Dec 09 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <3>
R7C2 can only be <8>
R9C5 can only be <9>
R1C5 can only be <2>
R7C6 can only be <2>
R7C4 can only be <6>
R7C8 can only be <4>
R1C6 is the only square in row 1 that can be <9>
R3C2 is the only square in row 3 that can be <4>
R3C8 is the only square in column 8 that can be <2>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C7 - removing <1> from <1567> leaving <567>
Intersection of column 9 with block 6. The values <36> 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 these values.
R4C7 - removing <6> from <256> leaving <25>
Squares R4C4 and R4C7 in row 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 row.
R4C6 - removing <5> from <45> leaving <4>
R4C9 - removing <5> from <356> leaving <36>
R6C3 is the only square in row 6 that can be <4>
Intersection of column 3 with block 1. The value <8> 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.
R2C1 - removing <8> from <258> leaving <25>
R3C1 - removing <8> from <3578> leaving <357>
Squares R2C7<158>, R4C7<25>, R6C7<258> and R8C7<15> in column 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1258>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <58> from <5678> leaving <67>
R9C7 - removing <5> from <567> leaving <67>
Squares R1C2 and R9C2 in column 2 and R1C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C4 - removing <5> from <358> leaving <38>
Intersection of block 2 with row 3. The value <5> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C1 - removing <5> from <357> leaving <37>
R3C9 - removing <5> from <578> leaving <78>
Squares R3C1<37>, R4C1<369>, R5C1<68>, R6C1<38> and R7C1<79> in column 1 form a comprehensive naked set. These 5 squares can only contain the 5 possibilities <36789>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C1 - removing <9> from <259> leaving <25>
Squares R4C4, R4C7, R6C4 and R6C7 form a Type-4 Unique Rectangle on <25>.
R6C4 - removing <5> from <125> leaving <12>
R6C7 - removing <5> from <258> leaving <28>
Squares R3C1 (XY), R6C1 (XZ) and R3C9 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R6C9 - removing <8> from <358> leaving <35>
Squares R9C3 (XY), R4C3 (XZ) and R7C1 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R4C1 - removing <9> from <369> leaving <36>
R8C3 - removing <9> from <29> leaving <2>
R8C1 can only be <5>
R2C3 can only be <8>
R8C7 can only be <1>
R2C1 can only be <2>
R9C2 can only be <3>
R8C9 can only be <9>
R2C7 can only be <5>
R7C9 can only be <7>
R9C3 can only be <7>
R1C2 can only be <5>
R9C7 can only be <6>
R1C3 can only be <3>
R7C1 can only be <9>
R9C8 can only be <5>
R1C7 can only be <7>
R1C8 can only be <6>
R1C4 can only be <8>
R4C3 can only be <9>
R3C1 can only be <7>
R9C4 can only be <1>
R3C6 can only be <5>
R3C9 can only be <8>
R2C9 can only be <1>
R4C7 can only be <2>
R3C4 can only be <3>
R6C6 can only be <1>
R5C9 can only be <6>
R4C4 can only be <5>
R6C7 can only be <8>
R5C1 can only be <8>
R4C9 can only be <3>
R6C4 can only be <2>
R9C6 can only be <8>
R6C1 can only be <3>
R4C1 can only be <6>
R6C9 can only be <5>
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