Jul 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <4>
R2C6 can only be <3>
R4C2 can only be <8>
R6C2 can only be <1>
R6C5 can only be <9>
R2C1 can only be <8>
R8C6 can only be <9>
R3C5 can only be <6>
R1C5 can only be <2>
R6C8 can only be <6>
R4C5 can only be <5>
R5C6 can only be <1>
R4C8 can only be <9>
R5C4 can only be <7>
R5C5 can only be <8>
R8C4 can only be <5>
R7C9 is the only square in row 7 that can be <8>
R9C9 is the only square in row 9 that can be <9>
R1C8 is the only square in column 8 that can be <1>
Squares R2C9 and R5C9 in column 9 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 column.
R3C9 - removing <5> from <345> leaving <34>
R8C9 - removing <2> from <236> leaving <36>
Squares R1C1<349>, R3C1<134>, R5C1<49> and R7C1<13> in column 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1349>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C1 - removing <3> from <236> leaving <26>
R9C1 - removing <34> from <2346> leaving <26>
Squares R3C3 and R3C7 in row 3 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.
R5C7 - removing <5> from <25> leaving <2>
R9C3 - removing <5> from <457> leaving <47>
R9C7 - removing <5> from <23567> leaving <2367>
R5C9 can only be <5>
R2C9 can only be <2>
Squares R1C3<479>, R5C3<49> and R9C3<47> in column 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <479>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C3 - removing <4> from <145> leaving <15>
R7C3 - removing <7> from <157> leaving <15>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <7> from <347> leaving <34>
R9C2 - removing <7> from <3457> leaving <345>
R9C8 - removing <7> from <257> leaving <25>
Squares R5C1, R5C3, R1C1 and R1C3 form a Type-4 Unique Rectangle on <49>.
R1C1 - removing <4> from <349> leaving <39>
R1C3 - removing <4> from <479> leaving <79>
Squares R1C1 (XY), R1C2 (XZ) and R5C1 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C1 - removing <4> from <134> leaving <13>
R3C9 is the only square in row 3 that can be <4>
R1C2 is the only square in row 1 that can be <4>
R9C3 is the only square in row 9 that can be <4>
R5C3 can only be <9>
R5C1 can only be <4>
R1C3 can only be <7>
R2C2 can only be <5>
R2C8 can only be <7>
R9C2 can only be <3>
R3C3 can only be <1>
R8C8 can only be <2>
R3C1 can only be <3>
R7C3 can only be <5>
R8C1 can only be <6>
R9C8 can only be <5>
R9C5 can only be <7>
R8C2 can only be <7>
R7C1 can only be <1>
R9C7 can only be <6>
R7C5 can only be <3>
R9C1 can only be <2>
R1C7 can only be <3>
R8C9 can only be <3>
R1C1 can only be <9>
R1C9 can only be <6>
R3C7 can only be <5>
R7C7 can only be <7>
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