Mar 20 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 can only be <9>
R4C2 is the only square in row 4 that can be <2>
R5C6 is the only square in row 5 that can be <3>
R2C6 is the only square in column 6 that can be <2>
Intersection of row 5 with block 6. The value <8> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <8> from <1678> leaving <167>
Intersection of column 1 with block 7. The value <4> 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 <4> from <34589> leaving <3589>
R8C2 - removing <4> from <1345689> leaving <135689>
R9C2 - removing <4> from <1348> leaving <138>
Intersection of block 6 with column 8. The values <16> only appears in one or more of squares R4C8, R5C8 and R6C8 of block 6. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain these values.
R1C8 - removing <1> from <123> leaving <23>
R2C8 - removing <1> from <134578> leaving <34578>
R3C8 - removing <1> from <14578> leaving <4578>
R8C8 - removing <1> from <1234789> leaving <234789>
R9C8 - removing <1> from <1348> leaving <348>
Squares R8C1<458>, R8C4<45> and R8C6<48> in row 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <58> from <135689> leaving <1369>
R8C5 - removing <458> from <3458> leaving <3>
R8C7 - removing <48> from <13478> leaving <137>
R8C8 - removing <48> from <234789> leaving <2379>
R8C9 - removing <8> from <1278> leaving <127>
Squares R1C2 and R1C9 in row 1 and R9C2 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 9 can be removed.
R2C2 - removing <1> from <135678> leaving <35678>
R2C9 - removing <1> from <178> leaving <78>
R3C2 - removing <1> from <1578> leaving <578>
R8C2 - removing <1> from <169> leaving <69>
R8C9 - removing <1> from <127> leaving <27>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <3> from <35678> leaving <5678>
R2C8 - removing <3> from <34578> leaving <4578>
R7C2 - removing <3> from <3589> leaving <589>
R7C8 - removing <3> from <3489> leaving <489>
Squares R2C2<5678>, R3C2<578>, R5C2<479>, R6C2<479>, R7C2<589> and R8C2<69> in column 2 form a comprehensive naked set. These 6 squares can only contain the 6 possibilities <456789>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C2 - removing <8> from <138> leaving <13>
Squares R7C3<39>, R8C2<69>, R8C3<169> and R9C2<13> in block 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <9> from <589> leaving <58>
Squares R8C7 (XY), R9C9 (XZ) and R5C7 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R7C7 - removing <8> from <348> leaving <34>
Squares R8C9 (XY), R1C9 (XZ) and R8C7 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R2C7 - removing <1> from <13478> leaving <3478>
R3C7 - removing <1> from <1478> leaving <478>
R9C9 - removing <1> from <18> leaving <8>
R9C1 can only be <4>
R2C9 can only be <7>
R8C9 can only be <2>
R1C9 can only be <1>
R9C8 can only be <3>
R9C2 can only be <1>
R1C8 can only be <2>
R7C7 can only be <4>
R1C2 can only be <3>
R7C8 can only be <9>
R3C7 can only be <8>
R7C3 can only be <3>
R8C8 can only be <7>
R8C7 can only be <1>
R6C8 can only be <1>
R2C7 can only be <3>
R5C7 can only be <7>
R5C3 can only be <9>
R4C8 can only be <6>
R4C4 can only be <1>
R5C8 can only be <8>
R5C2 can only be <4>
R8C3 can only be <6>
R8C2 can only be <9>
R2C3 can only be <1>
R3C3 can only be <7>
R3C2 can only be <5>
R4C5 can only be <8>
R4C6 can only be <7>
R7C5 can only be <5>
R6C6 can only be <4>
R5C4 can only be <6>
R6C2 can only be <7>
R8C6 can only be <8>
R7C2 can only be <8>
R6C5 can only be <9>
R8C4 can only be <4>
R2C4 can only be <9>
R8C1 can only be <5>
R2C5 can only be <4>
R6C4 can only be <5>
R2C8 can only be <5>
R3C5 can only be <1>
R2C1 can only be <8>
R3C8 can only be <4>
R2C2 can only be <6>
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