Oct 05 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C5 can only be <2>
R1C7 is the only square in row 1 that can be <4>
R1C3 is the only square in row 1 that can be <7>
R1C1 is the only square in row 1 that can be <3>
R2C6 is the only square in row 2 that can be <1>
R3C7 is the only square in row 3 that can be <3>
R8C3 is the only square in row 8 that can be <3>
R2C9 is the only square in column 9 that can be <9>
Squares R2C7 and R7C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C7 - removing <5> from <12567> leaving <1267>
R6C7 - removing <5> from <12567> leaving <1267>
R9C7 - removing <58> from <125678> leaving <1267>
Intersection of row 2 with block 1. The value <2> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <2> from <2589> leaving <589>
Intersection of row 5 with block 5. The values <36> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <6> from <1679> leaving <179>
R4C6 - removing <6> from <2456> leaving <245>
R6C5 - removing <6> from <16789> leaving <1789>
R6C6 - removing <6> from <256> leaving <25>
Squares R5C2<25>, R5C4<12> and R5C8<125> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <125>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C5 - removing <1> from <136> leaving <36>
R5C6 - removing <25> from <2356> leaving <36>
Squares R1C2 and R1C8 in row 1 and R5C2 and R5C8 in row 5 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
R4C8 - removing <5> from <125> leaving <12>
R6C2 - removing <5> from <259> leaving <29>
R9C2 - removing <5> from <258> leaving <28>
R9C8 - removing <5> from <1258> leaving <128>
Intersection of block 7 with column 3. The value <5> only appears in one or more of squares R7C3, R8C3 and R9C3 of block 7. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R2C3 - removing <5> from <258> leaving <28>
R4C3 - removing <5> from <12569> leaving <1269>
R6C3 - removing <5> from <12569> leaving <1269>
Squares R2C3 and R2C7 in row 2 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C3 - removing <8> from <89> leaving <9>
R9C3 - removing <8> from <2568> leaving <256>
R3C5 can only be <8>
R6C4 is the only square in row 6 that can be <8>
R6C2 is the only square in column 2 that can be <9>
Squares R1C2 (XY), R5C2 (XZ) and R2C3 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R4C3 - removing <2> from <126> leaving <16>
R6C3 - removing <2> from <126> leaving <16>
Squares R4C3 and R6C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C3 - removing <6> from <256> leaving <25>
R8C1 is the only square in block 7 that can be <6>
R8C9 can only be <7>
R8C4 can only be <1>
R8C7 can only be <2>
R5C4 can only be <2>
R5C2 can only be <5>
R1C4 can only be <9>
R6C6 can only be <5>
R6C1 can only be <2>
R4C6 can only be <4>
R1C5 can only be <6>
R1C6 can only be <2>
R5C5 can only be <3>
R4C4 can only be <7>
R9C6 can only be <3>
R5C8 can only be <1>
R1C2 can only be <8>
R5C6 can only be <6>
R9C5 can only be <7>
R4C8 can only be <2>
R9C8 can only be <8>
R2C1 can only be <5>
R9C4 can only be <4>
R6C5 can only be <1>
R9C2 can only be <2>
R1C8 can only be <5>
R7C7 can only be <5>
R2C3 can only be <2>
R2C7 can only be <8>
R9C3 can only be <5>
R4C7 can only be <6>
R4C3 can only be <1>
R4C9 can only be <5>
R6C7 can only be <7>
R9C7 can only be <1>
R9C9 can only be <6>
R6C3 can only be <6>
R4C5 can only be <9>
R7C3 can only be <8>
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