Jul 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <5>
R5C5 is the only square in row 5 that can be <9>
R9C9 is the only square in row 9 that can be <5>
R9C1 is the only square in row 9 that can be <6>
R2C2 is the only square in column 2 that can be <1>
R2C3 is the only square in row 2 that can be <2>
R9C5 is the only square in row 9 that can be <2>
R8C2 is the only square in row 8 that can be <2>
R5C1 is the only square in column 1 that can be <2>
Squares R6C3 and R6C5 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <8> from <158> leaving <15>
R6C6 - removing <8> from <568> leaving <56>
R6C7 - removing <4> from <146> leaving <16>
Squares R2C7 and R2C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C7 - removing <7> from <1379> leaving <139>
R1C9 - removing <7> from <1378> leaving <138>
R3C8 - removing <7> from <789> leaving <89>
R3C9 - removing <7> from <378> leaving <38>
Squares R3C1 and R3C8 in row 3 and R7C1 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 8 can be removed.
R1C1 - removing <9> from <39> leaving <3>
R8C8 - removing <9> from <489> leaving <48>
R3C9 is the only square in row 3 that can be <3>
Squares R5C2 and R5C4 in row 5 and R7C2 and R7C4 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 4 can be removed.
R4C4 - removing <3> from <238> leaving <28>
Squares R3C4 and R4C4 in column 4 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 column.
R7C4 - removing <8> from <358> leaving <35>
Squares R3C1 and R3C2 in row 3, R5C2 and R5C8 in row 5 and R7C1, R7C2 and R7C8 in row 7 form a Swordfish pattern on possibility <4>. All other instances of this possibility in columns 1, 2 and 8 can be removed.
R8C8 - removing <4> from <48> leaving <8>
R8C5 can only be <3>
R3C8 can only be <9>
R7C9 can only be <7>
R3C1 can only be <4>
R1C7 can only be <1>
R7C8 can only be <4>
R5C9 can only be <1>
R9C7 can only be <3>
R7C4 can only be <5>
R9C3 can only be <7>
R1C9 can only be <8>
R6C7 can only be <6>
R1C5 can only be <7>
R3C2 can only be <7>
R7C1 can only be <9>
R1C3 can only be <9>
R5C4 can only be <3>
R6C6 can only be <5>
R2C7 can only be <7>
R8C3 can only be <4>
R7C6 can only be <8>
R6C4 can only be <1>
R3C6 can only be <2>
R7C2 can only be <3>
R5C8 can only be <7>
R8C7 can only be <9>
R6C3 can only be <8>
R2C8 can only be <6>
R4C7 can only be <4>
R3C4 can only be <8>
R4C6 can only be <7>
R5C6 can only be <6>
R4C5 can only be <8>
R5C2 can only be <4>
R6C5 can only be <4>
R4C3 can only be <3>
R4C4 can only be <2>
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