Mar 19 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C6 can only be <2>
R3C4 is the only square in row 3 that can be <2>
R2C7 is the only square in row 2 that can be <2>
R3C9 is the only square in row 3 that can be <8>
R4C9 is the only square in row 4 that can be <5>
R2C8 is the only square in row 2 that can be <5>
R4C5 is the only square in row 4 that can be <9>
R6C1 is the only square in row 6 that can be <5>
R6C4 is the only square in row 6 that can be <6>
R5C1 is the only square in column 1 that can be <8>
R5C5 is the only square in column 5 that can be <2>
R9C8 is the only square in column 8 that can be <8>
R5C9 is the only square in column 9 that can be <3>
R5C2 can only be <1>
R5C8 can only be <9>
R3C2 can only be <4>
R7C8 can only be <6>
R3C1 can only be <1>
R4C6 is the only square in row 4 that can be <1>
R4C4 is the only square in row 4 that can be <4>
R2C6 is the only square in row 2 that can be <4>
R8C1 is the only square in row 8 that can be <4>
Squares R4C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <3> from <369> leaving <69>
R8C2 - removing <3> from <369> leaving <69>
Squares R1C2<69>, R1C7<149>, R1C8<14> and R1C9<169> in row 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1469>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C3 - removing <6> from <367> leaving <37>
R1C5 - removing <1> from <137> leaving <37>
R2C5 is the only square in column 5 that can be <1>
Squares R2C1 and R2C9 in row 2 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C9 - removing <9> from <169> leaving <16>
R8C9 - removing <9> from <179> leaving <17>
Squares R1C3 and R8C4 form a remote naked pair. <37> can be removed from any square that is common to their groups.
R8C3 - removing <37> from <1367> leaving <16>
Intersection of row 8 with block 8. The values <38> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R9C5 - removing <3> from <357> leaving <57>
Squares R4C2, R4C3, R9C2 and R9C3 form a Type-1 Unique Rectangle on <23>.
R9C3 - removing <23> from <1237> leaving <17>
R9C2 is the only square in row 9 that can be <2>
R4C2 can only be <3>
R4C3 can only be <2>
R9C1 is the only square in row 9 that can be <3>
Squares R1C3 and R1C5 in row 1 and R9C3 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 5 can be removed.
R2C3 - removing <7> from <367> leaving <36>
R8C5 - removing <7> from <3578> leaving <358>
Squares R6C5, R6C6, R8C5 and R8C6 form a Type-1 Unique Rectangle on <38>.
R8C5 - removing <38> from <358> leaving <5>
R9C5 can only be <7>
R9C3 can only be <1>
R1C5 can only be <3>
R8C4 can only be <3>
R1C3 can only be <7>
R6C5 can only be <8>
R2C4 can only be <7>
R2C1 can only be <9>
R6C6 can only be <3>
R8C6 can only be <8>
R9C7 can only be <5>
R8C3 can only be <6>
R2C9 can only be <6>
R7C1 can only be <7>
R1C2 can only be <6>
R2C3 can only be <3>
R1C9 can only be <1>
R7C9 can only be <9>
R8C7 can only be <1>
R8C2 can only be <9>
R8C9 can only be <7>
R6C7 can only be <4>
R1C8 can only be <4>
R6C8 can only be <1>
R1C7 can only be <9>
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