Jan 11 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 is the only square in row 5 that can be <8>
R4C1 is the only square in row 4 that can be <8>
R6C5 is the only square in row 6 that can be <2>
R9C1 is the only square in row 9 that can be <7>
Squares R5C8 and R8C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <3> from <3578> leaving <578>
R2C8 - removing <3> from <357> leaving <57>
R9C8 - removing <34> from <348> leaving <8>
R1C9 is the only square in row 1 that can be <8>
Squares R1C8 and R2C8 in block 3 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 block.
R2C9 - removing <5> from <359> leaving <39>
Intersection of block 2 with row 1. The value <9> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
R1C1 - removing <9> from <12369> leaving <1236>
Intersection of block 8 with row 9. The value <4> 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.
R9C2 - removing <4> from <23456> leaving <2356>
R9C9 - removing <4> from <12346> leaving <1236>
Squares R1C6<19>, R4C6<49> and R9C6<14> in column 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <149>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C6 - removing <14> from <1346> leaving <36>
R6C6 - removing <4> from <346> leaving <36>
R5C4 is the only square in row 5 that can be <1>
Squares R6C4 and R9C4 in column 4 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.
R4C4 - removing <45> from <4579> leaving <79>
Squares R5C2 and R8C2 in column 2 and R5C8 and R8C8 in column 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 5 and 8 can be removed.
R8C1 - removing <4> from <346> leaving <36>
R8C9 - removing <4> from <1346> leaving <136>
Squares R1C3 and R9C3 in column 3 and R1C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C1 - removing <6> from <1236> leaving <123>
R1C2 - removing <6> from <2356> leaving <235>
R9C2 - removing <6> from <2356> leaving <235>
R9C9 - removing <6> from <1236> leaving <123>
Squares R1C2<235>, R2C2<35> and R9C2<235> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <235>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C2 - removing <35> from <3456> leaving <46>
R8C5 is the only square in row 8 that can be <5>
R4C5 can only be <7>
R9C4 can only be <4>
R9C6 can only be <1>
R6C4 can only be <5>
R1C6 can only be <9>
R1C4 can only be <7>
R4C6 can only be <4>
R4C4 can only be <9>
R2C5 can only be <1>
R4C9 can only be <5>
R1C8 can only be <5>
R1C3 can only be <6>
R2C8 can only be <7>
R1C7 can only be <3>
R9C3 can only be <5>
R3C1 can only be <9>
R1C2 can only be <2>
R9C7 can only be <6>
R2C9 can only be <9>
R2C1 can only be <3>
R3C9 can only be <6>
R1C1 can only be <1>
R9C2 can only be <3>
R2C2 can only be <5>
R8C1 can only be <6>
R8C2 can only be <4>
R6C1 can only be <4>
R8C8 can only be <3>
R5C2 can only be <6>
R7C1 can only be <2>
R8C9 can only be <1>
R5C8 can only be <4>
R9C9 can only be <2>
R7C9 can only be <4>
R5C6 can only be <3>
R6C6 can only be <6>
R6C9 can only be <3>
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