>
R2C3 can only be <7>
R3C7 can only be <1>
R7C4 can only be <7>
R3C8 can only be <9>
R8C7 can only be <4>
R3C2 can only be <3>
R1C8 can only be <4>
R7C3 can only be <4>
R8C3 can only be <1>
R9C8 can only be <8>
R9C2 can only be <7>
R7C8 can only be <1>
R3C3 can only be <8>
R6C2 can only be <1>
R6C3 can only be <9>
R6C5 can only be <6>
R7C2 can only be <8>
R5C3 can only be <6>
R6C8 can only be <3>
R5C5 can only be <1>
R4C8 can only be <6>
R4C3 can only be <3>
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