Jul 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <3>
R6C4 can only be <7>
R7C4 can only be <2>
R5C4 can only be <5>
R3C4 can only be <8>
R3C6 can only be <5>
R4C4 can only be <1>
R1C3 is the only square in row 1 that can be <1>
R3C7 is the only square in row 3 that can be <2>
R4C7 is the only square in row 4 that can be <5>
R4C6 is the only square in row 4 that can be <8>
R5C5 is the only square in row 5 that can be <2>
R5C2 is the only square in row 5 that can be <7>
R6C6 is the only square in row 6 that can be <3>
R9C9 is the only square in row 9 that can be <1>
R9C3 is the only square in column 3 that can be <5>
Squares R2C2 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <9> from <789> leaving <78>
R2C9 - removing <59> from <5789> leaving <78>
Squares R7C6 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C1 - removing <9> from <3479> leaving <347>
R7C3 - removing <69> from <4679> leaving <47>
R7C7 - removing <69> from <3469> leaving <34>
R3C3 is the only square in column 3 that can be <6>
R7C3 is the only square in column 3 that can be <7>
Squares R8C2 and R8C5 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C1 - removing <9> from <249> leaving <24>
R8C8 - removing <69> from <24569> leaving <245>
R8C9 - removing <69> from <569> leaving <5>
Squares R5C8 and R7C9 form a remote naked pair. <69> can be removed from any square that is common to their groups.
R9C8 - removing <69> from <269> leaving <2>
R8C8 can only be <4>
R8C1 can only be <2>
R7C7 can only be <3>
R7C1 can only be <4>
R1C7 is the only square in row 1 that can be <4>
Squares R4C3, R4C5, R6C3 and R6C5 form a Type-1 Unique Rectangle on <49>.
R6C5 - removing <49> from <469> leaving <6>
R6C7 can only be <9>
R8C5 can only be <9>
R5C6 can only be <9>
R6C3 can only be <4>
R9C7 can only be <6>
R5C8 can only be <6>
R8C2 can only be <6>
R4C5 can only be <4>
R7C6 can only be <6>
R7C9 can only be <9>
R4C3 can only be <9>
R1C8 can only be <5>
R3C9 can only be <7>
R1C2 can only be <3>
R2C8 can only be <9>
R2C2 can only be <5>
R3C1 can only be <9>
R2C9 can only be <8>
R1C1 can only be <8>
R9C2 can only be <9>
R2C1 can only be <7>
R1C9 can only be <6>
R9C1 can only be <3>
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