Jan 21 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C4 can only be <8>
R1C1 is the only square in row 1 that can be <9>
R2C3 is the only square in row 2 that can be <5>
R6C5 is the only square in row 6 that can be <9>
R8C9 is the only square in row 8 that can be <9>
R5C4 is the only square in column 4 that can be <2>
R5C5 is the only square in row 5 that can be <3>
R3C4 is the only square in column 4 that can be <3>
R7C6 is the only square in column 6 that can be <8>
R9C9 is the only square in column 9 that can be <4>
R8C1 is the only square in row 8 that can be <4>
Squares R7C1 and R8C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C1 - removing <6> from <3678> leaving <378>
R9C2 - removing <6> from <67> leaving <7>
R9C3 - removing <6> from <3678> leaving <378>
Intersection of column 5 with block 2. The value <7> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C6 - removing <7> from <167> leaving <16>
Squares R1C2 and R5C2 in column 2 and R1C8 and R5C8 in column 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 1 and 5 can be removed.
R5C1 - removing <1> from <1678> leaving <678>
R1C3 - removing <1> from <1367> leaving <367>
R1C5 - removing <1> from <167> leaving <67>
R5C6 - removing <1> from <167> leaving <67>
R1C7 - removing <1> from <12368> leaving <2368>
R1C9 - removing <1> from <1678> leaving <678>
R5C9 - removing <1> from <158> leaving <58>
Squares R5C2 (XY), R6C3 (XZ) and R5C6 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R5C1 - removing <7> from <678> leaving <68>
R6C6 - removing <7> from <147> leaving <14>
R5C6 is the only square in row 5 that can be <7>
R6C3 is the only square in row 6 that can be <7>
Intersection of row 5 with block 4. The value <6> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C3 - removing <6> from <168> leaving <18>
Squares R6C6, R6C7, R4C6 and R4C7 form a Type-4 Unique Rectangle on <14>.
R4C6 - removing <1> from <146> leaving <46>
R4C7 - removing <1> from <148> leaving <48>
Squares R4C3 (XY), R8C3 (XZ) and R5C1 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R7C1 - removing <6> from <16> leaving <1>
R8C3 can only be <6>
R8C5 can only be <2>
R1C3 can only be <3>
R8C7 can only be <1>
R6C7 can only be <4>
R9C3 can only be <8>
R6C6 can only be <1>
R4C7 can only be <8>
R9C1 can only be <3>
R4C3 can only be <1>
R5C2 can only be <6>
R5C9 can only be <5>
R5C1 can only be <8>
R1C2 can only be <1>
R5C8 can only be <1>
R7C9 can only be <6>
R3C6 can only be <6>
R7C4 can only be <5>
R9C7 can only be <2>
R9C8 can only be <5>
R1C7 can only be <6>
R9C5 can only be <6>
R1C8 can only be <2>
R1C5 can only be <7>
R2C7 can only be <3>
R3C1 can only be <7>
R4C6 can only be <4>
R4C4 can only be <6>
R4C5 can only be <5>
R1C9 can only be <8>
R2C5 can only be <1>
R2C9 can only be <7>
R2C1 can only be <6>
R3C9 can only be <1>
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