Jul 31 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 can only be <8>
R5C3 is the only square in column 3 that can be <9>
R2C4 is the only square in column 4 that can be <9>
Squares R7C4 and R8C4 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C6 - removing <3> from <345> leaving <45>
R8C5 - removing <37> from <123457> leaving <1245>
R8C6 - removing <3> from <2345> leaving <245>
R9C5 - removing <37> from <12347> leaving <124>
R2C6 is the only square in column 6 that can be <3>
Intersection of row 9 with block 7. The value <3> 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 <3> from <347> leaving <47>
R8C1 - removing <3> from <134678> leaving <14678>
R8C2 - removing <3> from <34678> leaving <4678>
R8C3 - removing <3> from <1368> leaving <168>
Intersection of column 1 with block 4. The value <3> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C2 - removing <3> from <378> leaving <78>
Intersection of column 3 with block 7. The value <1> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C1 - removing <1> from <14678> leaving <4678>
Intersection of column 6 with block 8. The value <4> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C5 - removing <4> from <1245> leaving <125>
R9C5 - removing <4> from <124> leaving <12>
Intersection of column 7 with block 3. The value <8> 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.
R1C8 - removing <8> from <2578> leaving <257>
R2C8 - removing <8> from <24578> leaving <2457>
Squares R1C5 and R1C8 in row 1 and R9C5 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 5 and 8 can be removed.
R2C5 - removing <2> from <257> leaving <57>
R2C8 - removing <2> from <2457> leaving <457>
R8C5 - removing <2> from <125> leaving <15>
R8C8 - removing <2> from <24579> leaving <4579>
Squares R3C6 and R3C9 in row 3 and R7C6 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 6 and 9 can be removed.
R2C9 - removing <5> from <12457> leaving <1247>
R4C9 - removing <5> from <579> leaving <79>
R8C6 - removing <5> from <245> leaving <24>
R8C9 - removing <5> from <234579> leaving <23479>
R4C8 is the only square in row 4 that can be <5>
R6C8 is the only square in column 8 that can be <8>
R6C2 can only be <6>
R6C1 can only be <1>
R8C8 is the only square in column 8 that can be <9>
Squares R7C4, R8C4, R7C9 and R8C9 form a Type-4 Unique Rectangle on <37>.
R7C9 - removing <7> from <3457> leaving <345>
R8C9 - removing <7> from <2347> leaving <234>
Squares R3C6 (XY), R3C1 (XZ) and R7C6 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R7C1 - removing <4> from <47> leaving <7>
R7C4 can only be <3>
R5C1 can only be <3>
R8C4 can only be <7>
R5C5 can only be <4>
R4C1 can only be <8>
R6C5 can only be <9>
R6C9 can only be <4>
R4C5 can only be <3>
R7C9 can only be <5>
R7C6 can only be <4>
R3C9 can only be <2>
R8C7 can only be <4>
R8C2 can only be <8>
R8C6 can only be <2>
R9C7 can only be <7>
R9C8 can only be <2>
R5C7 can only be <1>
R9C5 can only be <1>
R1C8 can only be <7>
R8C9 can only be <3>
R2C8 can only be <4>
R3C1 can only be <4>
R3C6 can only be <5>
R2C9 can only be <1>
R4C2 can only be <7>
R8C1 can only be <6>
R4C9 can only be <9>
R5C9 can only be <7>
R2C1 can only be <2>
R8C3 can only be <1>
R2C2 can only be <5>
R8C5 can only be <5>
R9C3 can only be <3>
R1C5 can only be <2>
R2C5 can only be <7>
R9C2 can only be <4>
R1C3 can only be <8>
R1C7 can only be <5>
R2C3 can only be <6>
R1C2 can only be <3>
R2C7 can only be <8>
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