Jan 06 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C6 can only be <8>
R6C4 can only be <2>
R4C4 can only be <6>
R5C5 can only be <4>
R2C5 can only be <2>
R6C6 can only be <9>
R2C4 can only be <7>
R8C4 can only be <8>
R8C6 can only be <2>
R8C5 can only be <9>
R2C6 can only be <4>
R3C5 can only be <8>
R7C5 can only be <3>
R2C1 is the only square in row 2 that can be <3>
R5C3 is the only square in row 5 that can be <8>
R9C2 is the only square in row 9 that can be <3>
R9C3 is the only square in row 9 that can be <2>
R9C9 is the only square in row 9 that can be <9>
R7C2 is the only square in row 7 that can be <9>
R1C3 is the only square in row 1 that can be <9>
R2C9 is the only square in column 9 that can be <6>
Intersection of column 1 with block 1. The value <7> 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.
R1C2 - removing <7> from <1247> leaving <124>
R3C2 - removing <7> from <2457> leaving <245>
Intersection of column 2 with block 1. The values <24> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
R1C1 - removing <4> from <147> leaving <17>
R3C1 - removing <4> from <457> leaving <57>
Squares R3C1 and R3C9 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <5> from <245> leaving <24>
R3C8 - removing <57> from <2457> leaving <24>
Intersection of block 4 with column 2. The values <157> only appears in one or more of squares R4C2, R5C2 and R6C2 of block 4. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain these values.
R1C2 - removing <1> from <124> leaving <24>
Intersection of block 6 with column 8. The value <5> only appears in one or more of squares R4C8, R5C8 and R6C8 of block 6. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R7C8 - removing <5> from <458> leaving <48>
Squares R3C1 and R3C9 in row 3 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
R8C1 - removing <5> from <145> leaving <14>
R8C9 - removing <5> from <157> leaving <17>
Squares R3C2, R3C8, R1C2 and R1C8 form a Type-1 Unique Rectangle on <24>.
R1C8 - removing <24> from <12478> leaving <178>
R1C2 is the only square in row 1 that can be <2>
R3C2 can only be <4>
R3C8 can only be <2>
R1C7 is the only square in row 1 that can be <4>
R8C1 is the only square in row 8 that can be <4>
R7C8 is the only square in row 7 that can be <4>
Squares R3C9 (XY), R2C7 (XZ) and R8C9 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R8C7 - removing <1> from <157> leaving <57>
R1C9 - removing <1> from <178> leaving <78>
R9C7 - removing <1> from <16> leaving <6>
R5C8 is the only square in row 5 that can be <6>
R8C9 is the only square in column 9 that can be <1>
R8C3 can only be <5>
R9C8 can only be <8>
R9C1 can only be <1>
R7C9 can only be <5>
R7C1 can only be <8>
R3C9 can only be <7>
R8C7 can only be <7>
R2C3 can only be <1>
R5C7 can only be <1>
R1C1 can only be <7>
R1C8 can only be <1>
R1C9 can only be <8>
R3C1 can only be <5>
R6C8 can only be <5>
R2C7 can only be <5>
R5C2 can only be <7>
R6C2 can only be <1>
R4C8 can only be <7>
R4C2 can only be <5>
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