Jan 03 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <7>
R2C2 is the only square in row 2 that can be <8>
R5C5 is the only square in row 5 that can be <7>
R5C4 is the only square in row 5 that can be <5>
R2C4 can only be <9>
R8C4 can only be <2>
R7C5 can only be <9>
R5C7 is the only square in row 5 that can be <8>
R8C9 is the only square in row 8 that can be <1>
R8C5 is the only square in row 8 that can be <8>
R9C3 is the only square in row 9 that can be <8>
R9C1 is the only square in row 9 that can be <7>
R1C3 is the only square in row 1 that can be <7>
R1C2 is the only square in column 2 that can be <5>
R6C5 is the only square in column 5 that can be <2>
R8C1 is the only square in block 7 that can be <9>
Intersection of block 1 with column 1. The value <2> only appears in one or more of squares R1C1, R2C1 and R3C1 of block 1. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
R5C1 - removing <2> from <126> leaving <16>
Intersection of block 7 with column 2. The value <6> only appears in one or more of squares R7C2, R8C2 and R9C2 of block 7. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain this value.
R5C2 - removing <6> from <236> leaving <23>
Squares R1C7<2349>, R1C8<349>, R1C9<2349> and R2C9<23> in block 3 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2349>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <3> from <356> leaving <56>
Squares R6C3 and R6C7 in row 6 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 7 can be removed.
R1C7 - removing <3> from <2349> leaving <249>
R5C3 - removing <3> from <12369> leaving <1269>
Squares R3C3 and R3C7 in row 3 and R6C3 and R6C7 in row 6 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 7 can be removed.
R4C3 - removing <6> from <69> leaving <9>
R4C7 - removing <6> from <469> leaving <49>
R5C3 - removing <6> from <1269> leaving <129>
R4C7 can only be <4>
R4C5 can only be <6>
R9C5 can only be <4>
R5C6 can only be <4>
R8C6 can only be <6>
R8C2 can only be <3>
R8C8 can only be <4>
R5C2 can only be <2>
R7C3 can only be <2>
R5C3 can only be <1>
R9C2 can only be <6>
R5C1 can only be <6>
R3C3 can only be <6>
R7C7 can only be <3>
R6C7 can only be <6>
R3C7 can only be <5>
R6C3 can only be <3>
R2C1 can only be <2>
R3C5 can only be <1>
R2C8 can only be <6>
R2C9 can only be <3>
R1C1 can only be <1>
R2C5 can only be <5>
R5C9 can only be <9>
R1C8 can only be <9>
R1C5 can only be <3>
R5C8 can only be <3>
R9C9 can only be <2>
R9C7 can only be <9>
R1C9 can only be <4>
R1C7 can only be <2>
R9C8 can only be <5>
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