Sep 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <9>
R8C5 can only be <3>
R4C5 is the only square in row 4 that can be <5>
R5C5 is the only square in row 5 that can be <2>
R5C6 is the only square in row 5 that can be <4>
R3C7 is the only square in row 3 that can be <4>
R1C5 is the only square in row 1 that can be <4>
R3C3 is the only square in row 3 that can be <2>
R6C6 is the only square in row 6 that can be <8>
R3C6 is the only square in column 6 that can be <3>
R3C4 can only be <1>
R5C9 is the only square in column 9 that can be <1>
R5C2 can only be <3>
R6C4 is the only square in row 6 that can be <3>
R1C9 is the only square in column 9 that can be <9>
Intersection of column 3 with block 4. The value <6> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C1 - removing <6> from <69> leaving <9>
R6C7 is the only square in row 6 that can be <9>
R4C4 is the only square in row 4 that can be <9>
R7C3 is the only square in row 7 that can be <9>
Squares R4C3 and R6C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <1> from <137> leaving <37>
R9C3 - removing <1> from <137> leaving <37>
Intersection of block 8 with row 7. The value <7> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.
R7C1 - removing <7> from <1357> leaving <135>
R7C7 - removing <7> from <567> leaving <56>
R7C9 - removing <7> from <3567> leaving <356>
Intersection of block 3 with column 9. The value <6> only appears in one or more of squares R1C9, R2C9 and R3C9 of block 3. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
R7C9 - removing <6> from <356> leaving <35>
R9C9 - removing <6> from <35678> leaving <3578>
Squares R2C1 and R2C9 in row 2 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C1 - removing <7> from <1357> leaving <135>
R9C1 - removing <7> from <13578> leaving <1358>
R9C9 - removing <7> from <3578> leaving <358>
Squares R4C7 and R7C4 form a remote naked pair. <67> can be removed from any square that is common to their groups.
R7C7 - removing <6> from <56> leaving <5>
R7C9 can only be <3>
R7C1 can only be <1>
R9C9 can only be <8>
R8C9 can only be <7>
R7C6 can only be <7>
R9C2 can only be <5>
R7C4 can only be <6>
R4C6 can only be <1>
R8C1 can only be <8>
R2C9 can only be <6>
R9C1 can only be <3>
R1C2 can only be <1>
R2C1 can only be <7>
R3C9 can only be <5>
R3C1 can only be <6>
R4C3 can only be <6>
R6C5 can only be <6>
R6C3 can only be <1>
R9C5 can only be <1>
R5C4 can only be <7>
R9C3 can only be <7>
R1C1 can only be <5>
R1C3 can only be <3>
R4C7 can only be <7>
R1C7 can only be <2>
R5C8 can only be <6>
R9C8 can only be <2>
R9C7 can only be <6>
R1C8 can only be <7>
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