Mar 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 is the only square in row 5 that can be <1>
R7C3 is the only square in row 7 that can be <1>
R8C8 is the only square in row 8 that can be <6>
R8C5 is the only square in row 8 that can be <8>
R9C2 is the only square in row 9 that can be <7>
R1C2 is the only square in column 2 that can be <8>
R5C8 is the only square in column 8 that can be <7>
R4C6 is the only square in column 6 that can be <7>
Intersection of row 3 with block 1. The value <6> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <6> from <269> leaving <29>
R3C3 is the only square in column 3 that can be <6>
Intersection of block 6 with column 9. The value <4> only appears in one or more of squares R4C9, R5C9 and R6C9 of block 6. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
R2C9 - removing <4> from <2459> leaving <259>
R7C9 - removing <4> from <2345> leaving <235>
Squares R3C1 and R3C9 in row 3 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
R2C1 - removing <5> from <2579> leaving <279>
R2C9 - removing <5> from <259> leaving <29>
R6C1 - removing <5> from <569> leaving <69>
R6C6 is the only square in row 6 that can be <5>
R5C6 can only be <3>
R9C6 can only be <4>
R1C6 can only be <6>
R7C7 is the only square in row 7 that can be <4>
Squares R1C4 and R1C7 in row 1 and R9C4 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 4 and 7 can be removed.
R3C7 - removing <3> from <38> leaving <8>
R5C7 can only be <9>
R4C9 can only be <4>
R6C9 can only be <8>
R5C4 is the only square in row 5 that can be <8>
Squares R9C4 and R9C7 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C3 - removing <2> from <259> leaving <59>
Squares R5C2 and R5C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <2> from <269> leaving <69>
Squares R4C1 and R6C1 in column 1 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 column.
R2C1 - removing <9> from <279> leaving <27>
R8C1 - removing <9> from <239> leaving <23>
Squares R1C3 and R1C8 in row 1 and R9C3 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 8 can be removed.
R2C8 - removing <9> from <459> leaving <45>
Squares R8C2 (XY), R5C2 (XZ) and R9C3 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R5C3 - removing <5> from <25> leaving <2>
R5C2 can only be <5>
R1C3 can only be <9>
R1C8 can only be <4>
R9C3 can only be <5>
R1C4 can only be <3>
R2C8 can only be <5>
R2C2 can only be <2>
R9C8 can only be <9>
R3C9 can only be <3>
R3C5 can only be <7>
R1C7 can only be <2>
R8C9 can only be <2>
R9C4 can only be <2>
R9C7 can only be <3>
R2C9 can only be <9>
R2C1 can only be <7>
R8C2 can only be <9>
R3C1 can only be <5>
R2C5 can only be <4>
R8C1 can only be <3>
R7C9 can only be <5>
R4C4 can only be <6>
R7C5 can only be <3>
R6C5 can only be <9>
R4C1 can only be <9>
R6C4 can only be <4>
R6C1 can only be <6>
R4C5 can only be <2>
R7C1 can only be <2>
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