Aug 20 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <9>
R6C8 can only be <6>
R8C6 can only be <9>
R2C6 can only be <7>
R8C4 can only be <2>
R5C4 can only be <6>
R5C6 can only be <5>
R7C5 can only be <1>
R9C5 can only be <5>
R3C1 is the only square in row 3 that can be <5>
R9C2 is the only square in row 9 that can be <6>
Intersection of block 6 with row 5. The value <3> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C1 - removing <3> from <1349> leaving <149>
R5C5 - removing <3> from <239> leaving <29>
R1C1 is the only square in column 1 that can be <3>
R1C3 is the only square in row 1 that can be <8>
Squares R1C2 and R1C8 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C7 - removing <19> from <179> leaving <7>
R1C9 - removing <1> from <1467> leaving <467>
Squares R3C7 and R7C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C7 - removing <2> from <123> leaving <13>
R9C7 - removing <29> from <1239> leaving <13>
Squares R1C2 and R1C8 in row 1 and R4C2 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 8 can be removed.
R9C8 - removing <1> from <129> leaving <29>
Squares R7C7 and R9C8 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <2> from <278> leaving <78>
R9C9 - removing <2> from <1237> leaving <137>
Squares R2C1 and R2C9 in row 2 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 9 can be removed.
R5C1 - removing <1> from <149> leaving <49>
R5C9 - removing <1> from <123> leaving <23>
R9C1 - removing <1> from <129> leaving <29>
R9C9 - removing <1> from <137> leaving <37>
Squares R9C1 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C3 - removing <9> from <179> leaving <17>
Squares R1C5, R1C9, R3C5 and R3C9 form a Type-1 Unique Rectangle on <46>.
R3C9 - removing <46> from <246> leaving <2>
R3C7 can only be <9>
R5C9 can only be <3>
R5C7 can only be <1>
R9C9 can only be <7>
R9C3 can only be <1>
R7C9 can only be <8>
R3C3 can only be <4>
R7C7 can only be <2>
R1C8 can only be <1>
R9C7 can only be <3>
R4C8 can only be <2>
R9C8 can only be <9>
R7C1 can only be <9>
R8C9 can only be <1>
R8C1 can only be <8>
R2C9 can only be <4>
R9C1 can only be <2>
R1C2 can only be <9>
R2C1 can only be <1>
R1C9 can only be <6>
R3C5 can only be <6>
R5C3 can only be <9>
R1C5 can only be <4>
R4C5 can only be <3>
R5C1 can only be <4>
R5C5 can only be <2>
R7C3 can only be <7>
R6C2 can only be <3>
R6C5 can only be <9>
R4C2 can only be <1>
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