Jan 27 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C2 can only be <1>
R7C4 can only be <2>
R8C2 can only be <6>
R4C2 can only be <4>
R9C2 can only be <8>
R3C7 is the only square in row 3 that can be <2>
R3C5 is the only square in row 3 that can be <1>
R4C3 is the only square in row 4 that can be <6>
R2C5 is the only square in column 5 that can be <6>
Squares R1C1 and R2C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C1 - removing <5> from <57> leaving <7>
R9C1 - removing <5> from <235> leaving <23>
R4C1 can only be <1>
R7C7 is the only square in row 7 that can be <7>
R5C4 is the only square in column 4 that can be <1>
R5C3 is the only square in row 5 that can be <7>
R4C4 is the only square in column 4 that can be <7>
Squares R6C1 and R6C3 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C5 - removing <3> from <3458> leaving <458>
R6C6 - removing <3> from <3458> leaving <458>
Squares R2C9 and R8C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <45> from <14567> leaving <167>
R4C9 - removing <5> from <58> leaving <8>
R6C9 - removing <45> from <14578> leaving <178>
R9C9 - removing <45> from <456> leaving <6>
R1C7 is the only square in row 1 that can be <6>
R1C9 is the only square in row 1 that can be <1>
R6C9 can only be <7>
R1C8 is the only square in row 1 that can be <7>
R6C7 is the only square in row 6 that can be <1>
R6C5 is the only square in column 5 that can be <8>
Squares R1C1 and R2C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C3 - removing <5> from <458> leaving <48>
R1C1 is the only square in row 1 that can be <5>
R2C1 can only be <9>
R3C8 is the only square in column 8 that can be <9>
Intersection of column 5 with block 5. The value <9> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C6 - removing <9> from <349> leaving <34>
Squares R6C6 and R8C5 form a remote naked pair. <45> can be removed from any square that is common to their groups.
R4C5 - removing <5> from <59> leaving <9>
R5C5 - removing <4> from <349> leaving <39>
R9C6 - removing <45> from <3459> leaving <39>
R4C7 can only be <5>
R5C5 can only be <3>
R9C7 can only be <4>
R6C8 can only be <4>
R5C6 can only be <4>
R7C5 can only be <5>
R5C7 can only be <9>
R3C6 can only be <8>
R6C6 can only be <5>
R2C8 can only be <5>
R7C3 can only be <3>
R8C5 can only be <4>
R8C9 can only be <5>
R9C4 can only be <9>
R2C9 can only be <4>
R9C6 can only be <3>
R1C4 can only be <4>
R9C1 can only be <2>
R1C3 can only be <8>
R3C3 can only be <4>
R1C6 can only be <9>
R6C3 can only be <2>
R9C3 can only be <5>
R6C1 can only be <3>
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