Jul 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 is the only square in row 1 that can be <1>
R1C1 is the only square in row 1 that can be <9>
R5C5 is the only square in row 5 that can be <7>
R5C4 is the only square in row 5 that can be <1>
R8C2 is the only square in row 8 that can be <8>
R9C5 is the only square in row 9 that can be <1>
R8C8 is the only square in row 8 that can be <1>
R9C2 is the only square in column 2 that can be <9>
R2C3 is the only square in column 3 that can be <8>
R7C3 is the only square in column 3 that can be <7>
R5C3 is the only square in block 4 that can be <3>
R5C7 is the only square in block 6 that can be <9>
Squares R9C4 and R9C9 in row 9 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.
R9C7 - removing <6> from <256> leaving <25>
Intersection of row 3 with block 3. The value <8> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <8> from <568> leaving <56>
Intersection of row 4 with block 5. The values <89> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R6C5 - removing <8> from <3468> leaving <346>
R6C6 - removing <8> from <34568> leaving <3456>
Intersection of column 8 with block 3. The value <5> 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.
R1C7 - removing <5> from <56> leaving <6>
R3C7 - removing <5> from <5678> leaving <678>
Squares R4C1<256>, R4C3<25>, R4C4<2456> and R4C8<246> in row 4 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2456>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C5 - removing <46> from <4689> leaving <89>
R4C6 - removing <456> from <45689> leaving <89>
Squares R3C4 and R3C9 in row 3 and R9C4 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 4 and 9 can be removed.
R2C9 - removing <3> from <347> leaving <47>
R6C4 - removing <3> from <23456> leaving <2456>
R7C9 - removing <3> from <369> leaving <69>
R8C4 - removing <3> from <34> leaving <4>
R8C9 - removing <3> from <379> leaving <79>
R4C8 is the only square in row 4 that can be <4>
R1C8 can only be <5>
R2C8 can only be <3>
R3C4 is the only square in row 3 that can be <3>
R9C4 can only be <6>
R9C9 can only be <3>
R4C1 is the only square in row 4 that can be <6>
R3C2 is the only square in row 3 that can be <6>
R3C1 is the only square in row 3 that can be <5>
R8C1 can only be <3>
R2C2 can only be <2>
R8C5 can only be <9>
R7C1 can only be <2>
R8C9 can only be <7>
R4C5 can only be <8>
R7C6 can only be <3>
R8C7 can only be <5>
R2C9 can only be <4>
R3C9 can only be <8>
R2C1 can only be <7>
R5C2 can only be <4>
R2C5 can only be <6>
R3C7 can only be <7>
R6C9 can only be <6>
R4C6 can only be <9>
R1C5 can only be <4>
R5C6 can only be <6>
R6C2 can only be <5>
R5C8 can only be <2>
R2C6 can only be <5>
R7C8 can only be <6>
R6C7 can only be <8>
R6C4 can only be <2>
R4C3 can only be <2>
R4C4 can only be <5>
R7C9 can only be <9>
R9C3 can only be <5>
R6C6 can only be <4>
R9C7 can only be <2>
R1C6 can only be <8>
R6C5 can only be <3>
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