Jan 30 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 is the only square in row 1 that can be <2>
R2C9 is the only square in row 2 that can be <2>
R5C1 is the only square in row 5 that can be <8>
R5C3 is the only square in row 5 that can be <3>
R7C2 is the only square in row 7 that can be <8>
R8C6 is the only square in row 8 that can be <2>
R4C5 is the only square in row 4 that can be <2>
R8C8 is the only square in row 8 that can be <8>
R9C2 is the only square in row 9 that can be <3>
R9C8 is the only square in column 8 that can be <9>
Intersection of row 1 with block 1. The value <9> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. 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 <9> from <34679> leaving <3467>
R2C3 - removing <9> from <459> leaving <45>
Intersection of row 3 with block 3. The value <1> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <1> from <157> leaving <57>
Intersection of row 5 with block 6. The value <4> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <4> from <1467> leaving <167>
R6C7 - removing <4> from <1457> leaving <157>
R6C8 - removing <4> from <1457> leaving <157>
Intersection of row 9 with block 9. The value <6> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C9 - removing <6> from <1456> leaving <145>
R8C7 - removing <6> from <14567> leaving <1457>
R8C9 - removing <6> from <14567> leaving <1457>
Intersection of column 1 with block 1. The values <37> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
R1C2 - removing <7> from <157> leaving <15>
R2C2 - removing <7> from <4567> leaving <456>
Intersection of column 8 with block 3. The value <4> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. 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 <4> from <4567> leaving <567>
R3C9 - removing <4> from <14567> leaving <1567>
Intersection of block 7 with row 8. The value <5> only appears in one or more of squares R8C1, R8C2 and R8C3 of block 7. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C7 - removing <5> from <1457> leaving <147>
R8C9 - removing <5> from <1457> leaving <147>
Squares R3C4<37>, R3C5<57> and R3C6<357> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <357>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C1 - removing <37> from <3467> leaving <46>
R3C8 - removing <57> from <14567> leaving <146>
R3C9 - removing <57> from <1567> leaving <16>
R2C1 is the only square in column 1 that can be <3>
R1C1 is the only square in column 1 that can be <7>
R1C8 can only be <5>
R1C2 can only be <1>
R1C3 can only be <9>
R6C7 is the only square in row 6 that can be <5>
R6C8 is the only square in row 6 that can be <1>
R3C9 is the only square in row 3 that can be <1>
R4C3 is the only square in row 4 that can be <1>
R7C4 is the only square in row 7 that can be <1>
R8C7 is the only square in row 8 that can be <1>
R5C7 is the only square in column 7 that can be <4>
Squares R4C2 and R6C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <4> from <456> leaving <56>
R8C2 - removing <4> from <456> leaving <56>
Intersection of row 3 with block 2. The values <357> 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.
R2C4 - removing <7> from <789> leaving <89>
R2C6 - removing <57> from <5789> leaving <89>
Squares R2C4, R2C6, R6C4 and R6C6 form a Type-3 Unique Rectangle on <89>. Upon close inspection, it is clear that:
(R6C4 or R6C6)<47>, R5C5<67>, R4C6<347> and R4C4<367> form a naked quad on <3467> in block 5. No other squares in the block can contain these possibilities
R6C5 - removing <7> from <79> leaving <9>
Squares R4C2, R6C2, R4C6 and R6C6 form a Type-4 Unique Rectangle on <47>.
R4C6 - removing <7> from <347> leaving <34>
R6C6 - removing <7> from <478> leaving <48>
Squares R4C4 (XYZ), R3C4 (XZ) and R5C5 (YZ) form an XYZ-Wing pattern on <7>. All squares that are buddies of all three squares cannot be <7>.
R6C4 - removing <7> from <78> leaving <8>
R6C6 can only be <4>
R2C4 can only be <9>
R6C2 can only be <7>
R4C6 can only be <3>
R2C6 can only be <8>
R4C2 can only be <4>
R3C4 is the only square in row 3 that can be <3>
R8C1 is the only square in row 8 that can be <9>
R7C6 is the only square in row 7 that can be <9>
Squares R5C9 and R8C4 form a remote naked pair. <67> can be removed from any square that is common to their groups.
R8C9 - removing <7> from <47> leaving <4>
R8C3 can only be <5>
R7C9 can only be <5>
R7C5 can only be <6>
R8C2 can only be <6>
R2C3 can only be <4>
R3C1 can only be <6>
R3C8 can only be <4>
R7C1 can only be <4>
R2C2 can only be <5>
R5C5 can only be <7>
R8C4 can only be <7>
R4C4 can only be <6>
R9C6 can only be <5>
R3C6 can only be <7>
R3C5 can only be <5>
R4C8 can only be <7>
R2C8 can only be <6>
R5C9 can only be <6>
R9C9 can only be <7>
R9C7 can only be <6>
R2C7 can only be <7>
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