Feb 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 can only be <8>
R4C9 can only be <3>
R5C4 can only be <8>
R5C6 can only be <4>
R5C7 can only be <9>
R6C1 can only be <2>
R4C5 can only be <5>
R6C9 can only be <4>
R5C5 can only be <2>
R5C9 can only be <6>
R7C7 can only be <3>
R6C5 can only be <3>
R5C1 can only be <7>
R5C3 can only be <1>
R7C3 can only be <4>
Intersection of row 8 with block 7. The value <3> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <3> from <359> leaving <59>
Intersection of row 8 with block 9. The value <1> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C9 - removing <1> from <1259> leaving <259>
Intersection of block 2 with row 1. The value <3> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
R1C1 - removing <3> from <3459> leaving <459>
R1C8 - removing <3> from <3489> leaving <489>
Squares R7C8<679>, R8C8<69> and R9C8<679> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <679>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <9> from <489> leaving <48>
R2C8 - removing <9> from <3489> leaving <348>
R3C8 - removing <9> from <349> leaving <34>
Intersection of column 8 with block 9. The values <679> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C9 - removing <9> from <1259> leaving <125>
R9C9 - removing <9> from <259> leaving <25>
Squares R1C2 and R1C9 in row 1 and R9C2 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 9 can be removed.
R2C2 - removing <2> from <1289> leaving <189>
R2C9 - removing <2> from <129> leaving <19>
R8C2 - removing <2> from <269> leaving <69>
R8C9 - removing <2> from <125> leaving <15>
Squares R8C2 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C1 - removing <9> from <359> leaving <35>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
R8C1 - removing <5> from <35> leaving <3>
R8C9 - removing <5> from <15> leaving <1>
R2C9 can only be <9>
R2C1 can only be <4>
Squares R1C1 and R9C1 in column 1 and R1C4 and R9C4 in column 4 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C2 - removing <9> from <1289> leaving <128>
R9C2 - removing <9> from <2679> leaving <267>
R1C5 - removing <9> from <149> leaving <14>
R9C5 - removing <9> from <169> leaving <16>
R9C8 - removing <9> from <679> leaving <67>
Squares R3C2 (XY), R3C7 (XZ) and R1C1 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R1C9 - removing <5> from <25> leaving <2>
R3C3 - removing <5> from <35> leaving <3>
R9C9 can only be <5>
R2C7 can only be <1>
R2C2 can only be <8>
R3C7 can only be <5>
R3C8 can only be <4>
R2C3 can only be <2>
R8C7 can only be <2>
R1C8 can only be <8>
R8C3 can only be <5>
R9C1 can only be <9>
R1C2 can only be <1>
R2C8 can only be <3>
R9C4 can only be <3>
R1C1 can only be <5>
R8C2 can only be <6>
R9C6 can only be <1>
R1C4 can only be <9>
R9C5 can only be <6>
R1C6 can only be <3>
R1C5 can only be <4>
R3C2 can only be <9>
R3C5 can only be <1>
R8C8 can only be <9>
R7C2 can only be <7>
R9C8 can only be <7>
R7C5 can only be <9>
R9C2 can only be <2>
R7C8 can only be <6>
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