Feb 06 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 can only be <1>
R9C4 can only be <9>
R5C5 can only be <6>
R6C5 can only be <8>
R2C1 is the only square in row 2 that can be <6>
R2C5 is the only square in row 2 that can be <9>
R3C3 is the only square in row 3 that can be <5>
R3C7 is the only square in row 3 that can be <8>
R4C9 is the only square in row 4 that can be <5>
R8C1 is the only square in row 8 that can be <5>
R8C7 is the only square in row 8 that can be <6>
R8C9 is the only square in row 8 that can be <8>
R3C5 is the only square in column 5 that can be <7>
R7C7 is the only square in column 7 that can be <4>
R7C5 can only be <3>
R7C3 can only be <9>
R7C8 can only be <2>
R8C5 can only be <4>
R9C6 can only be <8>
R8C3 can only be <3>
R7C2 can only be <8>
R5C2 is the only square in row 5 that can be <9>
R6C9 is the only square in row 6 that can be <9>
R4C3 is the only square in column 3 that can be <4>
R6C1 is the only square in block 4 that can be <3>
Squares R5C4 and R5C6 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C3 - removing <2> from <127> leaving <17>
R5C7 - removing <2> from <1237> leaving <137>
Intersection of row 2 with block 3. The value <3> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. 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 <3> from <1347> leaving <147>
R1C9 - removing <3> from <123> leaving <12>
R3C8 - removing <3> from <134> leaving <14>
Intersection of row 3 with block 2. The value <2> 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 this value.
R1C4 - removing <2> from <126> leaving <16>
R1C6 - removing <2> from <236> leaving <36>
Intersection of column 7 with block 6. The value <1> 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 this value.
R5C8 - removing <1> from <137> leaving <37>
Intersection of column 9 with block 3. The value <2> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. 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 <2> from <237> leaving <37>
Squares R9C1, R9C2, R1C1 and R1C2 form a Type-3 Unique Rectangle on <47>. Upon close inspection, it is clear that:
(R1C1 or R1C2)<23>, R1C9<12>, R1C6<36> and R1C4<16> form a naked quad on <1236> in row 1. No other squares in the row can contain these possibilities
R1C8 - removing <1> from <147> leaving <47>
Squares R1C1 (XYZ), R1C8 (XZ) and R2C3 (YZ) form an XYZ-Wing pattern on <7>. All squares that are buddies of all three squares cannot be <7>.
R1C2 - removing <7> from <347> leaving <34>
R9C2 is the only square in column 2 that can be <7>
R9C1 can only be <4>
Squares R2C3 and R4C7 form a remote naked pair. <27> can be removed from any square that is common to their groups.
R2C7 - removing <7> from <37> leaving <3>
R2C9 can only be <2>
R2C3 can only be <7>
R1C9 can only be <1>
R1C4 can only be <6>
R9C9 can only be <3>
R3C8 can only be <4>
R5C3 can only be <1>
R1C1 can only be <2>
R3C2 can only be <3>
R1C8 can only be <7>
R5C7 can only be <7>
R6C3 can only be <2>
R5C8 can only be <3>
R4C7 can only be <2>
R9C8 can only be <1>
R6C7 can only be <1>
R4C1 can only be <7>
R1C6 can only be <3>
R7C4 can only be <5>
R1C2 can only be <4>
R3C6 can only be <2>
R3C4 can only be <1>
R5C6 can only be <5>
R5C4 can only be <2>
R7C6 can only be <6>
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