Jul 17 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <4>
R2C8 can only be <8>
R2C1 is the only square in row 2 that can be <1>
R4C5 is the only square in row 4 that can be <2>
R5C5 is the only square in row 5 that can be <1>
R7C7 is the only square in row 7 that can be <1>
R6C5 is the only square in column 5 that can be <6>
R9C5 is the only square in column 5 that can be <9>
Intersection of row 4 with block 5. The value <7> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <7> from <4579> leaving <459>
R5C6 - removing <7> from <4578> leaving <458>
Intersection of block 2 with row 3. The value <3> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C1 - removing <3> from <3679> leaving <679>
R3C7 - removing <3> from <356> leaving <56>
R3C9 - removing <3> from <23569> leaving <2569>
Intersection of block 8 with row 7. The value <4> 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 <4> from <479> leaving <79>
R7C3 - removing <4> from <2479> leaving <279>
Squares R3C7<56>, R4C7<68> and R6C7<58> in column 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <568>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <5> from <345> leaving <34>
R9C7 - removing <58> from <3458> leaving <34>
R9C9 is the only square in row 9 that can be <8>
Squares R3C3 and R3C9 in row 3 and R7C3 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 3 and 9 can be removed.
R1C3 - removing <2> from <2789> leaving <789>
R1C9 - removing <2> from <2359> leaving <359>
R9C3 - removing <2> from <247> leaving <47>
Squares R9C1<347>, R9C3<47> and R9C7<34> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <347>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C2 - removing <3> from <235> leaving <25>
R9C8 - removing <47> from <2457> leaving <25>
Intersection of row 9 with block 7. The value <7> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <7> from <79> leaving <9>
R7C3 - removing <7> from <279> leaving <29>
R8C1 - removing <7> from <3467> leaving <346>
R7C3 can only be <2>
R9C2 can only be <5>
R9C8 can only be <2>
R1C2 is the only square in row 1 that can be <2>
R3C9 is the only square in row 3 that can be <2>
R3C3 is the only square in row 3 that can be <9>
R1C9 is the only square in row 1 that can be <9>
R4C4 is the only square in row 4 that can be <9>
R4C6 is the only square in row 4 that can be <7>
R5C2 is the only square in row 5 that can be <9>
R4C3 is the only square in column 3 that can be <6>
R4C7 can only be <8>
R6C7 can only be <5>
R3C7 can only be <6>
R5C8 can only be <7>
R3C1 can only be <7>
R2C9 can only be <3>
R5C9 can only be <6>
R2C2 can only be <6>
R1C7 can only be <4>
R1C3 can only be <8>
R1C1 can only be <3>
R6C3 can only be <4>
R1C8 can only be <5>
R9C7 can only be <3>
R1C5 can only be <7>
R8C8 can only be <4>
R8C2 can only be <3>
R6C4 can only be <3>
R9C3 can only be <7>
R5C1 can only be <8>
R6C6 can only be <8>
R3C4 can only be <5>
R9C1 can only be <4>
R8C1 can only be <6>
R8C5 can only be <5>
R3C6 can only be <3>
R5C4 can only be <4>
R5C6 can only be <5>
R7C4 can only be <7>
R7C6 can only be <4>
R7C9 can only be <5>
R8C9 can only be <7>
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