Jun 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C3 can only be <2>
R3C9 is the only square in row 3 that can be <5>
R6C1 is the only square in row 6 that can be <9>
R7C1 is the only square in row 7 that can be <2>
R9C2 is the only square in row 9 that can be <9>
R7C2 can only be <1>
R7C6 can only be <9>
R8C8 is the only square in row 8 that can be <9>
R6C9 is the only square in column 9 that can be <6>
Squares R4C2 and R5C2 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 <468> leaving <68>
Squares R4C2 and R5C2 in block 4 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 block.
R4C1 - removing <4> from <134> leaving <13>
Squares R7C4 and R7C5 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C4 - removing <35> from <13456> leaving <146>
R9C5 - removing <35> from <356> leaving <6>
R1C1 is the only square in row 1 that can be <6>
R2C2 can only be <8>
R8C2 can only be <6>
R1C3 can only be <1>
R2C3 can only be <5>
R5C3 can only be <3>
R2C1 can only be <4>
R8C3 can only be <8>
R4C1 can only be <1>
R2C9 is the only square in column 9 that can be <1>
Squares R1C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C5 - removing <48> from <1348> leaving <13>
R4C5 - removing <48> from <248> leaving <2>
R5C5 - removing <4> from <1245> leaving <125>
R8C9 is the only square in column 9 that can be <2>
Intersection of row 1 with block 3. The value <7> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. 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 <7> from <237> leaving <23>
R2C8 - removing <7> from <237> leaving <23>
Squares R2C7 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C4 - removing <3> from <367> leaving <67>
Squares R2C7 and R2C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C8 - removing <3> from <348> leaving <48>
R2C8 is the only square in column 8 that can be <3>
R2C7 can only be <2>
R5C8 is the only square in row 5 that can be <2>
Squares R5C2 and R5C7 in row 5 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 row.
R5C4 - removing <47> from <14567> leaving <156>
R5C6 - removing <47> from <1467> leaving <16>
Intersection of column 7 with block 6. The value <4> 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.
R6C8 - removing <4> from <478> leaving <78>
Intersection of row 6 with block 5. The value <4> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C6 - removing <4> from <478> leaving <78>
Squares R5C2, R5C7, R4C2 and R4C7 form a Type-1 Unique Rectangle on <47>.
R4C7 - removing <47> from <347> leaving <3>
R8C7 can only be <5>
R8C1 can only be <3>
R9C7 can only be <7>
R9C9 can only be <3>
R5C7 can only be <4>
R9C1 can only be <5>
R5C2 can only be <7>
R4C2 can only be <4>
Squares R6C8 (XY), R6C4 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C4 - removing <4> from <134> leaving <13>
Squares R3C4 and R3C5 in row 3 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 row.
R3C6 - removing <1> from <148> leaving <48>
Squares R3C8 and R6C5 form a remote naked pair. <48> can be removed from any square that is common to their groups.
R6C8 - removing <8> from <78> leaving <7>
R6C4 can only be <4>
R4C9 can only be <8>
R4C6 can only be <7>
R1C9 can only be <7>
R6C5 can only be <8>
R8C4 can only be <1>
R1C5 can only be <4>
R8C6 can only be <4>
R3C4 can only be <3>
R3C6 can only be <8>
R1C8 can only be <8>
R3C8 can only be <4>
R3C5 can only be <1>
R7C4 can only be <5>
R5C5 can only be <5>
R2C6 can only be <6>
R5C4 can only be <6>
R7C5 can only be <3>
R2C4 can only be <7>
R5C6 can only be <1>
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