Jan 22 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 is the only square in row 1 that can be <3>
R1C7 is the only square in row 1 that can be <5>
R1C5 is the only square in row 1 that can be <7>
R2C4 is the only square in row 2 that can be <5>
R3C1 is the only square in row 3 that can be <6>
R4C7 is the only square in row 4 that can be <9>
R5C9 is the only square in row 5 that can be <1>
R9C9 can only be <2>
R3C9 can only be <9>
R7C9 can only be <7>
R5C2 is the only square in row 5 that can be <5>
R5C8 is the only square in row 5 that can be <7>
R5C4 is the only square in row 5 that can be <3>
R5C1 is the only square in row 5 that can be <9>
R6C8 is the only square in row 6 that can be <3>
R6C3 is the only square in row 6 that can be <7>
R8C3 is the only square in row 8 that can be <3>
R9C5 is the only square in row 9 that can be <9>
R2C6 is the only square in row 2 that can be <9>
Squares R1C1 and R1C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <2> from <124> leaving <14>
R3C2 - removing <28> from <1248> leaving <14>
Squares R5C5 and R5C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <24> from <2468> leaving <68>
R6C5 - removing <2> from <268> leaving <68>
Squares R4C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C5 - removing <6> from <1246> leaving <124>
Intersection of row 8 with block 8. The value <2> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <2> from <268> leaving <68>
R7C6 - removing <2> from <1248> leaving <148>
Intersection of row 9 with block 7. The value <8> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <8> from <248> leaving <24>
R7C2 - removing <8> from <1248> leaving <124>
Intersection of column 1 with block 7. The value <4> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <4> from <124> leaving <12>
R9C3 - removing <4> from <148> leaving <18>
Intersection of column 2 with block 4. The value <8> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. 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 <8> from <248> leaving <24>
Squares R3C2 and R3C6 in row 3 and R7C2 and R7C6 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 6 can be removed.
R8C6 - removing <1> from <124> leaving <24>
Squares R5C6 and R8C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C6 - removing <2> from <128> leaving <18>
R7C6 - removing <4> from <148> leaving <18>
Intersection of block 8 with row 8. The values <24> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain these values.
R8C7 - removing <4> from <146> leaving <16>
Squares R5C5, R5C6, R8C5 and R8C6 form a Type-1 Unique Rectangle on <24>.
R8C5 - removing <24> from <124> leaving <1>
R8C7 can only be <6>
R2C5 can only be <2>
R7C6 can only be <8>
R8C4 can only be <2>
R6C7 can only be <2>
R7C8 can only be <4>
R2C7 can only be <4>
R5C5 can only be <4>
R3C4 can only be <8>
R2C3 can only be <1>
R9C7 can only be <1>
R3C8 can only be <2>
R3C6 can only be <1>
R7C4 can only be <6>
R3C2 can only be <4>
R4C8 can only be <6>
R4C5 can only be <8>
R5C6 can only be <2>
R8C6 can only be <4>
R6C2 can only be <8>
R7C1 can only be <2>
R9C3 can only be <8>
R4C2 can only be <2>
R6C5 can only be <6>
R7C2 can only be <1>
R1C1 can only be <8>
R9C1 can only be <4>
R1C3 can only be <2>
R4C3 can only be <4>
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