Jul 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 is the only square in row 5 that can be <5>
R7C5 is the only square in block 8 that can be <9>
R9C9 is the only square in column 9 that can be <9>
R9C3 is the only square in row 9 that can be <4>
R1C9 is the only square in row 1 that can be <4>
R3C2 is the only square in row 3 that can be <4>
R7C8 is the only square in row 7 that can be <4>
Squares R7C1 and R7C9 in row 7 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 row.
R7C2 - removing <13> from <13568> leaving <568>
R7C3 - removing <13> from <13568> leaving <568>
R7C7 - removing <3> from <358> leaving <58>
Squares R8C4 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <36> from <13568> leaving <158>
R8C3 - removing <36> from <135678> leaving <1578>
R8C7 - removing <3> from <3578> leaving <578>
R8C8 - removing <3> from <1357> leaving <157>
Squares R1C3 and R5C3 in column 3 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.
R2C3 - removing <3> from <356> leaving <56>
R3C3 - removing <13> from <13567> leaving <567>
R8C3 - removing <1> from <1578> leaving <578>
Intersection of row 1 with block 1. The value <1> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <1> from <1237> leaving <237>
Intersection of column 3 with block 7. The value <8> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <8> from <568> leaving <56>
R8C2 - removing <8> from <158> leaving <15>
Intersection of column 7 with block 9. The values <78> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C8 - removing <7> from <157> leaving <15>
Squares R8C2 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <5> from <578> leaving <78>
R8C7 - removing <5> from <578> leaving <78>
Intersection of block 7 with column 1. The value <3> only appears in one or more of squares R7C1, R8C1 and R9C1 of block 7. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
R1C1 - removing <3> from <123> leaving <12>
R3C1 - removing <3> from <237> leaving <27>
Squares R4C4<39>, R5C4<369> and R8C4<36> in column 4 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.
R2C4 - removing <3> from <234> leaving <24>
R6C4 - removing <3> from <234> leaving <24>
Squares R4C4<39>, R4C5<37> and R4C8<379> in row 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <379>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <3> from <138> leaving <18>
R4C6 - removing <3> from <138> leaving <18>
Squares R8C4, R8C6, R5C4 and R5C6 form a Type-4 Unique Rectangle on <36>.
R5C4 - removing <3> from <369> leaving <69>
R5C6 - removing <3> from <136> leaving <16>
Squares R1C3 and R1C7 in row 1 and R5C3 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 7 can be removed.
R2C7 - removing <3> from <23569> leaving <2569>
R3C7 - removing <3> from <2356> leaving <256>
R9C7 - removing <3> from <37> leaving <7>
R9C1 can only be <3>
R8C7 can only be <8>
R8C3 can only be <7>
R7C7 can only be <5>
R7C1 can only be <1>
R7C9 can only be <3>
R1C1 can only be <2>
R8C2 can only be <5>
R7C2 can only be <6>
R8C8 can only be <1>
R3C9 can only be <1>
R1C7 can only be <3>
R3C1 can only be <7>
R1C3 can only be <1>
R5C7 can only be <9>
R3C8 can only be <5>
R3C3 can only be <6>
R2C8 can only be <9>
R5C4 can only be <6>
R7C3 can only be <8>
R2C2 can only be <3>
R5C3 can only be <3>
R2C6 can only be <4>
R6C2 can only be <8>
R2C4 can only be <2>
R3C7 can only be <2>
R2C3 can only be <5>
R3C5 can only be <3>
R2C7 can only be <6>
R5C6 can only be <1>
R8C4 can only be <3>
R4C6 can only be <8>
R6C6 can only be <3>
R4C2 can only be <1>
R6C8 can only be <7>
R8C6 can only be <6>
R4C4 can only be <9>
R4C5 can only be <7>
R6C5 can only be <2>
R4C8 can only be <3>
R6C4 can only be <4>
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