Jul 05 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 is the only square in row 2 that can be <8>
R2C2 is the only square in row 2 that can be <9>
R1C4 is the only square in row 1 that can be <9>
R4C7 is the only square in row 4 that can be <8>
R8C3 is the only square in row 8 that can be <6>
R9C9 is the only square in row 9 that can be <9>
R6C1 is the only square in row 6 that can be <9>
R5C8 is the only square in row 5 that can be <9>
R3C4 is the only square in column 4 that can be <3>
R7C4 is the only square in column 4 that can be <6>
R8C8 is the only square in column 8 that can be <3>
R6C7 is the only square in column 7 that can be <3>
Squares R7C2 and R8C2 in column 2 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 column.
R3C2 - removing <4> from <124> leaving <12>
R5C2 - removing <47> from <1247> leaving <12>
R5C1 is the only square in block 4 that can be <7>
Squares R6C3 and R9C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <14> from <1234> leaving <23>
R4C3 - removing <14> from <1234> leaving <23>
Squares R7C2 and R8C2 in block 7 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 block.
R7C1 - removing <4> from <458> leaving <58>
R9C1 - removing <4> from <1458> leaving <158>
R9C3 - removing <4> from <14> leaving <1>
R6C3 can only be <4>
Intersection of column 5 with block 8. The value <5> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C4 - removing <5> from <457> leaving <47>
Intersection of column 7 with block 9. The value <5> 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 this value.
R7C8 - removing <5> from <45> leaving <4>
R7C9 - removing <5> from <2457> leaving <247>
R7C2 can only be <7>
R2C8 can only be <1>
R3C8 can only be <5>
R7C9 can only be <2>
R8C2 can only be <4>
R7C6 can only be <8>
R7C1 can only be <5>
R9C1 can only be <8>
R3C2 is the only square in row 3 that can be <2>
R5C2 can only be <1>
R1C3 can only be <3>
R5C9 can only be <4>
R4C1 can only be <3>
R5C5 can only be <2>
R3C9 can only be <6>
R4C3 can only be <2>
R1C9 can only be <7>
R2C7 can only be <4>
R2C5 can only be <7>
R1C7 can only be <2>
R8C5 can only be <5>
R8C7 can only be <7>
R9C5 can only be <4>
R9C7 can only be <5>
R9C4 can only be <7>
R1C5 can only be <1>
R1C1 can only be <4>
R3C6 can only be <4>
R3C1 can only be <1>
R1C6 can only be <6>
R4C6 can only be <1>
R4C9 can only be <5>
R6C6 can only be <7>
R4C4 can only be <4>
R6C9 can only be <1>
R6C4 can only be <5>
R9C6 can only be <2>
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