Jun 30 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C4 can only be <9>
R8C2 can only be <5>
R7C8 can only be <2>
R7C9 can only be <6>
R7C5 can only be <1>
R8C7 can only be <9>
R8C3 can only be <2>
R4C7 can only be <7>
R9C7 can only be <3>
R9C1 can only be <9>
R9C2 can only be <1>
R2C7 can only be <6>
R5C7 can only be <1>
R7C2 can only be <3>
R1C4 is the only square in row 1 that can be <3>
R1C6 is the only square in row 1 that can be <2>
R1C2 is the only square in row 1 that can be <6>
R3C8 is the only square in row 3 that can be <9>
R2C3 is the only square in row 2 that can be <9>
R6C6 is the only square in row 6 that can be <1>
R8C5 is the only square in row 8 that can be <6>
R6C1 is the only square in row 6 that can be <6>
R5C6 is the only square in row 5 that can be <6>
R5C9 is the only square in row 5 that can be <9>
R4C6 is the only square in row 4 that can be <9>
Squares R2C1 and R3C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C1 - removing <5> from <235> leaving <23>
R5C1 - removing <5> from <235> leaving <23>
Squares R2C1 and R3C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C3 - removing <5> from <457> leaving <47>
Intersection of row 1 with block 3. The value <5> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C8 - removing <5> from <457> leaving <47>
Intersection of row 4 with block 5. The value <4> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <4> from <24578> leaving <2578>
R5C5 - removing <4> from <34578> leaving <3578>
Intersection of column 4 with block 5. The values <27> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R5C5 - removing <7> from <3578> leaving <358>
R6C5 - removing <7> from <578> leaving <58>
Squares R2C1, R3C1, R2C6 and R3C6 form a Type-2 Unique Rectangle on <58>.
R2C5 - removing <4> from <4578> leaving <578>
R3C5 - removing <4> from <4578> leaving <578>
R9C6 - removing <4> from <458> leaving <58>
R4C5 is the only square in column 5 that can be <4>
R4C1 is the only square in row 4 that can be <3>
R5C1 can only be <2>
R5C5 is the only square in row 5 that can be <3>
Squares R4C4, R4C9, R6C4 and R6C9 form a Type-4 Unique Rectangle on <25>.
R6C4 - removing <5> from <2578> leaving <278>
R6C9 - removing <5> from <258> leaving <28>
Squares R6C5 (XY), R4C4 (XZ) and R6C9 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R6C4 - removing <2> from <278> leaving <78>
R4C9 - removing <2> from <25> leaving <5>
R4C4 can only be <2>
R1C9 can only be <4>
R5C8 can only be <8>
R9C8 can only be <4>
R6C9 can only be <2>
R2C8 can only be <7>
R8C9 can only be <8>
R1C3 can only be <7>
R1C8 can only be <5>
R8C4 can only be <4>
R6C3 can only be <5>
R3C2 can only be <4>
R5C2 can only be <7>
R5C4 can only be <5>
R5C3 can only be <4>
R9C4 can only be <8>
R6C5 can only be <8>
R6C4 can only be <7>
R2C5 can only be <5>
R9C6 can only be <5>
R3C6 can only be <8>
R2C1 can only be <8>
R3C5 can only be <7>
R3C1 can only be <5>
R2C6 can only be <4>
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