Apr 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 can only be <7>
R2C5 can only be <3>
R1C1 can only be <4>
R1C6 can only be <1>
R1C9 can only be <3>
R3C5 can only be <4>
R3C4 can only be <6>
R2C8 is the only square in row 2 that can be <7>
R8C8 can only be <4>
R9C8 can only be <6>
R9C9 can only be <2>
R8C9 can only be <5>
R7C9 can only be <8>
R7C7 can only be <7>
R2C9 can only be <9>
R2C1 can only be <6>
R3C9 can only be <1>
R3C8 can only be <8>
R5C9 can only be <4>
R6C9 can only be <6>
R2C2 can only be <8>
R3C7 can only be <2>
R7C6 is the only square in row 7 that can be <4>
Intersection of column 3 with block 4. The values <47> 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 these values.
R5C1 - removing <7> from <1379> leaving <139>
Intersection of column 6 with block 5. The values <589> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <9> from <129> leaving <12>
R6C5 - removing <9> from <1279> leaving <127>
Squares R4C1<1239>, R4C2<1269>, R4C3<469>, R4C4<134>, R4C5<12> and R4C8<19> in row 4 form a comprehensive naked set. These 6 squares can only contain the 6 possibilities <123469>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C6 - removing <9> from <589> leaving <58>
R4C7 - removing <3> from <358> leaving <58>
Squares R5C1 and R5C4 in row 5 and R9C1 and R9C4 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 4 can be removed.
R4C1 - removing <1> from <1239> leaving <239>
R4C4 - removing <1> from <134> leaving <34>
R6C4 - removing <1> from <1347> leaving <347>
R7C1 - removing <1> from <159> leaving <59>
Squares R3C1 and R7C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C1 - removing <9> from <239> leaving <23>
R5C1 - removing <9> from <139> leaving <13>
R8C1 - removing <9> from <279> leaving <27>
Squares R3C1, R3C3, R7C1 and R7C3 form a Type-1 Unique Rectangle on <59>.
R7C3 - removing <59> from <569> leaving <6>
R4C2 is the only square in row 4 that can be <6>
R7C1 is the only square in row 7 that can be <5>
R3C1 can only be <9>
R3C3 can only be <5>
Intersection of column 3 with block 4. The values <479> 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 these values.
R6C2 - removing <9> from <129> leaving <12>
Squares R4C1 (XY), R4C5 (XZ) and R5C1 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R5C4 - removing <1> from <137> leaving <37>
R5C1 is the only square in row 5 that can be <1>
R9C1 can only be <7>
R6C2 can only be <2>
R8C2 can only be <9>
R4C1 can only be <3>
R8C5 can only be <7>
R7C2 can only be <1>
R8C1 can only be <2>
R6C5 can only be <1>
R9C4 can only be <1>
R7C5 can only be <9>
R4C4 can only be <4>
R4C3 can only be <9>
R6C8 can only be <9>
R4C5 can only be <2>
R6C6 can only be <5>
R4C8 can only be <1>
R5C3 can only be <7>
R5C4 can only be <3>
R6C3 can only be <4>
R5C7 can only be <8>
R6C4 can only be <7>
R5C6 can only be <9>
R4C7 can only be <5>
R6C7 can only be <3>
R4C6 can only be <8>
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