Jun 17 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 is the only square in row 1 that can be <6>
R1C7 is the only square in row 1 that can be <9>
R3C8 is the only square in row 3 that can be <8>
R5C4 is the only square in row 5 that can be <8>
R3C9 is the only square in column 9 that can be <3>
Squares R9C2 and R9C3 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C5 - removing <9> from <2789> leaving <278>
Squares R3C6 and R5C6 in column 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 column.
R2C6 - removing <47> from <2347> leaving <23>
R7C6 - removing <47> from <2467> leaving <26>
R8C6 - removing <4> from <346> leaving <36>
Squares R9C2 and R9C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <9> from <1459> leaving <145>
R8C3 - removing <3> from <345> leaving <45>
Squares R7C9 and R9C8 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C8 - removing <27> from <2567> leaving <56>
R9C7 - removing <7> from <78> leaving <8>
R8C5 is the only square in row 8 that can be <8>
Intersection of row 1 with block 1. The value <2> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C3 - removing <2> from <2457> leaving <457>
Intersection of column 3 with block 4. The value <1> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C2 - removing <1> from <1235> leaving <235>
R5C1 - removing <1> from <157> leaving <57>
R5C2 - removing <1> from <12569> leaving <2569>
R6C2 - removing <1> from <136> leaving <36>
Squares R3C1 and R5C1 in column 1 and R3C6 and R5C6 in column 6 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 3 and 5 can be removed.
R5C3 - removing <7> from <12579> leaving <1259>
R3C4 - removing <7> from <479> leaving <49>
R3C5 - removing <7> from <4579> leaving <459>
R5C7 - removing <7> from <14567> leaving <1456>
R5C8 - removing <7> from <24567> leaving <2456>
R5C9 - removing <7> from <27> leaving <2>
R7C9 can only be <7>
R9C8 can only be <2>
R9C5 can only be <7>
R4C5 can only be <1>
R6C5 can only be <4>
R5C6 can only be <7>
R5C1 can only be <5>
R3C6 can only be <4>
R3C4 can only be <9>
R7C1 can only be <1>
R3C1 can only be <7>
R3C5 can only be <5>
R7C4 can only be <4>
R3C2 can only be <1>
R2C5 can only be <2>
R7C2 can only be <5>
R8C4 can only be <3>
R8C6 can only be <6>
R2C4 can only be <7>
R8C7 can only be <5>
R7C6 can only be <2>
R8C3 can only be <4>
R4C7 can only be <7>
R7C8 can only be <6>
R2C7 can only be <4>
R2C6 can only be <3>
R7C5 can only be <9>
R2C3 can only be <5>
R1C8 can only be <7>
R5C8 can only be <4>
R6C8 can only be <3>
R1C3 can only be <2>
R1C2 can only be <4>
R4C3 can only be <3>
R4C2 can only be <2>
R4C8 can only be <5>
R9C3 can only be <9>
R6C2 can only be <6>
R6C7 can only be <1>
R5C2 can only be <9>
R6C3 can only be <7>
R5C7 can only be <6>
R9C2 can only be <3>
R5C3 can only be <1>
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