Dec 21 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <7>
R5C5 is the only square in row 5 that can be <1>
R5C6 is the only square in row 5 that can be <9>
R5C4 is the only square in row 5 that can be <4>
R5C9 is the only square in row 5 that can be <5>
R8C8 is the only square in row 8 that can be <5>
Squares R2C7 and R9C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C7 - removing <3> from <238> leaving <28>
Intersection of row 5 with block 4. The value <7> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. 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 <7> from <2378> leaving <238>
R6C2 - removing <7> from <2378> leaving <238>
Intersection of column 1 with block 1. The value <3> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C2 - removing <3> from <123579> leaving <12579>
R3C2 - removing <3> from <2379> leaving <279>
Intersection of column 9 with block 9. The value <7> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <7> from <2789> leaving <289>
R9C8 - removing <7> from <179> leaving <19>
Squares R2C7<39>, R3C8<89> and R3C9<38> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <389>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <9> from <1469> leaving <146>
R2C9 - removing <3> from <13> leaving <1>
R9C8 is the only square in column 8 that can be <1>
Squares R7C1<279>, R8C1<267>, R9C2<79> and R9C3<67> in block 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2679>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <279> from <24789> leaving <48>
R8C2 - removing <27> from <12478> leaving <148>
R8C3 - removing <267> from <12678> leaving <18>
Intersection of block 7 with column 1. The value <2> only appears in one or more of squares R7C1, R8C1 and R9C1 of block 7. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
R2C1 - removing <2> from <23679> leaving <3679>
R3C1 - removing <2> from <2379> leaving <379>
R5C1 - removing <2> from <27> leaving <7>
Intersection of block 7 with row 9. The value <7> only appears in one or more of squares R9C1, R9C2 and R9C3 of block 7. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C5 - removing <7> from <367> leaving <36>
Squares R7C2<48>, R7C5<47> and R7C9<78> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <478>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C8 - removing <8> from <289> leaving <29>
Squares R3C1<39>, R3C8<89> and R3C9<38> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <389>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <9> from <279> leaving <27>
Squares R5C3 and R8C3 in column 3 and R5C7 and R8C7 in column 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 5 and 8 can be removed.
R8C2 - removing <8> from <148> leaving <14>
R8C9 - removing <8> from <378> leaving <37>
Squares R8C4 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C6 - removing <7> from <467> leaving <46>
Squares R3C1 and R3C8 in row 3 and R7C1 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 8 can be removed.
R2C1 - removing <9> from <369> leaving <36>
Squares R1C5 (XY), R7C5 (XZ) and R2C4 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R8C4 - removing <7> from <37> leaving <3>
R3C5 - removing <7> from <27> leaving <2>
R3C2 can only be <7>
R8C9 can only be <7>
R9C5 can only be <6>
R7C9 can only be <8>
R9C3 can only be <7>
R8C6 can only be <4>
R9C2 can only be <9>
R7C2 can only be <4>
R3C9 can only be <3>
R8C7 can only be <2>
R8C2 can only be <1>
R2C6 can only be <7>
R7C5 can only be <7>
R8C1 can only be <6>
R5C7 can only be <8>
R7C8 can only be <9>
R9C7 can only be <3>
R7C1 can only be <2>
R2C7 can only be <9>
R2C4 can only be <5>
R6C6 can only be <2>
R3C8 can only be <8>
R3C1 can only be <9>
R5C3 can only be <2>
R6C8 can only be <7>
R4C6 can only be <6>
R4C8 can only be <2>
R4C5 can only be <3>
R2C1 can only be <3>
R8C3 can only be <8>
R1C2 can only be <5>
R1C5 can only be <4>
R2C2 can only be <2>
R1C8 can only be <6>
R1C3 can only be <1>
R2C8 can only be <4>
R2C3 can only be <6>
R6C4 can only be <8>
R4C2 can only be <8>
R6C5 can only be <5>
R6C2 can only be <3>
R4C4 can only be <7>
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