Jul 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 can only be <2>
R6C4 can only be <4>
R7C4 can only be <2>
R3C4 can only be <1>
R4C4 can only be <8>
R5C4 can only be <7>
R3C3 is the only square in row 3 that can be <7>
R3C2 is the only square in row 3 that can be <6>
R2C9 is the only square in row 2 that can be <6>
R2C8 is the only square in row 2 that can be <9>
R4C5 is the only square in row 4 that can be <1>
R4C7 is the only square in row 4 that can be <2>
R5C5 is the only square in row 5 that can be <2>
R6C6 is the only square in row 6 that can be <9>
R7C2 is the only square in row 7 that can be <9>
R9C9 is the only square in row 9 that can be <9>
R2C7 is the only square in column 7 that can be <1>
R2C5 is the only square in row 2 that can be <8>
R1C5 can only be <5>
Squares R1C1 and R9C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C1 - removing <3> from <3456> leaving <456>
R8C1 - removing <3> from <356> leaving <56>
Squares R3C7 and R3C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <3> from <238> leaving <28>
R1C9 - removing <3> from <238> leaving <28>
Squares R1C8 and R1C9 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C2 - removing <2> from <123> leaving <13>
Intersection of column 7 with block 9. The value <8> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <8> from <358> leaving <35>
R8C8 - removing <8> from <234578> leaving <23457>
R8C9 - removing <8> from <238> leaving <23>
Squares R1C1, R1C2, R9C1 and R9C2 form a Type-1 Unique Rectangle on <13>.
R9C2 - removing <13> from <123> leaving <2>
R2C3 is the only square in row 2 that can be <2>
R9C1 is the only square in row 9 that can be <1>
R1C1 can only be <3>
R1C2 can only be <1>
Squares R5C2 and R8C2 in column 2 and R5C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 5 and 8 can be removed.
R8C3 - removing <3> from <3568> leaving <568>
R8C5 - removing <3> from <367> leaving <67>
R5C6 - removing <3> from <356> leaving <56>
R8C7 - removing <3> from <3458> leaving <458>
R5C8 - removing <3> from <358> leaving <58>
R8C8 - removing <3> from <23457> leaving <2457>
Squares R2C1, R2C2, R5C1 and R5C2 form a Type-4 Unique Rectangle on <45>.
R5C1 - removing <5> from <456> leaving <46>
R5C2 - removing <5> from <345> leaving <34>
Intersection of block 4 with column 3. The value <5> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R7C3 - removing <5> from <3568> leaving <368>
R8C3 - removing <5> from <568> leaving <68>
Intersection of row 7 with block 9. The value <5> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. 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 <5> from <458> leaving <48>
R8C8 - removing <5> from <2457> leaving <247>
Squares R5C8 (XY), R7C8 (XZ) and R5C9 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R8C9 - removing <3> from <23> leaving <2>
R1C9 can only be <8>
R1C8 can only be <2>
R5C9 can only be <3>
R5C2 can only be <4>
R6C7 can only be <5>
R5C8 can only be <8>
R5C1 can only be <6>
R2C2 can only be <5>
R2C1 can only be <4>
R8C2 can only be <3>
R5C6 can only be <5>
R8C1 can only be <5>
R6C3 can only be <3>
R4C6 can only be <3>
R6C5 can only be <6>
R4C3 can only be <5>
R8C5 can only be <7>
R8C8 can only be <4>
R9C5 can only be <3>
R8C7 can only be <8>
R3C8 can only be <3>
R9C8 can only be <7>
R7C6 can only be <6>
R3C7 can only be <4>
R7C8 can only be <5>
R7C3 can only be <8>
R8C3 can only be <6>
R7C7 can only be <3>
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