Feb 26 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <1>
R1C4 is the only square in row 1 that can be <8>
R3C9 is the only square in row 3 that can be <9>
R7C2 is the only square in row 7 that can be <8>
R6C2 can only be <6>
R5C7 is the only square in row 5 that can be <6>
Squares R1C6 and R1C7 in row 1 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 row.
R1C3 - removing <2> from <246> leaving <46>
R1C5 - removing <7> from <467> leaving <46>
Squares R4C2 and R5C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <2> from <12> leaving <1>
R4C3 - removing <24> from <12478> leaving <178>
R5C1 - removing <2> from <23> leaving <3>
R6C1 can only be <9>
R6C9 is the only square in row 6 that can be <3>
R7C6 is the only square in row 7 that can be <9>
R2C3 is the only square in column 3 that can be <1>
Intersection of column 9 with block 6. The value <2> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C7 - removing <2> from <2457> leaving <457>
Intersection of block 1 with row 3. The value <2> only appears in one or more of squares R3C1, R3C2 and R3C3 of block 1. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C4 - removing <2> from <1246> leaving <146>
R3C6 - removing <2> from <1257> leaving <157>
Squares R1C6 and R1C7 in row 1 and R8C6 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 6 and 7 can be removed.
R3C6 - removing <7> from <157> leaving <15>
R4C7 - removing <7> from <457> leaving <45>
R6C7 - removing <7> from <17> leaving <1>
R7C8 is the only square in column 8 that can be <1>
Squares R6C3, R6C8, R4C3 and R4C8 form a Type-1 Unique Rectangle on <78>.
R4C8 - removing <78> from <578> leaving <5>
R4C7 can only be <4>
R3C8 can only be <7>
R6C8 can only be <8>
R1C7 can only be <2>
R4C2 can only be <2>
R9C7 can only be <9>
R5C9 can only be <2>
R5C3 can only be <4>
R4C9 can only be <7>
R6C3 can only be <7>
R9C3 can only be <2>
R8C7 can only be <7>
R1C6 can only be <7>
R2C7 can only be <5>
R3C2 can only be <4>
R4C3 can only be <8>
R7C9 can only be <4>
R1C3 can only be <6>
R8C6 can only be <3>
R7C1 can only be <6>
R1C5 can only be <4>
R8C3 can only be <9>
R3C1 can only be <2>
R9C5 can only be <5>
R7C4 can only be <2>
R7C5 can only be <7>
R2C4 can only be <3>
R8C4 can only be <6>
R2C6 can only be <2>
R9C6 can only be <1>
R3C5 can only be <6>
R9C4 can only be <4>
R3C6 can only be <5>
R3C4 can only be <1>
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