Mar 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 can only be <5>
R5C5 can only be <1>
R1C5 can only be <2>
R3C5 can only be <7>
R7C5 can only be <3>
R9C5 can only be <4>
R1C7 is the only square in row 1 that can be <4>
R8C8 is the only square in row 8 that can be <9>
Squares R7C2 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C1 - removing <28> from <2578> leaving <57>
R7C8 - removing <2> from <257> leaving <57>
Squares R1C4 and R2C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C4 - removing <5> from <567> leaving <67>
R9C4 - removing <5> from <567> leaving <67>
Squares R8C6 and R9C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <5> from <158> leaving <18>
R2C6 - removing <5> from <158> leaving <18>
R1C4 is the only square in row 1 that can be <5>
R2C4 can only be <9>
Intersection of column 8 with block 3. The value <2> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C9 - removing <2> from <1268> leaving <168>
Squares R4C1 and R4C8 in row 4 and R7C1 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 8 can be removed.
R5C1 - removing <7> from <3679> leaving <369>
R9C1 - removing <7> from <235678> leaving <23568>
Squares R3C1, R3C2 and R3C9 in row 3, R4C1 and R4C2 in row 4 and R7C2 and R7C9 in row 7 form a Swordfish pattern on possibility <8>. All other instances of this possibility in columns 1, 2 and 9 can be removed.
R1C1 - removing <8> from <689> leaving <69>
R1C9 - removing <8> from <168> leaving <16>
R2C2 - removing <8> from <1238> leaving <123>
R9C1 - removing <8> from <23568> leaving <2356>
R9C9 - removing <8> from <238> leaving <23>
Squares R1C1<69>, R5C1<369> and R6C1<369> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C1 - removing <6> from <268> leaving <28>
R9C1 - removing <36> from <2356> leaving <25>
Squares R9C1 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C7 - removing <5> from <3578> leaving <378>
R9C9 - removing <2> from <23> leaving <3>
R5C7 is the only square in column 7 that can be <3>
R5C3 is the only square in row 5 that can be <7>
R4C1 can only be <8>
R4C2 can only be <4>
R3C1 can only be <2>
R4C8 can only be <7>
R7C8 can only be <5>
R7C1 can only be <7>
R2C8 can only be <2>
R8C7 can only be <7>
R8C4 can only be <6>
R9C7 can only be <8>
R9C3 can only be <6>
R2C7 can only be <5>
R7C9 can only be <2>
R3C8 can only be <6>
R9C1 can only be <5>
R6C8 can only be <4>
R1C9 can only be <1>
R7C2 can only be <8>
R8C3 can only be <3>
R9C4 can only be <7>
R9C6 can only be <2>
R8C6 can only be <5>
R1C6 can only be <8>
R3C9 can only be <8>
R3C2 can only be <1>
R8C2 can only be <2>
R2C3 can only be <8>
R1C3 can only be <9>
R2C6 can only be <1>
R2C2 can only be <3>
R1C1 can only be <6>
R6C2 can only be <6>
R6C9 can only be <9>
R5C1 can only be <9>
R6C1 can only be <3>
R5C9 can only be <6>
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