Oct 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 is the only square in row 4 that can be <7>
R5C9 is the only square in row 5 that can be <1>
R9C1 is the only square in row 9 that can be <6>
R2C2 is the only square in column 2 that can be <6>
R7C4 is the only square in column 4 that can be <9>
R3C6 is the only square in column 6 that can be <8>
R6C6 is the only square in column 6 that can be <6>
R5C1 is the only square in block 4 that can be <8>
Squares R4C2 and R4C4 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C7 - removing <3> from <368> leaving <68>
R4C9 - removing <3> from <368> leaving <68>
Intersection of row 6 with block 4. The value <5> only appears in one or more of squares R6C1, R6C2 and R6C3 of row 6. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C2 - removing <5> from <3459> leaving <349>
Intersection of row 6 with block 6. The value <2> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C8 - removing <2> from <239> leaving <39>
Intersection of column 2 with block 7. The value <5> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <5> from <145> leaving <14>
R7C3 - removing <5> from <13458> leaving <1348>
R8C3 - removing <5> from <134589> leaving <13489>
Intersection of column 4 with block 2. The value <1> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <1> from <1456> leaving <456>
R2C5 - removing <1> from <147> leaving <47>
R3C5 - removing <1> from <14567> leaving <4567>
Intersection of column 4 with block 5. The value <3> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <3> from <2345> leaving <245>
Intersection of column 6 with block 8. The value <7> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C5 - removing <7> from <12347> leaving <1234>
R8C5 - removing <7> from <1347> leaving <134>
Intersection of column 7 with block 3. The values <19> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R2C8 - removing <9> from <2489> leaving <248>
R3C8 - removing <9> from <349> leaving <34>
Intersection of block 4 with column 2. The value <4> only appears in one or more of squares R4C2, R5C2 and R6C2 of block 4. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain this value.
R7C2 - removing <4> from <345> leaving <35>
R8C2 - removing <4> from <3459> leaving <359>
Squares R1C9<46>, R3C8<34> and R3C9<346> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <346>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C7 - removing <6> from <16> leaving <1>
R2C8 - removing <4> from <248> leaving <28>
R3C7 - removing <36> from <1369> leaving <19>
R3C7 can only be <9>
R4C7 is the only square in column 7 that can be <6>
R4C9 can only be <8>
Intersection of column 7 with block 9. The values <35> 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.
R7C9 - removing <3> from <2347> leaving <247>
R8C8 - removing <3> from <348> leaving <48>
R8C9 - removing <3> from <347> leaving <47>
Squares R8C6 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <4> from <13489> leaving <1389>
R8C5 - removing <4> from <134> leaving <13>
R8C8 - removing <4> from <48> leaving <8>
R2C8 can only be <2>
R2C7 can only be <8>
R6C9 is the only square in row 6 that can be <2>
R7C3 is the only square in row 7 that can be <8>
R3C8 is the only square in column 8 that can be <4>
R1C9 can only be <6>
R3C9 can only be <3>
R3C5 is the only square in row 3 that can be <6>
R3C3 is the only square in row 3 that can be <7>
R2C5 is the only square in row 2 that can be <7>
Squares R1C3 and R1C5 in row 1 and R9C3 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 3 and 5 can be removed.
R2C3 - removing <4> from <149> leaving <19>
R5C5 - removing <4> from <245> leaving <25>
R7C5 - removing <4> from <1234> leaving <123>
Squares R8C6, R8C9, R7C6 and R7C9 form a Type-1 Unique Rectangle on <47>.
R7C6 - removing <47> from <247> leaving <2>
R5C6 can only be <4>
R8C6 can only be <7>
R4C4 can only be <3>
R8C9 can only be <4>
R7C9 can only be <7>
R4C2 can only be <4>
R5C4 can only be <5>
R5C5 can only be <2>
R3C4 can only be <1>
R3C1 can only be <5>
R2C4 can only be <4>
R1C5 can only be <5>
R6C1 can only be <9>
R1C3 can only be <4>
R6C8 can only be <3>
R2C1 can only be <1>
R5C2 can only be <3>
R6C3 can only be <5>
R5C8 can only be <9>
R9C3 can only be <3>
R2C3 can only be <9>
R7C1 can only be <4>
R7C2 can only be <5>
R7C7 can only be <3>
R8C2 can only be <9>
R7C5 can only be <1>
R8C7 can only be <5>
R9C7 can only be <2>
R9C5 can only be <4>
R8C3 can only be <1>
R8C5 can only be <3>
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