Sep 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <5>
R5C9 can only be <6>
R4C6 can only be <4>
R4C2 can only be <9>
R6C6 can only be <1>
R6C4 can only be <6>
R5C5 can only be <2>
R4C8 can only be <3>
R9C5 can only be <8>
R2C5 is the only square in row 2 that can be <4>
R2C8 is the only square in row 2 that can be <6>
R2C3 is the only square in row 2 that can be <9>
R3C5 is the only square in column 5 that can be <3>
Intersection of row 3 with block 3. The value <2> 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.
R2C7 - removing <2> from <258> leaving <58>
Intersection of column 3 with block 7. The value <8> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. 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 <8> from <2678> leaving <267>
R8C2 - removing <8> from <234678> leaving <23467>
Intersection of block 8 with row 8. The values <25> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain these values.
R8C2 - removing <2> from <23467> leaving <3467>
R8C7 - removing <2> from <2489> leaving <489>
R8C8 - removing <2> from <124789> leaving <14789>
Squares R2C7<58>, R3C7<25> and R7C7<28> in column 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <258>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C7 - removing <5> from <459> leaving <49>
R8C7 - removing <8> from <489> leaving <49>
Intersection of column 7 with block 3. The value <5> 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.
R1C8 - removing <5> from <158> leaving <18>
R3C8 - removing <5> from <1257> leaving <127>
Squares R2C4 and R8C4 in column 4 and R2C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C1 - removing <1> from <137> leaving <37>
R2C2 - removing <1> from <13578> leaving <3578>
R8C5 - removing <1> from <156> leaving <56>
R8C8 - removing <1> from <14789> leaving <4789>
R5C1 is the only square in column 1 that can be <1>
Squares R6C2 and R6C8 in row 6 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 8 can be removed.
R5C2 - removing <4> from <457> leaving <57>
R5C8 - removing <4> from <459> leaving <59>
R8C2 - removing <4> from <3467> leaving <367>
R8C8 - removing <4> from <4789> leaving <789>
Squares R8C1<37>, R8C2<367>, R8C4<12>, R8C5<56>, R8C6<25> and R8C9<17> in row 8 form a comprehensive naked set. These 6 squares can only contain the 6 possibilities <123567>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <7> from <478> leaving <48>
R8C8 - removing <7> from <789> leaving <89>
Squares R7C7<28>, R8C7<49>, R8C8<89> and R9C8<24> in block 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2489>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C8 - removing <28> from <1278> leaving <17>
Squares R2C1 and R8C1 in column 1 and R2C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C2 - removing <7> from <3578> leaving <358>
R8C2 - removing <7> from <367> leaving <36>
Squares R1C8 (XY), R1C5 (XZ) and R2C7 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R2C6 - removing <5> from <25> leaving <2>
R2C4 can only be <1>
R8C6 can only be <5>
R8C5 can only be <6>
R2C9 can only be <7>
R8C4 can only be <2>
R1C5 can only be <5>
R2C1 can only be <3>
R8C9 can only be <1>
R8C2 can only be <3>
R7C5 can only be <1>
R7C8 can only be <7>
R8C1 can only be <7>
R7C3 can only be <8>
R7C7 can only be <2>
R8C3 can only be <4>
R7C2 can only be <6>
R3C7 can only be <5>
R9C8 can only be <4>
R8C7 can only be <9>
R9C2 can only be <2>
R8C8 can only be <8>
R5C7 can only be <4>
R1C8 can only be <1>
R6C8 can only be <5>
R1C2 can only be <8>
R3C8 can only be <2>
R3C3 can only be <7>
R2C7 can only be <8>
R6C2 can only be <4>
R5C8 can only be <9>
R2C2 can only be <5>
R5C2 can only be <7>
R3C2 can only be <1>
R5C3 can only be <5>
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