Sep 24 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <4>
R1C2 is the only square in row 1 that can be <8>
R3C5 is the only square in row 3 that can be <3>
R3C7 is the only square in row 3 that can be <8>
R5C6 is the only square in row 5 that can be <4>
R8C6 is the only square in row 8 that can be <3>
R4C9 is the only square in row 4 that can be <3>
R9C4 is the only square in row 9 that can be <8>
Squares R8C2 and R8C7 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <5> from <457> leaving <47>
R8C5 - removing <5> from <457> leaving <47>
Intersection of row 3 with block 3. The value <7> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <7> from <2479> leaving <249>
R1C9 - removing <7> from <2467> leaving <246>
Intersection of block 9 with row 9. The value <4> only appears in one or more of squares R9C7, R9C8 and R9C9 of block 9. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C1 - removing <4> from <12469> leaving <1269>
R9C5 - removing <4> from <456> leaving <56>
Squares R9C5 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <6> from <1269> leaving <129>
R9C2 - removing <56> from <1569> leaving <19>
R9C8 - removing <5> from <1245> leaving <124>
Squares R9C5 and R9C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C5 - removing <56> from <4567> leaving <47>
Squares R7C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <7> from <2567> leaving <256>
R4C5 - removing <7> from <1579> leaving <159>
R6C5 - removing <7> from <1579> leaving <159>
Intersection of column 8 with block 6. The value <5> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C7 - removing <5> from <259> leaving <29>
R5C7 - removing <5> from <2569> leaving <269>
Squares R4C6<57>, R5C4<35> and R6C4<357> in block 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <357>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <5> from <159> leaving <19>
R6C5 - removing <5> from <159> leaving <19>
Squares R4C1<129>, R4C5<19> and R4C7<29> in row 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <129>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C8 - removing <29> from <2579> leaving <57>
Squares R8C3, R8C5, R7C3 and R7C5 form a Type-1 Unique Rectangle on <47>.
R7C3 - removing <47> from <24567> leaving <256>
R7C5 is the only square in row 7 that can be <7>
R8C5 can only be <4>
R8C3 can only be <7>
R7C1 is the only square in row 7 that can be <4>
R3C3 is the only square in column 3 that can be <4>
R3C8 can only be <7>
R3C9 can only be <6>
R4C8 can only be <5>
R6C9 can only be <7>
R4C6 can only be <7>
R1C4 is the only square in row 1 that can be <7>
R5C7 is the only square in column 7 that can be <6>
Squares R9C5, R9C6, R1C5 and R1C6 form a Type-1 Unique Rectangle on <56>.
R1C5 - removing <56> from <256> leaving <2>
R1C9 can only be <4>
R2C5 can only be <6>
R1C8 can only be <9>
R9C9 can only be <2>
R2C3 can only be <9>
R9C5 can only be <5>
R1C6 can only be <5>
R9C6 can only be <6>
R7C7 can only be <5>
R1C1 can only be <6>
R5C8 can only be <2>
R5C3 can only be <5>
R2C8 can only be <1>
R4C7 can only be <9>
R7C2 can only be <6>
R8C7 can only be <1>
R8C2 can only be <5>
R2C7 can only be <2>
R9C8 can only be <4>
R4C5 can only be <1>
R5C4 can only be <3>
R6C3 can only be <6>
R5C2 can only be <9>
R6C4 can only be <5>
R7C3 can only be <2>
R4C1 can only be <2>
R6C5 can only be <9>
R9C2 can only be <1>
R6C1 can only be <1>
R6C2 can only be <3>
R9C1 can only be <9>
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