Sep 19 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <8>
R8C4 can only be <2>
R9C7 can only be <8>
R5C4 can only be <5>
R9C3 can only be <4>
R2C4 can only be <7>
R9C5 can only be <7>
R1C7 is the only square in row 1 that can be <7>
R2C8 is the only square in row 2 that can be <4>
R8C3 is the only square in row 8 that can be <8>
R2C7 is the only square in column 7 that can be <2>
Squares R3C8 and R3C9 in row 3 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 row.
R3C2 - removing <5> from <1257> leaving <127>
R3C5 - removing <5> from <15> leaving <1>
Squares R4C5 and R5C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C5 - removing <49> from <2489> leaving <28>
Intersection of column 3 with block 4. The values <23> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C1 - removing <2> from <267> leaving <67>
R5C2 - removing <23> from <123467> leaving <1467>
R6C2 - removing <23> from <2357> leaving <57>
Intersection of column 7 with block 6. The values <35> 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.
R4C8 - removing <5> from <1569> leaving <169>
R6C8 - removing <5> from <578> leaving <78>
Squares R1C3<56>, R2C3<156> and R4C3<156> in column 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <156>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C3 - removing <16> from <1236> leaving <23>
R6C3 - removing <5> from <235> leaving <23>
Squares R5C1 and R7C1 in column 1 and R5C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 5 and 7 can be removed.
R5C2 - removing <6> from <1467> leaving <147>
R7C2 - removing <6> from <236> leaving <23>
R5C8 - removing <6> from <16789> leaving <1789>
R7C8 - removing <6> from <569> leaving <59>
Squares R1C3, R1C5, R2C3 and R2C5 form a Type-1 Unique Rectangle on <56>.
R2C3 - removing <56> from <156> leaving <1>
Squares R4C3<56>, R5C1<67> and R6C2<57> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <567>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <56> from <1456> leaving <14>
R5C2 - removing <7> from <147> leaving <14>
Squares R5C9 (XY), R5C1 (XZ) and R6C8 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R6C2 - removing <7> from <57> leaving <5>
R5C8 - removing <7> from <1789> leaving <189>
R6C7 can only be <3>
R2C2 can only be <6>
R4C3 can only be <6>
R6C3 can only be <2>
R2C5 can only be <5>
R8C2 can only be <3>
R1C3 can only be <5>
R1C5 can only be <6>
R5C1 can only be <7>
R3C1 can only be <2>
R6C5 can only be <8>
R5C3 can only be <3>
R6C8 can only be <7>
R5C5 can only be <2>
R7C2 can only be <2>
R3C2 can only be <7>
R7C1 can only be <6>
R7C9 can only be <5>
R7C8 can only be <9>
R3C9 can only be <8>
R3C8 can only be <5>
R5C9 can only be <6>
R7C5 can only be <3>
R4C8 can only be <1>
R8C7 can only be <1>
R8C8 can only be <6>
R5C7 can only be <9>
R4C2 can only be <4>
R5C8 can only be <8>
R5C6 can only be <4>
R4C7 can only be <5>
R4C5 can only be <9>
R5C2 can only be <1>
R8C5 can only be <4>
R8C6 can only be <9>
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