Jun 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 is the only square in row 1 that can be <1>
R1C4 is the only square in row 1 that can be <9>
R4C9 is the only square in row 4 that can be <9>
R8C9 can only be <6>
R1C7 is the only square in row 1 that can be <6>
R3C7 can only be <7>
R5C7 can only be <5>
R4C5 is the only square in row 4 that can be <6>
R4C4 is the only square in row 4 that can be <1>
R5C3 is the only square in row 5 that can be <1>
R5C8 is the only square in row 5 that can be <6>
R6C1 is the only square in row 6 that can be <9>
R8C5 is the only square in row 8 that can be <1>
R7C8 is the only square in row 7 that can be <1>
R8C7 is the only square in row 8 that can be <9>
R7C7 can only be <8>
R7C3 is the only square in row 7 that can be <9>
R9C9 is the only square in row 9 that can be <5>
R1C2 is the only square in column 2 that can be <7>
R6C6 is the only square in column 6 that can be <5>
Squares R5C1 and R7C1 in column 1 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 column.
R2C1 - removing <3> from <35> leaving <5>
R3C1 - removing <3> from <3568> leaving <568>
R9C1 - removing <3> from <368> leaving <68>
R3C5 is the only square in row 3 that can be <5>
Intersection of row 6 with block 5. The value <3> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <3> from <2347> leaving <247>
Intersection of column 3 with block 1. The value <4> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <4> from <348> leaving <38>
Intersection of column 6 with block 8. The values <78> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C5 - removing <7> from <2347> leaving <234>
R9C4 - removing <7> from <347> leaving <34>
Squares R4C2 and R4C6 in row 4 and R8C2 and R8C6 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 6 can be removed.
R5C2 - removing <2> from <234> leaving <34>
R7C6 - removing <2> from <2347> leaving <347>
Squares R2C3 and R3C3 in column 3, R2C4, R3C4 and R9C4 in column 4 and R2C8 and R9C8 in column 8 form a Swordfish pattern on possibility <4>. All other instances of this possibility in rows 2, 3 and 9 can be removed.
R2C5 - removing <4> from <2347> leaving <237>
R9C6 - removing <4> from <3478> leaving <378>
R3C9 - removing <4> from <234> leaving <23>
Squares R2C8 (XY), R3C9 (XZ) and R2C3 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R3C3 - removing <3> from <346> leaving <46>
R3C2 - removing <3> from <38> leaving <8>
R3C1 can only be <6>
R8C2 can only be <2>
R8C6 can only be <8>
R4C2 can only be <4>
R7C1 can only be <3>
R3C3 can only be <4>
R9C1 can only be <8>
R2C3 can only be <3>
R4C6 can only be <2>
R5C2 can only be <3>
R5C1 can only be <2>
R9C3 can only be <6>
R5C9 can only be <7>
R5C5 can only be <4>
R7C9 can only be <4>
R6C8 can only be <2>
R2C8 can only be <4>
R7C5 can only be <2>
R7C6 can only be <7>
R1C9 can only be <3>
R9C8 can only be <7>
R9C6 can only be <3>
R1C6 can only be <4>
R3C9 can only be <2>
R3C4 can only be <3>
R2C5 can only be <7>
R9C4 can only be <4>
R2C4 can only be <2>
R6C5 can only be <3>
R6C4 can only be <7>
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