Nov 09 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <3>
R6C4 can only be <4>
R7C4 can only be <6>
R3C4 can only be <9>
R2C3 is the only square in row 2 that can be <9>
R1C8 is the only square in row 1 that can be <9>
R3C6 is the only square in row 3 that can be <6>
R4C7 is the only square in row 4 that can be <8>
R2C9 is the only square in row 2 that can be <8>
R2C7 is the only square in row 2 that can be <1>
R5C5 is the only square in row 5 that can be <8>
R5C2 is the only square in row 5 that can be <9>
R8C3 is the only square in row 8 that can be <8>
R3C2 is the only square in row 3 that can be <8>
R7C8 is the only square in row 7 that can be <8>
R9C1 is the only square in row 9 that can be <6>
R5C3 is the only square in row 5 that can be <6>
R7C3 is the only square in column 3 that can be <1>
R7C6 is the only square in column 6 that can be <3>
R9C9 is the only square in row 9 that can be <3>
R9C5 is the only square in row 9 that can be <1>
R8C9 is the only square in row 8 that can be <1>
R3C7 is the only square in column 7 that can be <2>
Squares R1C2 and R1C9 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <57> from <2357> leaving <23>
R1C5 - removing <7> from <237> leaving <23>
Intersection of block 9 with column 7. The value <7> only appears in one or more of squares R7C7, R8C7 and R9C7 of block 9. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain this value.
R5C7 - removing <7> from <3457> leaving <345>
R6C7 - removing <7> from <357> leaving <35>
Intersection of block 6 with row 5. The values <47> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain these values.
R5C1 - removing <7> from <357> leaving <35>
Intersection of block 4 with column 3. The value <7> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R3C3 - removing <7> from <357> leaving <35>
Squares R4C3, R4C6, R6C3 and R6C6 form a Type-1 Unique Rectangle on <57>.
R6C3 - removing <57> from <357> leaving <3>
R6C7 can only be <5>
R3C3 can only be <5>
R5C1 can only be <5>
R6C6 can only be <7>
R5C9 can only be <7>
R3C8 can only be <7>
R4C3 can only be <7>
R1C2 can only be <7>
R3C5 can only be <3>
R5C8 can only be <4>
R1C9 can only be <5>
R4C6 can only be <5>
R8C1 can only be <7>
R5C7 can only be <3>
R9C8 can only be <5>
R8C7 can only be <4>
R2C1 can only be <2>
R8C5 can only be <5>
R7C7 can only be <7>
R9C2 can only be <4>
R2C5 can only be <7>
R1C1 can only be <3>
R1C5 can only be <2>
R7C5 can only be <4>
R7C2 can only be <5>
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