Nov 15 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <5>
R3C5 is the only square in column 5 that can be <8>
R3C7 can only be <4>
R2C8 is the only square in row 2 that can be <8>
R7C7 is the only square in row 7 that can be <8>
Intersection of column 1 with block 4. The value <4> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C2 - removing <4> from <3458> leaving <358>
R5C2 - removing <4> from <13456> leaving <1356>
R6C2 - removing <4> from <134568> leaving <13568>
Intersection of column 9 with block 6. The value <4> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <4> from <23459> leaving <2359>
R5C8 - removing <4> from <13459> leaving <1359>
R6C8 - removing <4> from <1345> leaving <135>
R5C4 is the only square in row 5 that can be <4>
R5C6 is the only square in row 5 that can be <7>
R8C4 is the only square in row 8 that can be <7>
Intersection of column 4 with block 5. The value <3> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. 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 <3569> leaving <569>
Squares R6C1<134>, R6C4<35>, R6C8<135> and R6C9<14> in row 6 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1345>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <135> from <13568> leaving <68>
R6C6 - removing <5> from <568> leaving <68>
Squares R6C1 and R8C1 in column 1 and R6C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 6 and 8 can be removed.
R8C2 - removing <1> from <1359> leaving <359>
R6C8 - removing <1> from <135> leaving <35>
R8C8 - removing <1> from <1369> leaving <369>
Squares R6C4 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <3> from <134> leaving <14>
Squares R5C3 and R9C3 in column 3 and R5C5 and R9C5 in column 5 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C2 - removing <5> from <1356> leaving <136>
R9C2 - removing <5> from <13459> leaving <1349>
R5C8 - removing <5> from <1359> leaving <139>
Squares R5C3, R7C3 and R9C3 in column 3, R7C5 and R9C5 in column 5 and R5C7 and R9C7 in column 7 form a Swordfish pattern on possibility <3>. All other instances of this possibility in rows 5, 7 and 9 can be removed.
R5C2 - removing <3> from <136> leaving <16>
R7C2 - removing <3> from <2349> leaving <249>
R9C2 - removing <3> from <1349> leaving <149>
R5C8 - removing <3> from <139> leaving <19>
R7C8 - removing <3> from <349> leaving <49>
R9C8 - removing <3> from <1349> leaving <149>
Squares R5C8<19>, R7C8<49> and R9C8<149> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <149>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C8 - removing <9> from <2359> leaving <235>
R8C8 - removing <9> from <369> leaving <36>
Intersection of row 4 with block 5. The value <9> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. 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 <9> from <569> leaving <56>
Squares R2C1 and R8C1 in column 1, R2C4 and R4C4 in column 4 and R2C6, R4C6 and R8C6 in column 6 form a Swordfish pattern on possibility <9>. All other instances of this possibility in rows 2, 4 and 8 can be removed.
R2C2 - removing <9> from <2369> leaving <236>
R8C2 - removing <9> from <359> leaving <35>
Squares R1C5 (XY), R5C5 (XZ) and R2C4 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R4C4 - removing <5> from <359> leaving <39>
R6C4 - removing <5> from <35> leaving <3>
R6C8 can only be <5>
R4C4 can only be <9>
R2C4 can only be <5>
Squares R4C1<34>, R4C8<23> and R4C9<24> in row 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <234>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <3> from <358> leaving <58>
Squares R8C6 (XY), R8C2 (XZ) and R7C5 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R7C3 - removing <3> from <23> leaving <2>
R1C3 can only be <6>
R1C5 can only be <9>
R3C3 can only be <1>
R7C5 can only be <3>
R2C6 can only be <6>
R2C9 can only be <2>
R6C6 can only be <8>
R2C2 can only be <3>
R4C9 can only be <4>
R1C8 can only be <7>
R3C2 can only be <7>
R4C1 can only be <3>
R6C9 can only be <1>
R6C2 can only be <6>
R4C6 can only be <5>
R6C1 can only be <4>
R8C9 can only be <6>
R5C8 can only be <9>
R9C5 can only be <5>
R8C8 can only be <3>
R9C3 can only be <3>
R5C5 can only be <6>
R8C6 can only be <9>
R1C2 can only be <2>
R3C8 can only be <6>
R2C1 can only be <9>
R8C2 can only be <5>
R4C8 can only be <2>
R5C3 can only be <5>
R4C2 can only be <8>
R5C2 can only be <1>
R5C7 can only be <3>
R7C8 can only be <4>
R7C2 can only be <9>
R9C8 can only be <1>
R8C1 can only be <1>
R9C7 can only be <9>
R9C2 can only be <4>
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