Nov 20 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C7 can only be <3>
R4C5 is the only square in row 4 that can be <7>
R6C2 is the only square in row 6 that can be <9>
R6C5 is the only square in row 6 that can be <2>
R8C8 is the only square in row 8 that can be <2>
R8C9 is the only square in row 8 that can be <9>
R5C5 is the only square in column 5 that can be <8>
R8C6 is the only square in column 6 that can be <7>
Squares R5C4 and R5C6 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <5> from <12456> leaving <1246>
R5C8 - removing <5> from <1456> leaving <146>
Squares R2C3<356>, R2C4<135>, R2C5<1356> and R2C6<35> in row 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1356>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <6> from <2679> leaving <279>
R2C2 - removing <356> from <23567> leaving <27>
R2C7 - removing <1> from <148> leaving <48>
R2C8 - removing <13> from <134789> leaving <4789>
R2C9 - removing <13> from <1348> leaving <48>
Squares R2C7 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C8 - removing <48> from <4789> leaving <79>
Intersection of row 2 with block 2. The value <1> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C5 - removing <1> from <1356> leaving <356>
Squares R1C8<37>, R2C8<79>, R3C8<139> and R9C8<13> in column 8 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1379>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C8 - removing <1> from <1458> leaving <458>
R5C8 - removing <1> from <146> leaving <46>
R7C8 - removing <13> from <1348> leaving <48>
Squares R4C3 and R8C3 in column 3 and R4C7 and R8C7 in column 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 4 and 8 can be removed.
R4C2 - removing <1> from <145> leaving <45>
R8C2 - removing <1> from <13468> leaving <3468>
R8C4 - removing <1> from <135> leaving <35>
R8C5 - removing <1> from <135> leaving <35>
R2C4 is the only square in column 4 that can be <1>
R7C5 is the only square in column 5 that can be <1>
Squares R8C4 and R8C5 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <3> from <3468> leaving <468>
R8C3 - removing <3> from <136> leaving <16>
R2C3 is the only square in column 3 that can be <3>
R2C6 can only be <5>
R1C2 can only be <7>
R2C5 can only be <6>
R5C6 can only be <3>
R5C4 can only be <5>
R1C8 can only be <3>
R2C2 can only be <2>
R9C8 can only be <1>
R3C9 can only be <1>
R2C1 can only be <9>
R3C5 can only be <3>
R8C5 can only be <5>
R3C8 can only be <9>
R5C9 can only be <4>
R8C4 can only be <3>
R5C8 can only be <6>
R2C9 can only be <8>
R9C2 can only be <3>
R2C8 can only be <7>
R3C1 can only be <6>
R2C7 can only be <4>
R7C9 can only be <3>
R3C2 can only be <5>
R5C1 can only be <2>
R8C1 can only be <4>
R4C2 can only be <4>
R5C2 can only be <1>
R6C8 can only be <5>
R6C3 can only be <6>
R4C8 can only be <8>
R7C2 can only be <8>
R8C7 can only be <8>
R7C1 can only be <7>
R8C2 can only be <6>
R4C7 can only be <1>
R7C8 can only be <4>
R4C3 can only be <5>
R8C3 can only be <1>
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