Mar 14 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 is the only square in row 2 that can be <3>
R7C9 is the only square in row 7 that can be <7>
R3C4 is the only square in column 4 that can be <5>
R8C7 is the only square in column 7 that can be <1>
R3C7 is the only square in column 7 that can be <6>
R3C1 is the only square in row 3 that can be <8>
R2C3 can only be <7>
R1C3 can only be <6>
R3C8 is the only square in row 3 that can be <2>
R1C1 is the only square in row 1 that can be <2>
R7C2 is the only square in row 7 that can be <6>
R4C2 is the only square in column 2 that can be <7>
R1C8 is the only square in column 8 that can be <7>
R1C2 is the only square in row 1 that can be <5>
Squares R5C2 and R6C1 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <1> from <136> leaving <36>
R5C1 - removing <14> from <1346> leaving <36>
Squares R4C1 and R5C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C1 - removing <3> from <349> leaving <49>
Intersection of row 4 with block 5. The value <1> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <1> from <1249> leaving <249>
R5C5 - removing <1> from <123489> leaving <23489>
R5C6 - removing <1> from <13489> leaving <3489>
R6C5 - removing <1> from <1247> leaving <247>
R6C6 - removing <1> from <147> leaving <47>
Intersection of row 7 with block 8. The values <14> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R8C6 - removing <4> from <3489> leaving <389>
R9C4 - removing <4> from <249> leaving <29>
R9C5 - removing <4> from <23489> leaving <2389>
Squares R2C7, R2C9, R9C7 and R9C9 form a Type-1 Unique Rectangle on <58>.
R9C9 - removing <58> from <458> leaving <4>
R9C2 can only be <9>
R9C4 can only be <2>
R2C2 can only be <1>
R8C1 can only be <4>
R2C1 can only be <9>
R5C2 can only be <4>
R5C4 can only be <9>
R6C1 can only be <1>
R4C4 can only be <1>
R6C8 can only be <5>
R6C9 can only be <2>
R9C8 can only be <3>
R5C9 can only be <6>
R9C5 can only be <8>
R8C8 can only be <6>
R4C5 can only be <3>
R7C4 can only be <4>
R4C1 can only be <6>
R5C6 can only be <8>
R5C5 can only be <2>
R5C1 can only be <3>
R5C8 can only be <1>
R4C9 can only be <9>
R8C9 can only be <8>
R8C3 can only be <3>
R2C9 can only be <5>
R9C7 can only be <5>
R7C5 can only be <1>
R2C7 can only be <8>
R7C6 can only be <3>
R1C5 can only be <4>
R7C3 can only be <8>
R8C6 can only be <9>
R3C6 can only be <7>
R1C6 can only be <1>
R6C5 can only be <7>
R3C5 can only be <9>
R6C6 can only be <4>
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