Jan 09 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C2 can only be <5>
R7C2 can only be <9>
R7C1 can only be <1>
R7C3 can only be <6>
R4C3 is the only square in row 4 that can be <7>
R4C6 is the only square in row 4 that can be <9>
R1C4 is the only square in row 1 that can be <9>
R2C1 is the only square in row 2 that can be <9>
R2C2 is the only square in row 2 that can be <8>
R2C6 is the only square in row 2 that can be <4>
R3C9 is the only square in row 3 that can be <9>
R4C1 is the only square in row 4 that can be <8>
R5C9 is the only square in row 5 that can be <4>
R6C4 is the only square in row 6 that can be <8>
R8C4 is the only square in row 8 that can be <7>
R7C7 is the only square in row 7 that can be <7>
R9C7 is the only square in row 9 that can be <4>
R4C8 is the only square in column 8 that can be <2>
Squares R5C1 and R6C1 in block 4 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 block.
R6C2 - removing <2> from <234> leaving <34>
Squares R6C2 and R6C3 in row 6 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.
R6C5 - removing <3> from <12356> leaving <1256>
R6C7 - removing <3> from <136> leaving <16>
R6C9 - removing <3> from <356> leaving <56>
Intersection of row 5 with block 5. The values <36> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <3> from <135> leaving <15>
R6C5 - removing <6> from <1256> leaving <125>
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.
R1C6 - removing <1> from <123> leaving <23>
R2C5 - removing <1> from <136> leaving <36>
R3C6 - removing <1> from <12356> leaving <2356>
R1C3 is the only square in row 1 that can be <1>
R8C6 is the only square in column 6 that can be <1>
R8C8 is the only square in row 8 that can be <8>
R7C6 is the only square in row 7 that can be <8>
Squares R2C5 and R8C5 in column 5 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 column.
R5C5 - removing <36> from <2356> leaving <25>
Squares R5C1 and R5C5 in row 5 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.
R5C4 - removing <25> from <2356> leaving <36>
R5C6 - removing <25> from <2356> leaving <36>
Intersection of column 8 with block 3. The value <1> 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.
R3C7 - removing <1> from <136> leaving <36>
Squares R5C1, R5C5, R6C1 and R6C5 form a Type-1 Unique Rectangle on <25>.
R6C5 - removing <25> from <125> leaving <1>
R6C7 can only be <6>
R4C5 can only be <5>
R6C9 can only be <5>
R3C7 can only be <3>
R6C1 can only be <2>
R4C9 can only be <3>
R3C3 can only be <4>
R4C7 can only be <1>
R5C5 can only be <2>
R8C9 can only be <6>
R5C1 can only be <5>
R8C5 can only be <3>
R9C8 can only be <5>
R7C8 can only be <3>
R3C2 can only be <2>
R6C3 can only be <3>
R6C2 can only be <4>
R7C4 can only be <5>
R2C5 can only be <6>
R2C8 can only be <1>
R2C4 can only be <3>
R3C8 can only be <6>
R3C6 can only be <5>
R1C2 can only be <3>
R3C4 can only be <1>
R1C6 can only be <2>
R9C6 can only be <6>
R5C4 can only be <6>
R5C6 can only be <3>
R9C4 can only be <2>
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