May 30 - Super Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R2C5 is the only square in row 2 that can be <2>

R5C5 is the only square in row 5 that can be <7>

R6C6 is the only square in row 6 that can be <2>

R7C5 is the only square in row 7 that can be <4>

R4C6 is the only square in row 4 that can be <4>

R5C7 is the only square in row 5 that can be <4>

R9C6 is the only square in column 6 that can be <8>

R9C3 can only be <2>

R7C3 can only be <8>

R7C7 is the only square in row 7 that can be <2>

Intersection of row 6 with block 5. The value <9> 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.

R5C4 - removing <9> from <13569> leaving <1356>

Intersection of column 2 with block 1. The value <8> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.

R2C1 - removing <8> from <158> leaving <15>

Intersection of block 2 with row 1. The value <1> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.

R1C2 - removing <1> from <1789> leaving <789>

R1C3 - removing <1> from <169> leaving <69>

Squares R4C9<56>, R6C9<36> and R7C9<35> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <356>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R2C9 - removing <5> from <159> leaving <19>

R3C9 - removing <5> from <1579> leaving <179>

R8C9 - removing <36> from <3679> leaving <79>

Intersection of column 9 with block 6. The value <6> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.

R5C8 - removing <6> from <356> leaving <35>

Squares R5C2<19>, R5C3<169> and R5C6<16> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <169>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R5C4 - removing <16> from <1356> leaving <35>

Squares R1C3<69>, R1C4<169> and R1C6<16> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <169>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R1C2 - removing <9> from <789> leaving <78>

R1C8 - removing <9> from <389> leaving <38>

Squares R1C2 and R1C7 in row 1 and R9C2 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 7 can be removed.

R3C7 - removing <7> from <57> leaving <5>

R8C2 - removing <7> from <17> leaving <1>

R5C2 can only be <9>

Intersection of row 2 with block 3. The value <9> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.

R3C9 - removing <9> from <179> leaving <17>

Squares R1C7 and R1C8 in row 1, R5C4 and R5C8 in row 5 and R9C4, R9C7 and R9C8 in row 9 form a Swordfish pattern on possibility <3>. All other instances of this possibility in columns 4, 7 and 8 can be removed.

R6C4 - removing <3> from <369> leaving <69>

R8C8 - removing <3> from <369> leaving <69>

Squares R9C2 (XY), R7C1 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.

R7C9 - removing <3> from <35> leaving <5>

R7C1 can only be <3>

R4C9 can only be <6>

R4C5 can only be <8>

R6C9 can only be <3>

R5C8 can only be <5>

R8C1 can only be <7>

R8C9 can only be <9>

R9C2 can only be <5>

R8C8 can only be <6>

R2C9 can only be <1>

R2C2 can only be <8>

R2C8 can only be <9>

R1C2 can only be <7>

R2C1 can only be <5>

R3C9 can only be <7>

R1C7 can only be <3>

R4C1 can only be <1>

R5C4 can only be <3>

R8C5 can only be <3>

R9C8 can only be <3>

R9C4 can only be <6>

R9C7 can only be <7>

R1C8 can only be <8>

R4C4 can only be <5>

R3C1 can only be <6>

R5C3 can only be <6>

R5C6 can only be <1>

R1C3 can only be <9>

R6C1 can only be <8>

R1C6 can only be <6>

R6C4 can only be <9>

R1C4 can only be <1>

R3C3 can only be <1>

R3C5 can only be <9>

R6C5 can only be <6>

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