Feb 04 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C2 can only be <4>
R1C5 is the only square in row 1 that can be <3>
R4C5 is the only square in row 4 that can be <7>
R5C8 is the only square in row 5 that can be <3>
R9C3 is the only square in column 3 that can be <9>
R8C3 is the only square in column 3 that can be <5>
R1C7 is the only square in column 7 that can be <7>
Squares R7C1 and R9C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C1 - removing <6> from <146> leaving <14>
R3C1 - removing <6> from <1467> leaving <147>
R5C1 - removing <8> from <1478> leaving <147>
Intersection of column 7 with block 6. The value <4> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C9 - removing <4> from <1458> leaving <158>
Squares R4C7<48>, R5C7<1458>, R6C7<145> and R8C7<18> in column 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <1> from <126> leaving <26>
R9C7 - removing <58> from <2568> leaving <26>
Intersection of column 7 with block 6. The values <45> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R5C9 - removing <5> from <158> leaving <18>
Squares R3C6 and R7C6 in column 6 and R3C8 and R7C8 in column 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 3 and 7 can be removed.
R3C1 - removing <1> from <147> leaving <47>
R3C5 - removing <1> from <1568> leaving <568>
R7C5 - removing <1> from <12589> leaving <2589>
R3C9 - removing <1> from <146> leaving <46>
R7C9 - removing <1> from <1568> leaving <568>
Squares R7C1<68>, R7C4<58> and R7C9<568> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <568>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C5 - removing <58> from <2589> leaving <29>
R7C6 - removing <5> from <159> leaving <19>
Squares R1C1 and R5C1 in column 1 and R1C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 1 and 5 can be removed.
R1C3 - removing <1> from <146> leaving <46>
R5C3 - removing <1> from <1248> leaving <248>
R5C7 - removing <1> from <1458> leaving <458>
Squares R2C7 (XY), R3C8 (XZ) and R2C5 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R3C6 - removing <1> from <15> leaving <5>
R5C6 can only be <9>
R7C6 can only be <1>
R7C8 can only be <2>
R8C5 can only be <8>
R7C5 can only be <9>
R3C8 can only be <1>
R9C7 can only be <6>
R8C7 can only be <1>
R3C5 can only be <6>
R7C4 can only be <5>
R9C1 can only be <8>
R2C7 can only be <2>
R3C4 can only be <8>
R3C9 can only be <4>
R2C5 can only be <1>
R3C1 can only be <7>
R1C9 can only be <6>
R7C9 can only be <8>
R5C4 can only be <6>
R9C5 can only be <2>
R7C1 can only be <6>
R5C9 can only be <1>
R9C9 can only be <5>
R1C3 can only be <4>
R2C3 can only be <6>
R3C2 can only be <2>
R5C2 can only be <7>
R5C1 can only be <4>
R1C1 can only be <1>
R4C3 can only be <8>
R6C3 can only be <1>
R4C7 can only be <4>
R5C3 can only be <2>
R6C7 can only be <5>
R5C5 can only be <5>
R5C7 can only be <8>
R6C5 can only be <4>
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