Oct 01 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <3>
R5C5 can only be <3>
R1C1 is the only square in row 1 that can be <7>
R1C6 is the only square in row 1 that can be <8>
R3C8 is the only square in row 3 that can be <6>
R4C2 is the only square in row 4 that can be <2>
R2C3 is the only square in row 2 that can be <2>
R4C1 is the only square in row 4 that can be <6>
R5C2 is the only square in row 5 that can be <7>
R5C8 is the only square in row 5 that can be <8>
R8C3 is the only square in row 8 that can be <7>
R8C7 is the only square in row 8 that can be <8>
R9C4 is the only square in row 9 that can be <2>
R2C7 is the only square in column 7 that can be <9>
Squares R1C5 and R2C6 in block 2 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.
R2C5 - removing <14> from <1456> leaving <56>
Squares R4C8 and R4C9 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C8 - removing <3> from <3459> leaving <459>
R6C9 - removing <3> from <3459> leaving <459>
Intersection of row 3 with block 1. The value <4> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C2 - removing <4> from <134> leaving <13>
Intersection of row 7 with block 7. The value <4> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C2 - removing <4> from <3459> leaving <359>
Intersection of row 7 with block 9. The value <1> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C9 - removing <1> from <1359> leaving <359>
Intersection of column 1 with block 4. The value <4> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C2 - removing <4> from <349> leaving <39>
Squares R3C3 and R7C3 in column 3 and R3C7 and R7C7 in column 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 3 and 7 can be removed.
R3C2 - removing <3> from <134> leaving <14>
R7C2 - removing <3> from <345> leaving <45>
R7C8 - removing <3> from <135> leaving <15>
Squares R5C1 and R5C9 in row 5 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 9 can be removed.
R6C1 - removing <9> from <349> leaving <34>
R6C9 - removing <9> from <459> leaving <45>
Squares R2C4, R2C5, R8C4 and R8C5 form a Type-1 Unique Rectangle on <56>.
R8C5 - removing <56> from <456> leaving <4>
R8C6 can only be <3>
R1C5 can only be <1>
R9C6 can only be <1>
R9C5 can only be <5>
R2C6 can only be <4>
R1C9 can only be <4>
R5C9 can only be <9>
R6C9 can only be <5>
R5C1 can only be <4>
R6C8 can only be <4>
R9C9 can only be <3>
R2C5 can only be <6>
R8C4 can only be <6>
R9C1 can only be <9>
R4C9 can only be <1>
R7C7 can only be <1>
R2C4 can only be <5>
R4C8 can only be <3>
R6C1 can only be <3>
R6C2 can only be <9>
R8C2 can only be <5>
R7C8 can only be <5>
R3C7 can only be <3>
R7C2 can only be <4>
R8C8 can only be <9>
R3C3 can only be <4>
R2C8 can only be <1>
R7C3 can only be <3>
R3C2 can only be <1>
R2C2 can only be <3>
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