Mar 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <6>
R6C8 can only be <1>
R7C7 can only be <7>
R4C1 is the only square in row 4 that can be <9>
R6C1 is the only square in row 6 that can be <2>
R5C7 is the only square in row 5 that can be <2>
R7C5 is the only square in row 7 that can be <2>
R7C3 is the only square in row 7 that can be <9>
Intersection of column 7 with block 3. The value <3> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <3> from <3456> leaving <456>
R3C9 - removing <3> from <34568> leaving <4568>
Intersection of block 4 with column 2. The values <37> only appears in one or more of squares R4C2, R5C2 and R6C2 of block 4. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain these values.
R2C2 - removing <7> from <457> leaving <45>
R8C2 - removing <7> from <1457> leaving <145>
Squares R2C2 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <45> from <14567> leaving <167>
R1C3 - removing <45> from <1457> leaving <17>
R3C1 - removing <45> from <456> leaving <6>
Squares R1C1 and R1C3 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C5 - removing <7> from <3479> leaving <349>
R1C6 - removing <7> from <567> leaving <56>
Squares R1C6 and R2C4 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C4 - removing <56> from <3569> leaving <39>
R2C6 - removing <56> from <567> leaving <7>
R8C5 is the only square in row 8 that can be <7>
R9C5 can only be <3>
R3C7 is the only square in row 3 that can be <3>
R1C7 can only be <4>
R1C5 can only be <9>
R9C7 can only be <8>
R1C4 can only be <3>
R8C4 is the only square in row 8 that can be <9>
Squares R1C9 and R9C4 form a remote naked pair. <56> can be removed from any square that is common to their groups.
R9C9 - removing <5> from <145> leaving <14>
Squares R1C1, R1C3, R9C1 and R9C3 form a Type-4 Unique Rectangle on <17>.
R9C1 - removing <1> from <1457> leaving <457>
R9C3 - removing <1> from <1457> leaving <457>
Squares R8C8 (XY), R9C9 (XZ) and R8C6 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R9C6 - removing <1> from <156> leaving <56>
R9C9 is the only square in row 9 that can be <1>
R7C9 can only be <5>
R7C1 can only be <1>
R1C9 can only be <6>
R3C9 can only be <8>
R8C8 can only be <4>
R4C8 can only be <6>
R5C8 can only be <8>
R1C6 can only be <5>
R3C5 can only be <4>
R2C8 can only be <5>
R1C1 can only be <7>
R8C2 can only be <5>
R8C6 can only be <1>
R2C2 can only be <4>
R1C3 can only be <1>
R9C1 can only be <4>
R9C6 can only be <6>
R2C4 can only be <6>
R2C5 can only be <8>
R4C2 can only be <7>
R3C3 can only be <5>
R9C4 can only be <5>
R5C3 can only be <4>
R4C9 can only be <4>
R6C2 can only be <3>
R5C9 can only be <3>
R5C1 can only be <5>
R9C3 can only be <7>
R5C2 can only be <1>
R6C9 can only be <7>
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