May 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <7>
R1C6 is the only square in row 1 that can be <5>
R1C9 is the only square in row 1 that can be <8>
R2C1 is the only square in row 2 that can be <2>
R2C3 is the only square in row 2 that can be <7>
R9C3 can only be <6>
R5C3 can only be <9>
R8C3 can only be <1>
R8C9 is the only square in row 8 that can be <6>
R9C4 is the only square in row 9 that can be <8>
R2C5 is the only square in row 2 that can be <8>
R6C6 is the only square in row 6 that can be <8>
R8C1 is the only square in column 1 that can be <5>
R3C1 is the only square in column 1 that can be <9>
R5C1 is the only square in column 1 that can be <3>
R4C5 is the only square in row 4 that can be <3>
R4C2 is the only square in column 2 that can be <6>
R4C6 is the only square in row 4 that can be <7>
R4C8 is the only square in column 8 that can be <5>
R7C9 is the only square in column 9 that can be <7>
R8C5 is the only square in column 5 that can be <7>
Squares R6C1 and R6C2 in row 6 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 row.
R6C4 - removing <4> from <149> leaving <19>
R6C5 - removing <4> from <24> leaving <2>
R6C8 - removing <4> from <1249> leaving <129>
R5C7 is the only square in row 5 that can be <2>
R8C6 is the only square in column 6 that can be <2>
Squares R5C6 and R5C9 in row 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 row.
R5C4 - removing <14> from <1456> leaving <56>
R5C5 - removing <4> from <456> leaving <56>
Squares R7C4 and R7C5 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <4> from <249> leaving <29>
R7C8 - removing <4> from <249> leaving <29>
Intersection of block 6 with column 9. The value <4> only appears in one or more of squares R4C9, R5C9 and R6C9 of block 6. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
R2C9 - removing <4> from <149> leaving <19>
Squares R1C2, R1C8, R3C2 and R3C8 form a Type-1 Unique Rectangle on <13>.
R3C8 - removing <13> from <1346> leaving <46>
R3C2 is the only square in row 3 that can be <3>
R1C2 can only be <1>
R1C8 can only be <3>
R3C6 is the only square in row 3 that can be <1>
R5C6 can only be <4>
R5C9 can only be <1>
R4C4 can only be <9>
R2C9 can only be <9>
R6C8 can only be <9>
R6C4 can only be <1>
R7C8 can only be <2>
R4C9 can only be <4>
R7C2 can only be <9>
R9C8 can only be <4>
R9C1 can only be <7>
R3C8 can only be <6>
R8C7 can only be <9>
R2C7 can only be <4>
R3C5 can only be <4>
R2C8 can only be <1>
R8C2 can only be <4>
R6C2 can only be <7>
R9C2 can only be <2>
R6C1 can only be <4>
R2C4 can only be <6>
R7C5 can only be <5>
R7C4 can only be <4>
R5C5 can only be <6>
R5C4 can only be <5>
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