Jan 19 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C3 can only be <2>
R5C3 can only be <6>
R4C3 can only be <1>
R1C6 is the only square in row 1 that can be <6>
R3C2 is the only square in row 3 that can be <2>
R4C4 is the only square in row 4 that can be <6>
R7C8 is the only square in row 7 that can be <5>
R8C2 is the only square in row 8 that can be <6>
R8C5 is the only square in row 8 that can be <7>
R9C9 is the only square in row 9 that can be <2>
R4C5 is the only square in row 4 that can be <2>
R5C8 is the only square in row 5 that can be <2>
R7C3 is the only square in column 3 that can be <4>
R8C7 is the only square in column 7 that can be <1>
R8C8 can only be <9>
R9C2 is the only square in block 7 that can be <9>
Squares R1C3 and R1C9 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <3> from <137> leaving <17>
Squares R8C1 and R9C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <3> from <1357> leaving <157>
R6C1 - removing <8> from <578> leaving <57>
Squares R3C6 and R7C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C6 - removing <39> from <3589> leaving <58>
R6C6 - removing <9> from <4589> leaving <458>
R8C6 - removing <3> from <348> leaving <48>
Squares R7C4 and R7C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C4 - removing <3> from <348> leaving <48>
Intersection of row 4 with block 6. The value <4> only appears in one or more of squares R4C7, R4C8 and R4C9 of row 4. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R6C7 - removing <4> from <4579> leaving <579>
Intersection of column 9 with block 3. The value <9> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C7 - removing <9> from <379> leaving <37>
Intersection of row 3 with block 2. The value <9> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C4 - removing <9> from <3479> leaving <347>
R2C5 - removing <9> from <349> leaving <34>
Intersection of column 5 with block 5. The value <9> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. 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 <9> from <389> leaving <38>
Squares R1C1, R1C8, R2C1 and R2C8 form a Type-4 Unique Rectangle on <17>.
R2C1 - removing <7> from <157> leaving <15>
R2C8 - removing <7> from <178> leaving <18>
Squares R1C1 and R6C1 in column 1 and R1C8 and R6C8 in column 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 1 and 6 can be removed.
R6C7 - removing <7> from <579> leaving <59>
Squares R1C3, R1C9, R2C3 and R2C9 form a Type-1 Unique Rectangle on <39>.
R2C9 - removing <39> from <389> leaving <8>
R2C8 can only be <1>
R4C9 can only be <4>
R4C7 can only be <5>
R8C9 can only be <3>
R8C1 can only be <8>
R1C9 can only be <9>
R9C7 can only be <4>
R9C4 can only be <8>
R1C3 can only be <3>
R2C1 can only be <5>
R1C8 can only be <7>
R4C2 can only be <8>
R6C7 can only be <9>
R6C5 can only be <4>
R5C7 can only be <7>
R8C6 can only be <4>
R9C1 can only be <3>
R5C4 can only be <3>
R2C3 can only be <9>
R1C1 can only be <1>
R6C8 can only be <8>
R3C7 can only be <3>
R2C2 can only be <7>
R6C1 can only be <7>
R3C6 can only be <9>
R5C2 can only be <5>
R5C6 can only be <8>
R5C5 can only be <9>
R2C4 can only be <4>
R7C4 can only be <9>
R6C6 can only be <5>
R2C5 can only be <3>
R7C6 can only be <3>
R3C4 can only be <7>
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