Jul 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C8 can only be <2>
R8C6 can only be <3>
R8C9 can only be <6>
R7C7 can only be <8>
R9C8 can only be <7>
R9C7 can only be <9>
R1C8 is the only square in row 1 that can be <6>
R1C7 is the only square in row 1 that can be <5>
R2C1 is the only square in row 2 that can be <6>
R2C5 is the only square in row 2 that can be <7>
R3C5 is the only square in row 3 that can be <9>
R5C2 is the only square in row 5 that can be <9>
R6C6 is the only square in row 6 that can be <9>
R8C3 is the only square in row 8 that can be <9>
R9C5 is the only square in row 9 that can be <6>
Squares R5C8 and R6C8 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C7 - removing <3> from <23> leaving <2>
R1C9 is the only square in column 9 that can be <2>
R1C3 is the only square in row 1 that can be <7>
R3C9 is the only square in row 3 that can be <7>
R4C5 is the only square in column 5 that can be <2>
Squares R8C4 and R8C5 in block 8 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 block.
R9C4 - removing <58> from <1258> leaving <12>
Intersection of row 3 with block 1. The value <8> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <8> from <348> leaving <34>
Squares R6C1 and R6C5 in row 6 and R7C1 and R7C5 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 5 can be removed.
R1C5 - removing <1> from <1348> leaving <348>
R5C1 - removing <1> from <1345> leaving <345>
R5C5 - removing <1> from <135> leaving <35>
R9C1 - removing <1> from <145> leaving <45>
R5C9 is the only square in row 5 that can be <1>
R4C9 can only be <4>
R5C1 is the only square in row 5 that can be <4>
R9C1 can only be <5>
R4C3 is the only square in column 3 that can be <5>
R8C4 is the only square in column 4 that can be <5>
R8C5 can only be <8>
R1C4 is the only square in row 1 that can be <8>
R1C6 is the only square in row 1 that can be <1>
Squares R5C5, R5C8, R6C5 and R6C8 form a Type-1 Unique Rectangle on <35>.
R6C5 - removing <35> from <135> leaving <1>
R6C1 can only be <3>
R7C5 can only be <4>
R4C4 can only be <3>
R7C3 can only be <3>
R1C5 can only be <3>
R9C6 can only be <2>
R9C4 can only be <1>
R2C6 can only be <4>
R1C2 can only be <4>
R5C5 can only be <5>
R2C4 can only be <2>
R2C7 can only be <3>
R3C7 can only be <4>
R4C2 can only be <1>
R5C8 can only be <3>
R6C8 can only be <5>
R7C1 can only be <1>
R3C3 can only be <8>
R9C2 can only be <8>
R3C2 can only be <3>
R9C3 can only be <4>
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