Jun 19 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C3 can only be <6>
R1C9 is the only square in row 1 that can be <8>
R1C8 is the only square in row 1 that can be <4>
R1C7 is the only square in row 1 that can be <1>
R7C7 can only be <2>
R7C1 can only be <1>
R7C9 can only be <7>
R4C5 is the only square in row 4 that can be <8>
R5C5 is the only square in row 5 that can be <3>
R9C1 is the only square in row 9 that can be <8>
R1C4 is the only square in column 4 that can be <9>
Squares R8C5 and R9C4 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C5 - removing <26> from <2467> leaving <47>
R9C6 - removing <2> from <247> leaving <47>
Intersection of row 1 with block 1. The values <36> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
R3C1 - removing <3> from <2359> leaving <259>
R3C3 - removing <3> from <359> leaving <59>
Intersection of column 3 with block 1. The value <5> 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.
R1C1 - removing <5> from <23567> leaving <2367>
R2C1 - removing <5> from <257> leaving <27>
R3C1 - removing <5> from <259> leaving <29>
Squares R2C1, R2C5 and R2C9 in row 2, R3C1 and R3C9 in row 3 and R8C1 and R8C5 in row 8 form a Swordfish pattern on possibility <2>. All other instances of this possibility in columns 1, 5 and 9 can be removed.
R1C1 - removing <2> from <2367> leaving <367>
R1C5 - removing <2> from <257> leaving <57>
Squares R5C8, R9C8, R5C9 and R9C9 form a Type-4 Unique Rectangle on <15>.
R5C9 - removing <5> from <1459> leaving <149>
R9C9 - removing <5> from <1356> leaving <136>
Squares R1C2 (XY), R3C1 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R5C1 - removing <9> from <4569> leaving <456>
R4C1 - removing <9> from <49> leaving <4>
R4C9 can only be <9>
R5C2 is the only square in row 5 that can be <9>
R9C2 can only be <2>
R9C4 can only be <6>
R1C2 can only be <6>
R8C1 can only be <3>
R5C4 can only be <2>
R8C5 can only be <2>
R5C6 can only be <4>
R5C9 can only be <1>
R9C6 can only be <7>
R6C5 can only be <6>
R5C8 can only be <5>
R9C9 can only be <3>
R6C1 can only be <5>
R8C9 can only be <6>
R1C1 can only be <7>
R9C3 can only be <9>
R3C3 can only be <5>
R9C5 can only be <4>
R1C6 can only be <2>
R9C7 can only be <5>
R1C5 can only be <5>
R2C1 can only be <2>
R1C3 can only be <3>
R2C5 can only be <7>
R2C9 can only be <5>
R3C1 can only be <9>
R3C9 can only be <2>
R6C9 can only be <4>
R3C7 can only be <3>
R5C1 can only be <6>
R9C8 can only be <1>
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