Sep 15 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <6>
R3C8 is the only square in row 3 that can be <6>
R6C9 is the only square in row 6 that can be <4>
R5C4 is the only square in row 5 that can be <4>
R6C3 is the only square in row 6 that can be <6>
R7C2 is the only square in row 7 that can be <6>
R8C5 is the only square in column 5 that can be <5>
R7C7 is the only square in column 7 that can be <4>
R7C9 is the only square in row 7 that can be <8>
Squares R5C3 and R5C7 in row 5 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 row.
R5C5 - removing <3> from <138> leaving <18>
R5C6 - removing <23> from <1238> leaving <18>
Intersection of row 7 with block 8. The value <1> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C6 - removing <1> from <127> leaving <27>
R9C6 - removing <1> from <123> leaving <23>
Intersection of column 2 with block 1. The value <7> 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.
R1C3 - removing <7> from <3579> leaving <359>
R2C1 - removing <7> from <2378> leaving <238>
R3C1 - removing <7> from <478> leaving <48>
R3C3 - removing <7> from <4579> leaving <459>
Intersection of column 3 with block 7. The value <7> 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.
R8C1 - removing <7> from <1247> leaving <124>
Intersection of column 8 with block 9. The value <2> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C7 - removing <2> from <1235> leaving <135>
Intersection of block 2 with row 3. The value <8> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C1 - removing <8> from <48> leaving <4>
R3C2 - removing <8> from <789> leaving <79>
R3C7 - removing <8> from <1578> leaving <157>
R8C3 is the only square in row 8 that can be <4>
R8C6 is the only square in row 8 that can be <7>
R7C3 is the only square in row 7 that can be <7>
Intersection of row 8 with block 9. The value <9> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C8 - removing <9> from <2359> leaving <235>
Squares R5C5, R5C6, R3C5 and R3C6 form a Type-1 Unique Rectangle on <18>.
R3C5 - removing <18> from <1789> leaving <79>
R3C6 is the only square in row 3 that can be <8>
R5C6 can only be <1>
R5C5 can only be <8>
R3C7 is the only square in row 3 that can be <1>
R1C4 is the only square in row 1 that can be <1>
R7C4 can only be <2>
R7C8 can only be <3>
R9C6 can only be <3>
R7C5 can only be <1>
R9C7 can only be <5>
R6C6 can only be <2>
R9C8 can only be <2>
R9C3 can only be <9>
R8C8 can only be <9>
R8C9 can only be <1>
R1C8 can only be <5>
R8C1 can only be <2>
R9C2 can only be <8>
R3C3 can only be <5>
R1C3 can only be <3>
R9C1 can only be <1>
R1C9 can only be <9>
R5C3 can only be <2>
R2C1 can only be <8>
R1C2 can only be <7>
R2C9 can only be <3>
R2C7 can only be <7>
R4C9 can only be <5>
R5C7 can only be <3>
R4C7 can only be <2>
R1C7 can only be <8>
R3C2 can only be <9>
R2C4 can only be <9>
R3C5 can only be <7>
R2C2 can only be <2>
R6C5 can only be <3>
R6C1 can only be <7>
R4C5 can only be <9>
R4C4 can only be <7>
R4C1 can only be <3>
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