Oct 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C6 can only be <4>
R2C2 is the only square in row 2 that can be <7>
R3C7 is the only square in row 3 that can be <1>
R3C4 is the only square in row 3 that can be <6>
R8C8 is the only square in row 8 that can be <9>
R5C6 is the only square in column 6 that can be <9>
R4C7 is the only square in row 4 that can be <9>
R6C6 is the only square in column 6 that can be <5>
R6C7 can only be <8>
R7C7 can only be <2>
R7C3 can only be <4>
R5C7 can only be <5>
R2C7 can only be <3>
R6C5 is the only square in row 6 that can be <6>
R1C5 is the only square in column 5 that can be <3>
R1C1 is the only square in row 1 that can be <9>
R2C5 is the only square in row 2 that can be <9>
R8C2 is the only square in column 2 that can be <3>
Squares R1C4 and R2C4 in column 4 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.
R4C4 - removing <8> from <148> leaving <14>
R5C4 - removing <8> from <148> leaving <14>
Squares R4C4 and R5C4 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <1> from <178> leaving <78>
R5C5 - removing <1> from <178> leaving <78>
Squares R4C5 and R5C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C5 - removing <8> from <128> leaving <12>
Squares R4C5, R5C5, R4C3 and R5C3 form a Type-2 Unique Rectangle on <78>.
R4C1 - removing <2> from <124> leaving <14>
R3C3 - removing <2> from <235> leaving <35>
R5C2 - removing <2> from <124> leaving <14>
R8C3 - removing <2> from <25> leaving <5>
R8C9 can only be <1>
R3C3 can only be <3>
R8C5 can only be <2>
R7C9 can only be <8>
R6C3 can only be <7>
R6C9 can only be <4>
R6C1 can only be <3>
R7C6 can only be <6>
R9C5 can only be <1>
R9C1 can only be <2>
R7C2 can only be <1>
R9C6 can only be <8>
R9C2 can only be <6>
R3C1 can only be <5>
R3C8 can only be <2>
R2C1 can only be <4>
R5C8 can only be <7>
R1C9 can only be <5>
R5C5 can only be <8>
R9C8 can only be <5>
R4C9 can only be <2>
R5C2 can only be <4>
R9C9 can only be <7>
R1C4 can only be <8>
R2C8 can only be <8>
R4C1 can only be <1>
R1C2 can only be <2>
R2C4 can only be <5>
R1C8 can only be <4>
R4C4 can only be <4>
R5C4 can only be <1>
R4C3 can only be <8>
R5C3 can only be <2>
R4C5 can only be <7>
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