Jul 15 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 is the only square in row 2 that can be <9>
R4C6 is the only square in row 4 that can be <3>
R1C6 can only be <6>
R1C5 can only be <2>
R5C2 is the only square in row 5 that can be <2>
R5C5 is the only square in row 5 that can be <9>
R6C4 is the only square in row 6 that can be <2>
R7C8 is the only square in row 7 that can be <2>
R2C1 is the only square in row 2 that can be <2>
R3C9 is the only square in row 3 that can be <2>
R8C1 is the only square in row 8 that can be <3>
R9C5 is the only square in column 5 that can be <6>
R3C2 is the only square in block 1 that can be <8>
Squares R2C6 and R3C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C6 - removing <7> from <789> leaving <89>
R8C6 - removing <17> from <1789> leaving <89>
Squares R2C6 and R3C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C4 - removing <17> from <1357> leaving <35>
R3C4 - removing <17> from <1357> leaving <35>
Squares R4C2 and R5C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <5> from <457> leaving <47>
Squares R4C1 and R6C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C1 - removing <4> from <458> leaving <58>
R9C1 - removing <4> from <458> leaving <58>
Squares R9C1 and R9C7 in row 9 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 row.
R9C3 - removing <5> from <145> leaving <14>
Squares R7C1 and R9C1 in block 7 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.
R7C2 - removing <5> from <569> leaving <69>
R7C3 - removing <5> from <456> leaving <46>
Intersection of block 9 with row 8. The value <4> only appears in one or more of squares R8C7, R8C8 and R8C9 of block 9. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C4 - removing <4> from <147> leaving <17>
Intersection of block 9 with column 7. The values <57> only appears in one or more of squares R7C7, R8C7 and R9C7 of block 9. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain these values.
R1C7 - removing <5> from <358> leaving <38>
R3C7 - removing <5> from <1356> leaving <136>
R5C7 - removing <5> from <135> leaving <13>
Squares R9C1, R9C7, R7C1 and R7C7 form a Type-1 Unique Rectangle on <58>.
R7C7 - removing <58> from <5678> leaving <67>
R7C1 is the only square in row 7 that can be <5>
R9C1 can only be <8>
R9C7 can only be <5>
R7C6 is the only square in row 7 that can be <8>
R8C6 can only be <9>
R7C2 is the only square in row 7 that can be <9>
Squares R2C4, R3C4, R2C8 and R3C8 form a Type-3 Unique Rectangle on <35>. Upon close inspection, it is clear that:
(R2C8 or R3C8)<16>, R8C8<46> and R6C8<146> form a naked triplet on <146> in column 8. No other squares in the column can contain these possibilities
R5C8 - removing <1> from <135> leaving <35>
Squares R5C3 (XY), R5C7 (XZ) and R1C3 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R1C7 - removing <3> from <38> leaving <8>
R1C9 can only be <5>
R1C3 can only be <3>
R4C9 can only be <4>
R4C1 can only be <7>
R6C9 can only be <6>
R6C8 can only be <1>
R8C9 can only be <8>
R4C5 can only be <1>
R6C1 can only be <4>
R4C2 can only be <5>
R6C5 can only be <7>
R5C7 can only be <3>
R2C2 can only be <6>
R5C3 can only be <1>
R9C3 can only be <4>
R5C8 can only be <5>
R9C4 can only be <1>
R7C3 can only be <6>
R8C4 can only be <7>
R2C8 can only be <3>
R8C2 can only be <1>
R2C4 can only be <5>
R3C8 can only be <6>
R3C7 can only be <1>
R8C8 can only be <4>
R7C7 can only be <7>
R7C4 can only be <4>
R8C7 can only be <6>
R2C3 can only be <7>
R3C4 can only be <3>
R3C6 can only be <7>
R2C6 can only be <1>
R3C3 can only be <5>
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