Feb 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C7 can only be <6>
R3C3 is the only square in row 3 that can be <9>
R4C8 is the only square in row 4 that can be <5>
R4C2 is the only square in row 4 that can be <4>
R4C4 is the only square in row 4 that can be <2>
R2C5 is the only square in row 2 that can be <2>
R4C9 is the only square in row 4 that can be <8>
R6C2 is the only square in row 6 that can be <2>
R5C7 is the only square in row 5 that can be <2>
R6C8 is the only square in row 6 that can be <4>
R6C4 is the only square in row 6 that can be <8>
R5C2 is the only square in row 5 that can be <8>
R6C6 is the only square in row 6 that can be <6>
R5C8 is the only square in row 5 that can be <6>
R7C8 is the only square in row 7 that can be <9>
R8C3 is the only square in column 3 that can be <4>
R2C7 is the only square in column 7 that can be <4>
Squares R4C6 and R8C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <3> from <347> leaving <47>
R2C6 - removing <3> from <379> leaving <79>
R9C6 - removing <13> from <1349> leaving <49>
Squares R5C9 and R6C9 in column 9 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 column.
R2C9 - removing <1> from <137> leaving <37>
R8C9 - removing <1> from <137> leaving <37>
R1C8 is the only square in block 3 that can be <1>
Intersection of column 2 with block 7. The value <1> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <1> from <13> leaving <3>
R8C1 - removing <1> from <1357> leaving <357>
Intersection of column 2 with block 1. The value <3> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <3> from <1357> leaving <157>
Squares R8C6<13>, R9C4<39>, R9C5<134> and R9C6<49> in block 8 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1349>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C5 - removing <1> from <158> leaving <58>
R8C4 - removing <3> from <356> leaving <56>
R8C5 - removing <13> from <13568> leaving <568>
Squares R3C2 and R3C5 in row 3 and R7C2 and R7C5 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 5 can be removed.
R8C5 - removing <5> from <568> leaving <68>
Squares R3C2 and R3C8 in row 3 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <7> from <37> leaving <3>
R1C4 can only be <6>
R1C5 can only be <4>
R8C4 can only be <5>
R1C6 can only be <7>
R2C6 can only be <9>
R9C6 can only be <4>
R8C1 can only be <7>
R2C4 can only be <3>
R7C5 can only be <8>
R2C9 can only be <7>
R9C4 can only be <9>
R3C5 can only be <5>
R2C3 can only be <1>
R8C9 can only be <3>
R3C8 can only be <3>
R3C2 can only be <7>
R9C8 can only be <7>
R7C7 can only be <1>
R8C5 can only be <6>
R7C2 can only be <5>
R8C7 can only be <8>
R9C2 can only be <1>
R8C6 can only be <1>
R9C5 can only be <3>
R5C5 can only be <1>
R2C1 can only be <5>
R5C3 can only be <7>
R5C9 can only be <9>
R4C6 can only be <3>
R5C1 can only be <3>
R6C9 can only be <1>
R6C1 can only be <9>
R4C1 can only be <1>
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