Mar 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C1 can only be <5>
R5C9 can only be <2>
R4C1 can only be <8>
R5C2 can only be <3>
R5C8 can only be <9>
R4C3 can only be <2>
R6C1 can only be <1>
R2C2 is the only square in row 2 that can be <8>
R2C1 is the only square in row 2 that can be <9>
R2C7 is the only square in row 2 that can be <6>
R3C1 is the only square in row 3 that can be <4>
R3C6 is the only square in row 3 that can be <8>
R4C9 is the only square in row 4 that can be <4>
R7C3 is the only square in column 3 that can be <8>
Squares R6C7 and R6C9 in row 6 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.
R6C4 - removing <5> from <257> leaving <27>
R6C5 - removing <5> from <567> leaving <67>
R6C6 - removing <5> from <2567> leaving <267>
Squares R7C9<567>, R8C9<567> and R9C8<57> in block 9 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.
R7C7 - removing <5> from <59> leaving <9>
R7C8 - removing <57> from <1457> leaving <14>
R8C8 - removing <57> from <1457> leaving <14>
R9C7 - removing <5> from <3589> leaving <389>
R9C9 - removing <567> from <35678> leaving <38>
R8C2 is the only square in column 2 that can be <9>
Squares R1C6<257>, R2C4<257> and R2C5<57> in block 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <257>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C4 - removing <257> from <12357> leaving <13>
R3C5 - removing <57> from <1357> leaving <13>
Squares R8C3<57>, R8C6<567> and R8C9<567> in row 8 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 row.
R8C5 - removing <567> from <14567> leaving <14>
Squares R8C5, R8C8, R7C5 and R7C8 form a Type-1 Unique Rectangle on <14>.
R7C5 - removing <14> from <14567> leaving <567>
R7C8 is the only square in row 7 that can be <4>
R8C8 can only be <1>
R8C5 can only be <4>
R7C4 is the only square in row 7 that can be <1>
R1C4 can only be <3>
R3C5 can only be <1>
R1C3 is the only square in row 1 that can be <1>
R3C7 is the only square in row 3 that can be <3>
R9C7 can only be <8>
R9C9 can only be <3>
R6C7 can only be <5>
R6C9 can only be <8>
R4C5 is the only square in row 4 that can be <3>
Squares R4C4, R4C6, R9C4 and R9C6 form a Type-3 Unique Rectangle on <59>. Upon close inspection, it is clear that:
(R9C4 or R9C6)<67> and R9C1<67> form a naked pair on <67> in row 9. No other squares in the row can contain these possibilities
R9C8 - removing <7> from <57> leaving <5>
R1C9 is the only square in column 9 that can be <5>
Squares R7C2 (XY), R8C3 (XZ) and R7C9 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R8C9 - removing <7> from <67> leaving <6>
R7C9 can only be <7>
Squares R7C5 (XY), R8C6 (XZ) and R6C5 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R6C6 - removing <7> from <267> leaving <26>
Squares R6C6 (XY), R1C6 (XZ) and R6C5 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R2C5 - removing <7> from <57> leaving <5>
R7C5 can only be <6>
R7C2 can only be <5>
R6C5 can only be <7>
R6C4 can only be <2>
R3C2 can only be <2>
R8C3 can only be <7>
R8C6 can only be <5>
R3C3 can only be <5>
R9C1 can only be <6>
R4C6 can only be <9>
R1C1 can only be <7>
R1C6 can only be <2>
R1C2 can only be <6>
R6C6 can only be <6>
R2C4 can only be <7>
R2C8 can only be <2>
R9C4 can only be <9>
R3C8 can only be <7>
R4C4 can only be <5>
R9C6 can only be <7>
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