Nov 04 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <3>
R3C5 is the only square in row 3 that can be <9>
R3C9 is the only square in row 3 that can be <2>
R4C4 is the only square in row 4 that can be <9>
R5C5 is the only square in row 5 that can be <4>
R3C1 is the only square in column 1 that can be <8>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C9 - removing <1> from <134> leaving <34>
R6C9 is the only square in column 9 that can be <1>
Intersection of row 6 with block 5. The value <2> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <2> from <1236> leaving <136>
R5C6 - removing <2> from <12378> leaving <1378>
Intersection of block 8 with row 9. The value <3> only appears in one or more of squares R9C4, R9C5 and R9C6 of block 8. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C1 - removing <3> from <34567> leaving <4567>
R9C3 - removing <3> from <23457> leaving <2457>
R9C7 - removing <3> from <2345> leaving <245>
R9C9 - removing <3> from <347> leaving <47>
Intersection of block 4 with column 1. The value <5> only appears in one or more of squares R4C1, R5C1 and R6C1 of block 4. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
R1C1 - removing <5> from <3457> leaving <347>
R9C1 - removing <5> from <4567> leaving <467>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 3 and 7 can be removed.
R1C3 - removing <4> from <3457> leaving <357>
R1C7 - removing <4> from <345> leaving <35>
R9C3 - removing <4> from <2457> leaving <257>
R9C7 - removing <4> from <245> leaving <25>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.
R2C3 - removing <5> from <45> leaving <4>
R2C7 - removing <5> from <458> leaving <48>
R8C3 - removing <5> from <23457> leaving <2347>
R8C7 - removing <5> from <2345> leaving <234>
R2C7 can only be <8>
R5C7 can only be <3>
R5C3 can only be <2>
R1C7 can only be <5>
R9C7 can only be <2>
R2C8 can only be <1>
R2C2 can only be <5>
R3C8 can only be <3>
R3C2 can only be <1>
R1C9 can only be <4>
R5C2 can only be <6>
R8C7 can only be <4>
R9C9 can only be <7>
R5C4 can only be <1>
R1C4 can only be <2>
R9C3 can only be <5>
R9C6 can only be <3>
R4C9 can only be <8>
R7C8 can only be <8>
R8C8 can only be <5>
R1C6 can only be <1>
R7C9 can only be <3>
R5C8 can only be <7>
R5C6 can only be <8>
R7C2 can only be <2>
R9C4 can only be <6>
R4C6 can only be <7>
R6C6 can only be <2>
R4C5 can only be <5>
R8C2 can only be <3>
R8C3 can only be <7>
R8C5 can only be <2>
R1C3 can only be <3>
R7C1 can only be <6>
R9C1 can only be <4>
R6C4 can only be <3>
R7C5 can only be <7>
R1C1 can only be <7>
R4C1 can only be <3>
R6C5 can only be <6>
R6C1 can only be <5>
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