Mar 21 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <9>
R5C7 can only be <9>
R4C8 can only be <6>
R6C4 can only be <2>
R6C6 can only be <6>
R4C6 can only be <1>
R5C3 can only be <1>
R5C8 can only be <2>
R5C2 can only be <8>
R1C1 is the only square in row 1 that can be <3>
R1C5 is the only square in row 1 that can be <2>
R3C9 is the only square in row 3 that can be <6>
R6C3 is the only square in row 6 that can be <9>
R7C5 is the only square in row 7 that can be <6>
R8C7 is the only square in row 8 that can be <3>
R8C3 is the only square in row 8 that can be <6>
R8C9 is the only square in row 8 that can be <8>
R9C4 is the only square in row 9 that can be <3>
R9C6 is the only square in row 9 that can be <8>
Intersection of row 1 with block 3. The value <1> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <1> from <1457> leaving <457>
R2C9 - removing <1> from <145> leaving <45>
Squares R2C9 and R6C9 in column 9 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 column.
R1C9 - removing <45> from <1459> leaving <19>
Intersection of row 3 with block 2. The values <79> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C6 - removing <9> from <459> leaving <45>
R2C5 - removing <7> from <157> leaving <15>
Intersection of row 9 with block 7. The value <4> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <4> from <12459> leaving <1259>
Intersection of column 3 with block 1. The value <5> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <5> from <12458> leaving <1248>
R3C1 - removing <5> from <1458> leaving <148>
R3C2 - removing <5> from <145> leaving <14>
Intersection of block 9 with row 7. The value <7> only appears in one or more of squares R7C7, R7C8 and R7C9 of block 9. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.
R7C4 - removing <7> from <47> leaving <4>
R1C4 can only be <8>
R1C8 can only be <9>
R3C4 can only be <7>
R1C9 can only be <1>
R7C8 can only be <7>
R7C7 can only be <1>
R2C8 can only be <8>
R2C7 is the only square in row 2 that can be <7>
R3C1 is the only square in row 3 that can be <8>
Squares R1C6 and R1C7 in row 1, R4C1 and R4C7 in row 4 and R7C1 and R7C6 in row 7 form a Swordfish pattern on possibility <5>. All other instances of this possibility in columns 1, 6 and 7 can be removed.
R3C6 - removing <5> from <459> leaving <49>
R8C1 - removing <5> from <59> leaving <9>
Squares R2C9 and R4C1 form a remote naked pair. <45> can be removed from any square that is common to their groups.
R2C1 - removing <4> from <124> leaving <12>
Squares R7C1 (XY), R9C3 (XZ) and R4C1 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R9C1 - removing <4> from <124> leaving <12>
R4C1 is the only square in column 1 that can be <4>
R4C7 can only be <5>
R6C2 can only be <5>
R1C7 can only be <4>
R6C9 can only be <4>
R8C2 can only be <7>
R2C9 can only be <5>
R8C5 can only be <5>
R2C5 can only be <1>
R7C6 can only be <9>
R1C6 can only be <5>
R2C1 can only be <2>
R3C5 can only be <9>
R3C6 can only be <4>
R9C5 can only be <7>
R3C2 can only be <1>
R3C3 can only be <5>
R7C9 can only be <2>
R7C1 can only be <5>
R9C9 can only be <9>
R2C3 can only be <4>
R9C1 can only be <1>
R9C3 can only be <2>
R9C2 can only be <4>
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