May 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 is the only square in row 1 that can be <5>
R3C3 is the only square in row 3 that can be <7>
R4C1 is the only square in row 4 that can be <5>
R5C2 is the only square in row 5 that can be <3>
R5C1 is the only square in row 5 that can be <7>
R7C4 is the only square in row 7 that can be <5>
R7C6 is the only square in row 7 that can be <3>
R1C4 is the only square in row 1 that can be <3>
R8C9 is the only square in row 8 that can be <3>
R9C7 is the only square in row 9 that can be <9>
R3C6 is the only square in row 3 that can be <9>
R1C8 is the only square in row 1 that can be <9>
R8C7 is the only square in column 7 that can be <7>
R5C9 is the only square in column 9 that can be <1>
R7C7 is the only square in column 7 that can be <1>
R7C1 can only be <9>
R2C3 is the only square in row 2 that can be <9>
Squares R9C2 and R9C5 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C4 - removing <16> from <1467> leaving <47>
R9C6 - removing <16> from <1467> leaving <47>
Squares R7C8 and R8C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C8 - removing <46> from <2468> leaving <28>
R6C8 - removing <6> from <268> leaving <28>
R5C7 is the only square in row 5 that can be <4>
Squares R1C5 and R1C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C4 - removing <18> from <12468> leaving <246>
R2C6 - removing <18> from <12468> leaving <246>
R3C4 - removing <8> from <2468> leaving <246>
Squares R5C8 and R6C8 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C7 - removing <8> from <568> leaving <56>
Squares R6C7 and R6C9 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <6> from <2678> leaving <278>
R6C6 - removing <6> from <2678> leaving <278>
Squares R9C4 and R9C6 in block 8 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 block.
R8C4 - removing <4> from <1468> leaving <168>
R8C6 - removing <4> from <1468> leaving <168>
Intersection of column 3 with block 4. The value <8> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C2 - removing <8> from <268> leaving <26>
Squares R6C7, R6C9, R2C7 and R2C9 form a Type-4 Unique Rectangle on <56>.
R2C7 - removing <6> from <568> leaving <58>
R2C9 - removing <6> from <456> leaving <45>
Intersection of row 2 with block 2. The value <6> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C4 - removing <6> from <246> leaving <24>
Squares R7C3, R7C8, R8C3 and R8C8 form a Type-1 Unique Rectangle on <46>.
R8C3 - removing <46> from <246> leaving <2>
R8C1 can only be <1>
R2C1 can only be <2>
R9C2 can only be <6>
R9C5 can only be <1>
R4C2 can only be <2>
R7C3 can only be <4>
R1C5 can only be <8>
R1C6 can only be <1>
R5C5 can only be <6>
R3C2 can only be <8>
R3C7 can only be <6>
R2C2 can only be <1>
R3C9 can only be <4>
R6C7 can only be <5>
R3C4 can only be <2>
R2C9 can only be <5>
R5C3 can only be <8>
R4C6 can only be <8>
R6C9 can only be <6>
R2C7 can only be <8>
R7C8 can only be <6>
R8C8 can only be <4>
R4C3 can only be <6>
R4C4 can only be <1>
R8C6 can only be <6>
R6C4 can only be <7>
R5C8 can only be <2>
R6C8 can only be <8>
R6C6 can only be <2>
R9C4 can only be <4>
R8C4 can only be <8>
R2C6 can only be <4>
R9C6 can only be <7>
R2C4 can only be <6>
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