Jul 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <2>
R7C3 can only be <2>
R5C3 is the only square in row 5 that can be <5>
R2C2 is the only square in row 2 that can be <5>
R4C5 is the only square in row 4 that can be <5>
R8C8 is the only square in row 8 that can be <5>
R3C2 is the only square in column 2 that can be <2>
R3C3 is the only square in row 3 that can be <4>
R2C4 is the only square in row 2 that can be <4>
R8C2 is the only square in row 8 that can be <4>
R9C8 is the only square in row 9 that can be <4>
R9C9 is the only square in row 9 that can be <2>
R5C7 is the only square in row 5 that can be <2>
R2C8 is the only square in row 2 that can be <2>
R6C5 is the only square in column 5 that can be <1>
R6C8 can only be <8>
Intersection of row 3 with block 3. The value <3> 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.
R1C8 - removing <3> from <1379> leaving <179>
R1C9 - removing <3> from <138> leaving <18>
Intersection of column 1 with block 7. The value <6> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <6> from <368> leaving <38>
R9C2 - removing <6> from <689> leaving <89>
Intersection of column 5 with block 8. The value <6> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C6 - removing <6> from <6789> leaving <789>
Squares R1C2 and R4C2 in column 2 and R1C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 1 and 4 can be removed.
R1C1 - removing <1> from <1389> leaving <389>
R1C9 - removing <1> from <18> leaving <8>
R3C7 can only be <3>
R3C8 can only be <9>
R3C5 can only be <8>
R2C1 is the only square in row 2 that can be <8>
R9C2 is the only square in row 9 that can be <8>
R7C2 can only be <3>
R7C8 can only be <7>
R7C5 can only be <6>
R1C8 can only be <1>
R1C2 can only be <9>
R4C8 can only be <3>
R2C9 can only be <6>
R2C7 can only be <7>
R8C9 can only be <3>
R4C6 can only be <6>
R5C9 can only be <1>
R5C1 can only be <9>
R7C7 can only be <8>
R9C5 can only be <9>
R8C7 can only be <6>
R9C1 can only be <6>
R1C5 can only be <7>
R1C1 can only be <3>
R6C2 can only be <6>
R2C3 can only be <1>
R2C6 can only be <9>
R8C3 can only be <9>
R4C2 can only be <1>
R6C6 can only be <7>
R5C4 can only be <8>
R8C1 can only be <1>
R5C6 can only be <3>
R8C4 can only be <7>
R6C4 can only be <9>
R8C6 can only be <8>
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