Aug 29 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C5 is the only square in row 3 that can be <4>
R3C8 is the only square in row 3 that can be <6>
R4C1 is the only square in row 4 that can be <8>
R7C1 is the only square in row 7 that can be <6>
R6C3 is the only square in row 6 that can be <6>
R4C6 is the only square in row 4 that can be <6>
R7C8 is the only square in row 7 that can be <8>
R7C4 is the only square in row 7 that can be <4>
R7C7 is the only square in row 7 that can be <9>
R5C2 is the only square in column 2 that can be <4>
R2C4 is the only square in column 4 that can be <9>
R2C8 is the only square in column 8 that can be <1>
Squares R7C5 and R7C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C6 - removing <27> from <12357> leaving <135>
R9C4 - removing <7> from <157> leaving <15>
R9C6 - removing <27> from <12357> leaving <135>
R7C6 is the only square in column 6 that can be <2>
R7C5 can only be <7>
R2C6 is the only square in row 2 that can be <7>
Intersection of row 6 with block 4. The value <1> only appears in one or more of squares R6C1, R6C2 and R6C3 of row 6. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C1 - removing <1> from <1235> leaving <235>
R5C3 - removing <1> from <1257> leaving <257>
Intersection of column 2 with block 4. The value <7> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C3 - removing <7> from <2579> leaving <259>
R5C3 - removing <7> from <257> leaving <25>
R5C4 is the only square in row 5 that can be <7>
R4C4 can only be <5>
R4C5 can only be <2>
R9C4 can only be <1>
R4C3 can only be <9>
R5C5 can only be <1>
R4C8 can only be <3>
R4C2 can only be <7>
R3C9 is the only square in row 3 that can be <9>
R1C1 is the only square in row 1 that can be <9>
R3C6 is the only square in row 3 that can be <8>
R1C9 is the only square in row 1 that can be <8>
R5C1 is the only square in row 5 that can be <3>
R6C8 is the only square in row 6 that can be <9>
R1C6 is the only square in column 6 that can be <1>
Squares R1C2 (XY), R2C1 (XZ) and R1C5 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R2C5 - removing <5> from <35> leaving <3>
R1C5 can only be <5>
Intersection of column 9 with block 9. The value <3> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <3> from <2357> leaving <257>
Squares R8C6, R9C6, R8C9 and R9C9 form a Type-4 Unique Rectangle on <35>.
R8C9 - removing <5> from <2357> leaving <237>
R9C9 - removing <5> from <2357> leaving <237>
Squares R2C1 and R6C1 in column 1 and R2C9 and R6C9 in column 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 2 and 6 can be removed.
R6C7 - removing <5> from <257> leaving <27>
Squares R5C3 (XY), R6C2 (XZ) and R3C3 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R3C2 - removing <1> from <13> leaving <3>
R3C7 can only be <5>
R1C2 can only be <2>
R3C3 can only be <1>
R2C9 can only be <2>
R1C7 can only be <3>
R6C2 can only be <1>
R2C1 can only be <5>
R6C1 can only be <2>
R6C7 can only be <7>
R9C1 can only be <4>
R5C3 can only be <5>
R6C9 can only be <5>
R8C7 can only be <2>
R5C8 can only be <2>
R8C3 can only be <7>
R9C8 can only be <5>
R8C1 can only be <1>
R9C6 can only be <3>
R8C8 can only be <4>
R8C9 can only be <3>
R9C3 can only be <2>
R8C6 can only be <5>
R9C9 can only be <7>
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