Oct 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <7>
R1C9 is the only square in row 1 that can be <7>
R4C6 is the only square in row 4 that can be <7>
R4C4 is the only square in row 4 that can be <2>
R2C8 is the only square in row 2 that can be <2>
R3C6 is the only square in row 3 that can be <2>
R4C1 is the only square in row 4 that can be <9>
R8C2 is the only square in row 8 that can be <2>
R9C3 is the only square in row 9 that can be <7>
R5C2 is the only square in column 2 that can be <8>
Intersection of row 6 with block 5. The value <9> 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.
R5C4 - removing <9> from <134569> leaving <13456>
R5C6 - removing <9> from <14569> leaving <1456>
Intersection of column 5 with block 5. The values <68> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R5C4 - removing <6> from <13456> leaving <1345>
R5C6 - removing <6> from <1456> leaving <145>
R6C4 - removing <68> from <34689> leaving <349>
R6C6 - removing <68> from <4689> leaving <49>
Intersection of column 7 with block 3. The values <58> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C8 - removing <8> from <368> leaving <36>
R9C8 is the only square in column 8 that can be <8>
Squares R1C2 and R1C8 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C4 - removing <6> from <1568> leaving <158>
R1C6 - removing <6> from <1568> leaving <158>
Intersection of column 6 with block 8. The value <6> 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 this value.
R7C4 - removing <6> from <45689> leaving <4589>
R9C4 - removing <6> from <3469> leaving <349>
Intersection of block 9 with row 8. The value <9> only appears in one or more of squares R8C7, R8C8 and R8C9 of block 9. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C6 - removing <9> from <459> leaving <45>
Squares R3C1 and R7C1 in column 1 and R3C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 3 and 7 can be removed.
R7C3 - removing <1> from <156> leaving <56>
R3C4 - removing <1> from <156> leaving <56>
R3C7 - removing <1> from <145> leaving <45>
Squares R4C5, R4C9, R6C5 and R6C9 form a Type-4 Unique Rectangle on <38>.
R6C5 - removing <3> from <368> leaving <68>
R6C9 - removing <3> from <348> leaving <48>
Squares R6C5 (XY), R6C1 (XZ) and R4C5 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R6C4 - removing <3> from <349> leaving <49>
R6C1 is the only square in row 6 that can be <3>
R5C3 can only be <6>
R2C3 can only be <1>
R7C3 can only be <5>
R8C3 can only be <3>
R8C5 can only be <5>
R8C6 can only be <4>
R5C5 can only be <3>
R8C8 can only be <9>
R6C6 can only be <9>
R8C7 can only be <1>
R5C8 can only be <4>
R4C5 can only be <8>
R5C7 can only be <9>
R6C9 can only be <8>
R6C4 can only be <4>
R9C6 can only be <6>
R6C5 can only be <6>
R4C9 can only be <3>
R7C9 can only be <4>
R9C1 can only be <4>
R7C6 can only be <8>
R7C4 can only be <9>
R3C9 can only be <1>
R9C2 can only be <9>
R3C1 can only be <6>
R9C4 can only be <3>
R7C2 can only be <6>
R3C4 can only be <5>
R3C8 can only be <3>
R7C1 can only be <1>
R1C2 can only be <3>
R2C2 can only be <4>
R3C7 can only be <4>
R5C4 can only be <1>
R1C6 can only be <1>
R2C7 can only be <8>
R1C8 can only be <6>
R5C6 can only be <5>
R1C4 can only be <8>
R1C7 can only be <5>
R2C4 can only be <6>
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