Dec 17 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C9 can only be <6>
R7C3 can only be <5>
R5C3 can only be <3>
R8C3 can only be <2>
R8C9 can only be <9>
R2C3 can only be <6>
R3C3 can only be <1>
R2C9 can only be <2>
R1C8 is the only square in row 1 that can be <6>
R2C2 is the only square in row 2 that can be <4>
R2C7 is the only square in row 2 that can be <9>
R4C5 is the only square in row 4 that can be <3>
R4C4 is the only square in row 4 that can be <9>
R4C2 is the only square in row 4 that can be <6>
R6C4 is the only square in row 6 that can be <6>
R7C7 is the only square in row 7 that can be <6>
R9C8 is the only square in row 9 that can be <2>
R8C4 is the only square in column 4 that can be <1>
R5C6 is the only square in column 6 that can be <2>
Squares R7C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C2 - removing <8> from <378> leaving <37>
Squares R1C2 and R1C5 in row 1 and R6C2 and R6C5 in row 6 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 5 can be removed.
R3C2 - removing <5> from <235> leaving <23>
R3C5 - removing <5> from <257> leaving <27>
R5C5 - removing <5> from <4578> leaving <478>
Intersection of row 3 with block 3. The value <5> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C8 - removing <5> from <357> leaving <37>
Squares R2C6 and R2C8 in row 2 and R4C6 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 6 and 8 can be removed.
R3C8 - removing <7> from <357> leaving <35>
R6C6 - removing <7> from <147> leaving <14>
R6C8 - removing <7> from <147> leaving <14>
Squares R6C6 and R6C8 in row 6 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 row.
R6C5 - removing <4> from <457> leaving <57>
Squares R1C5<25>, R3C5<27> and R6C5<57> in column 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <257>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <7> from <478> leaving <48>
Squares R9C2, R9C5, R7C2 and R7C5 form a Type-1 Unique Rectangle on <89>.
R7C5 - removing <89> from <489> leaving <4>
R7C8 can only be <8>
R5C5 can only be <8>
R8C6 can only be <8>
R7C2 can only be <9>
R2C6 can only be <7>
R9C5 can only be <9>
R9C2 can only be <8>
R2C8 can only be <3>
R4C6 can only be <1>
R3C5 can only be <2>
R2C1 can only be <5>
R3C8 can only be <5>
R3C2 can only be <3>
R1C5 can only be <5>
R3C7 can only be <7>
R8C8 can only be <4>
R4C8 can only be <7>
R6C6 can only be <4>
R5C7 can only be <4>
R5C4 can only be <5>
R8C7 can only be <5>
R6C8 can only be <1>
R1C2 can only be <2>
R6C5 can only be <7>
R2C4 can only be <8>
R5C1 can only be <7>
R8C2 can only be <7>
R8C1 can only be <3>
R6C2 can only be <5>
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