Jan 02 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C8 can only be <8>
R6C4 can only be <9>
R4C7 can only be <3>
R6C6 can only be <5>
R4C3 can only be <4>
R6C7 can only be <2>
R6C3 can only be <3>
R2C5 is the only square in row 2 that can be <5>
R2C9 is the only square in row 2 that can be <7>
R5C4 is the only square in row 5 that can be <1>
R5C6 is the only square in row 5 that can be <4>
R7C9 is the only square in row 7 that can be <5>
R5C9 can only be <9>
R5C7 can only be <5>
Intersection of row 2 with block 1. The value <2> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <2> from <12369> leaving <1369>
R1C3 - removing <2> from <1289> leaving <189>
R3C1 - removing <2> from <12369> leaving <1369>
R3C2 - removing <2> from <236> leaving <36>
Intersection of row 7 with block 8. The value <8> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C4 - removing <8> from <4678> leaving <467>
R9C6 - removing <8> from <3678> leaving <367>
Intersection of row 8 with block 7. The value <7> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <7> from <13479> leaving <1349>
R9C3 - removing <7> from <179> leaving <19>
Squares R3C1 and R3C8 in row 3 and R7C1 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 8 can be removed.
R1C1 - removing <1> from <1369> leaving <369>
R8C1 - removing <1> from <13479> leaving <3479>
R9C1 - removing <1> from <1349> leaving <349>
Squares R1C1 and R1C9 in row 1 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C1 - removing <3> from <1369> leaving <169>
R3C9 - removing <3> from <23> leaving <2>
R7C1 - removing <3> from <1234> leaving <124>
R9C1 - removing <3> from <349> leaving <49>
R9C9 - removing <3> from <348> leaving <48>
R1C4 is the only square in row 1 that can be <2>
R1C5 is the only square in row 1 that can be <4>
R8C5 can only be <1>
R8C7 can only be <9>
R9C5 can only be <6>
R8C3 can only be <7>
R5C3 can only be <2>
R5C2 can only be <6>
R2C3 can only be <8>
R2C7 can only be <6>
R2C1 can only be <2>
R5C1 can only be <7>
R3C2 can only be <3>
R3C8 can only be <1>
R7C2 can only be <2>
R7C8 can only be <3>
R1C7 can only be <8>
R7C6 can only be <8>
R8C9 can only be <4>
R8C1 can only be <3>
R9C9 can only be <8>
R9C7 can only be <1>
R1C9 can only be <3>
R7C4 can only be <4>
R4C6 can only be <6>
R9C3 can only be <9>
R4C4 can only be <8>
R1C6 can only be <9>
R7C1 can only be <1>
R9C4 can only be <7>
R9C1 can only be <4>
R1C3 can only be <1>
R9C6 can only be <3>
R3C4 can only be <6>
R1C1 can only be <6>
R3C6 can only be <7>
R3C1 can only be <9>
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