Jun 22 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 is the only square in row 2 that can be <2>
R2C8 is the only square in row 2 that can be <6>
R4C9 is the only square in row 4 that can be <2>
R6C5 is the only square in row 6 that can be <4>
R1C8 is the only square in column 8 that can be <1>
R9C1 is the only square in column 1 that can be <1>
R8C5 is the only square in row 8 that can be <1>
R8C2 is the only square in row 8 that can be <6>
R7C1 can only be <4>
R5C1 is the only square in row 5 that can be <6>
R7C5 is the only square in row 7 that can be <6>
R4C3 is the only square in block 4 that can be <8>
R4C2 is the only square in row 4 that can be <1>
R3C3 is the only square in row 3 that can be <1>
Intersection of row 6 with block 6. The value <3> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C8 - removing <3> from <3789> leaving <789>
R5C9 - removing <3> from <3589> leaving <589>
Intersection of column 7 with block 3. The value <8> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <8> from <3489> leaving <349>
R3C9 - removing <8> from <3489> leaving <349>
Squares R1C9, R3C9 and R8C9 in column 9 form a simple naked triplet. These 3 squares all contain the 3 possibilities <349>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C9 - removing <9> from <589> leaving <58>
R9C9 - removing <34> from <3458> leaving <58>
Intersection of row 9 with block 8. The value <4> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. 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 <4> from <2349> leaving <239>
Squares R5C2 and R5C8 in row 5 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <7> from <34579> leaving <3459>
R3C2 - removing <7> from <3479> leaving <349>
R6C8 - removing <7> from <379> leaving <39>
R8C8 - removing <7> from <2379> leaving <239>
R3C5 is the only square in row 3 that can be <7>
R1C1 is the only square in row 1 that can be <7>
R6C1 can only be <9>
R6C8 can only be <3>
R2C1 can only be <8>
R1C5 is the only square in row 1 that can be <8>
R3C7 is the only square in row 3 that can be <8>
Squares R7C8 and R8C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C8 - removing <9> from <789> leaving <78>
R9C8 - removing <2> from <278> leaving <78>
R9C6 is the only square in row 9 that can be <2>
R9C4 is the only square in row 9 that can be <4>
R4C7 is the only square in block 6 that can be <9>
R4C5 can only be <5>
R9C5 can only be <3>
R9C2 can only be <7>
R2C5 can only be <9>
R8C6 can only be <9>
R8C8 can only be <2>
R5C6 can only be <3>
R7C4 can only be <5>
R7C8 can only be <9>
R9C8 can only be <8>
R5C2 can only be <5>
R8C3 can only be <3>
R9C9 can only be <5>
R5C8 can only be <7>
R5C9 can only be <8>
R7C7 can only be <3>
R6C3 can only be <7>
R5C4 can only be <9>
R3C6 can only be <4>
R6C7 can only be <5>
R1C4 can only be <3>
R7C3 can only be <2>
R2C7 can only be <4>
R8C9 can only be <4>
R2C3 can only be <5>
R8C7 can only be <7>
R1C9 can only be <9>
R1C2 can only be <4>
R3C9 can only be <3>
R2C2 can only be <3>
R1C6 can only be <5>
R3C2 can only be <9>
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