Dec 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C6 can only be <8>
R5C8 can only be <5>
R5C4 can only be <1>
R1C4 can only be <6>
R2C8 is the only square in row 2 that can be <8>
R8C1 is the only square in row 8 that can be <8>
Squares R6C5 and R6C9 in row 6 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 row.
R6C4 - removing <3> from <235> leaving <25>
Squares R4C9 and R6C9 in column 9 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.
R1C9 - removing <3> from <13479> leaving <1479>
R2C9 - removing <36> from <13467> leaving <147>
R8C9 - removing <36> from <1346> leaving <14>
R9C9 - removing <3> from <13479> leaving <1479>
Intersection of block 8 with row 9. The value <2> only appears in one or more of squares R9C4, R9C5 and R9C6 of block 8. 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 <2> from <2349> leaving <349>
R9C8 - removing <2> from <2349> leaving <349>
R2C1 is the only square in column 1 that can be <2>
R2C3 can only be <4>
Squares R2C5 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C2 - removing <1> from <136> leaving <36>
R2C7 - removing <17> from <1367> leaving <36>
R7C7 is the only square in column 7 that can be <7>
R9C2 is the only square in row 9 that can be <7>
Squares R6C5, R6C9, R4C5 and R4C9 form a Type-1 Unique Rectangle on <36>.
R4C5 - removing <36> from <369> leaving <9>
R4C1 can only be <5>
R5C5 can only be <7>
R5C6 can only be <4>
R2C5 can only be <1>
R5C2 can only be <9>
R6C6 can only be <2>
R6C4 can only be <5>
R9C6 can only be <1>
R1C6 can only be <7>
R8C5 can only be <3>
R2C9 can only be <7>
R4C4 can only be <3>
R6C1 can only be <4>
R4C9 can only be <6>
R9C4 can only be <2>
R6C5 can only be <6>
R6C9 can only be <3>
R7C2 can only be <3>
R1C2 can only be <1>
R2C2 can only be <6>
R9C1 can only be <9>
R9C9 can only be <4>
R1C1 can only be <3>
R7C3 can only be <2>
R9C8 can only be <3>
R8C9 can only be <1>
R1C9 can only be <9>
R1C8 can only be <4>
R3C8 can only be <6>
R2C7 can only be <3>
R3C2 can only be <5>
R3C3 can only be <9>
R8C2 can only be <4>
R3C7 can only be <1>
R8C8 can only be <2>
R7C8 can only be <9>
R8C3 can only be <5>
R8C7 can only be <6>
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