May 28 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C3 can only be <7>
R4C3 can only be <9>
R2C2 is the only square in row 2 that can be <9>
R4C5 is the only square in row 4 that can be <7>
R5C8 is the only square in row 5 that can be <9>
R6C2 is the only square in row 6 that can be <3>
R5C2 can only be <2>
R4C2 can only be <1>
R8C6 is the only square in row 8 that can be <1>
R8C4 is the only square in row 8 that can be <9>
R6C5 is the only square in block 5 that can be <2>
Squares R2C5 and R3C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C4 - removing <4> from <2347> leaving <237>
R2C6 - removing <46> from <3467> leaving <37>
R3C4 - removing <4> from <24> leaving <2>
Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <7> from <278> leaving <28>
Intersection of block 8 with row 7. The value <7> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.
R7C2 - removing <7> from <4678> leaving <468>
R7C8 - removing <7> from <4678> leaving <468>
Squares R7C8<468>, R8C7<248>, R8C9<2468> and R9C9<46> in block 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <2468> from <234678> leaving <37>
R9C8 - removing <46> from <3467> leaving <37>
Squares R9C1 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C2 - removing <7> from <467> leaving <46>
Squares R3C2<48>, R7C2<468> and R9C2<46> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <4> from <457> leaving <57>
R8C2 - removing <468> from <45678> leaving <57>
Intersection of row 1 with block 3. The value <4> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <4> from <1248> leaving <128>
R2C8 - removing <4> from <124568> leaving <12568>
R2C9 - removing <4> from <2468> leaving <268>
R3C8 - removing <4> from <468> leaving <68>
Squares R2C3 and R8C3 in column 3 and R2C5 and R8C5 in column 5 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 8 can be removed.
R8C7 - removing <4> from <248> leaving <28>
R8C9 - removing <4> from <2468> leaving <268>
R6C7 is the only square in column 7 that can be <4>
R6C8 can only be <1>
R2C7 is the only square in row 2 that can be <1>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C8 - removing <8> from <2568> leaving <256>
R4C8 - removing <8> from <28> leaving <2>
R4C7 can only be <8>
R8C7 can only be <2>
Squares R2C3<45>, R2C5<46> and R2C8<56> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <456>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C9 - removing <6> from <268> leaving <28>
Intersection of column 9 with block 9. The value <6> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <6> from <468> leaving <48>
Squares R9C1, R9C8, R8C1 and R8C8 form a Type-1 Unique Rectangle on <37>.
R8C1 - removing <37> from <378> leaving <8>
R8C9 can only be <6>
R2C1 can only be <2>
R8C5 can only be <4>
R9C9 can only be <4>
R9C2 can only be <6>
R1C9 can only be <2>
R7C8 can only be <8>
R1C1 can only be <7>
R2C9 can only be <8>
R3C8 can only be <6>
R3C6 can only be <4>
R2C8 can only be <5>
R8C3 can only be <5>
R2C5 can only be <6>
R7C4 can only be <7>
R7C2 can only be <4>
R1C2 can only be <5>
R9C1 can only be <3>
R1C8 can only be <4>
R8C2 can only be <7>
R2C3 can only be <4>
R3C2 can only be <8>
R5C6 can only be <3>
R5C4 can only be <4>
R2C6 can only be <7>
R7C6 can only be <6>
R2C4 can only be <3>
R8C8 can only be <3>
R9C8 can only be <7>
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