Feb 20 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C7 can only be <6>
R8C7 can only be <8>
R5C7 can only be <9>
R9C9 can only be <4>
R2C8 is the only square in row 2 that can be <4>
R3C5 is the only square in row 3 that can be <9>
R4C1 is the only square in row 4 that can be <4>
R5C5 is the only square in row 5 that can be <1>
R7C5 can only be <2>
R7C2 can only be <1>
R7C8 can only be <5>
R8C8 can only be <1>
R5C8 is the only square in row 5 that can be <6>
R6C4 is the only square in row 6 that can be <6>
R1C5 is the only square in row 1 that can be <6>
R8C5 is the only square in row 8 that can be <4>
R8C6 is the only square in row 8 that can be <5>
R1C1 is the only square in column 1 that can be <1>
R6C1 is the only square in column 1 that can be <2>
Squares R5C1 and R5C3 in row 5 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 row.
R5C2 - removing <37> from <3578> leaving <58>
R5C9 - removing <7> from <578> leaving <58>
Squares R5C1 and R5C3 in block 4 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.
R4C2 - removing <3> from <3589> leaving <589>
R6C2 - removing <37> from <3789> leaving <89>
Intersection of row 1 with block 2. The value <3> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C4 - removing <3> from <12378> leaving <1278>
R2C5 - removing <3> from <38> leaving <8>
R2C6 - removing <3> from <1378> leaving <178>
R9C5 can only be <3>
R9C1 can only be <7>
R8C4 can only be <7>
R5C1 can only be <3>
R5C3 can only be <7>
Squares R5C2, R5C9, R4C2 and R4C9 form a Type-4 Unique Rectangle on <58>.
R4C2 - removing <8> from <589> leaving <59>
R4C9 - removing <8> from <258> leaving <25>
Intersection of row 4 with block 5. The value <8> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C6 - removing <8> from <389> leaving <39>
Squares R8C2, R8C3, R2C2 and R2C3 form a Type-1 Unique Rectangle on <23>.
R2C2 - removing <23> from <237> leaving <7>
R2C6 can only be <1>
R3C2 can only be <2>
R2C4 can only be <2>
R9C6 can only be <8>
R3C8 can only be <7>
R8C2 can only be <3>
R2C3 can only be <3>
R6C8 can only be <3>
R1C9 can only be <2>
R6C6 can only be <9>
R4C8 can only be <2>
R8C3 can only be <2>
R9C4 can only be <1>
R1C4 can only be <3>
R4C9 can only be <5>
R4C2 can only be <9>
R5C9 can only be <8>
R5C2 can only be <5>
R6C9 can only be <7>
R6C2 can only be <8>
R4C6 can only be <3>
R1C6 can only be <7>
R4C4 can only be <8>
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