Oct 29 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 is the only square in row 1 that can be <8>
R5C5 is the only square in row 5 that can be <8>
R6C9 is the only square in row 6 that can be <8>
R6C8 is the only square in row 6 that can be <9>
R6C2 is the only square in row 6 that can be <4>
R3C4 is the only square in column 4 that can be <6>
R2C8 is the only square in column 8 that can be <2>
Squares R5C4 and R5C6 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.
R5C2 - removing <2> from <1236> leaving <136>
R5C3 - removing <2> from <236> leaving <36>
Squares R4C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C5 - removing <7> from <1457> leaving <145>
R8C5 - removing <7> from <4579> leaving <459>
Intersection of row 8 with block 7. The values <27> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C1 - removing <27> from <23567> leaving <356>
R7C3 - removing <27> from <23467> leaving <346>
R9C2 - removing <7> from <357> leaving <35>
R9C3 - removing <7> from <347> leaving <34>
R3C3 is the only square in column 3 that can be <2>
R1C3 is the only square in column 3 that can be <7>
Intersection of column 4 with block 8. The value <4> only appears in one or more of squares R7C4, R8C4 and R9C4 of column 4. 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 <4> from <145> leaving <15>
R8C5 - removing <4> from <459> leaving <59>
Intersection of row 8 with block 9. The value <4> 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.
R7C7 - removing <4> from <1347> leaving <137>
R7C9 - removing <4> from <345> leaving <35>
R9C7 - removing <4> from <13479> leaving <1379>
R9C8 - removing <4> from <1345> leaving <135>
Squares R9C2<35>, R9C3<34> and R9C4<45> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <345>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C6 - removing <5> from <1579> leaving <179>
R9C7 - removing <3> from <1379> leaving <179>
R9C8 - removing <35> from <135> leaving <1>
R5C7 is the only square in column 7 that can be <1>
R5C8 is the only square in row 5 that can be <4>
R8C8 can only be <5>
R8C5 can only be <9>
R7C9 can only be <3>
R7C7 can only be <7>
R4C9 can only be <6>
R8C9 can only be <4>
R9C6 can only be <7>
R9C7 can only be <9>
R1C7 can only be <3>
R1C8 can only be <6>
R3C7 can only be <4>
R1C2 can only be <5>
R4C8 can only be <3>
R2C9 can only be <5>
R3C9 can only be <9>
R4C5 can only be <7>
R1C6 can only be <9>
R9C2 can only be <3>
R6C5 can only be <3>
R6C1 can only be <7>
R9C3 can only be <4>
R5C2 can only be <6>
R9C4 can only be <5>
R7C3 can only be <6>
R5C4 can only be <2>
R7C5 can only be <1>
R5C3 can only be <3>
R2C2 can only be <1>
R5C6 can only be <5>
R7C4 can only be <4>
R3C6 can only be <1>
R8C1 can only be <2>
R7C1 can only be <5>
R7C6 can only be <2>
R2C5 can only be <4>
R3C5 can only be <5>
R8C2 can only be <7>
R4C1 can only be <1>
R2C1 can only be <6>
R4C2 can only be <2>
R3C1 can only be <3>
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