Nov 21 - Super Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R2C7 is the only square in row 2 that can be <4>

R2C5 is the only square in row 2 that can be <9>

R3C2 is the only square in row 3 that can be <3>

R7C7 is the only square in row 7 that can be <1>

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

R4C3 is the only square in row 4 that can be <4>

R4C7 is the only square in row 4 that can be <9>

R4C5 is the only square in row 4 that can be <3>

R5C4 is the only square in row 5 that can be <4>

R7C2 is the only square in column 2 that can be <8>

Squares R4C8 and R7C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R3C8 - removing <25> from <2578> leaving <78>

R5C8 - removing <25> from <25678> leaving <678>

R6C8 - removing <2> from <2678> leaving <678>

Intersection of column 2 with block 4. The values <257> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.

R5C1 - removing <25> from <12569> leaving <169>

R5C3 - removing <25> from <12569> leaving <169>

R6C3 - removing <2> from <126> leaving <16>

Squares R1C5 and R1C9 in row 1 and R9C5 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 5 and 9 can be removed.

R2C9 - removing <8> from <2578> leaving <257>

R3C5 - removing <8> from <2578> leaving <257>

R5C5 - removing <8> from <128> leaving <12>

R5C9 - removing <8> from <23578> leaving <2357>

R6C5 - removing <8> from <128> leaving <12>

R8C5 - removing <8> from <2678> leaving <267>

R8C9 - removing <8> from <2358> leaving <235>

R5C6 is the only square in block 5 that can be <8>

Squares R5C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C5 - removing <2> from <258> leaving <58>

R3C5 - removing <2> from <257> leaving <57>

R8C5 - removing <2> from <267> leaving <67>

R9C5 - removing <2> from <268> leaving <68>

Intersection of block 2 with row 2. The value <2> only appears in one or more of squares R2C4, R2C5 and R2C6 of block 2. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain this value.

R2C1 - removing <2> from <125> leaving <15>

R2C3 - removing <2> from <1258> leaving <158>

R2C9 - removing <2> from <257> leaving <57>

Intersection of block 8 with row 8. The values <27> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain these values.

R8C1 - removing <2> from <2569> leaving <569>

R8C3 - removing <2> from <2569> leaving <569>

R8C7 - removing <2> from <2358> leaving <358>

R8C9 - removing <2> from <235> leaving <35>

Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 1 and 9 can be removed.

R5C9 - removing <2> from <2357> leaving <357>

Squares R2C9<57>, R5C9<357> and R8C9<35> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <357>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C9 - removing <5> from <258> leaving <28>

Squares R3C5 (XY), R1C5 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.

R1C9 - removing <8> from <28> leaving <2>

R1C1 can only be <5>

R9C9 can only be <8>

R9C5 can only be <6>

R1C5 can only be <8>

R2C1 can only be <1>

R2C4 can only be <2>

R2C3 can only be <8>

R3C3 can only be <2>

R2C6 can only be <7>

R8C4 can only be <8>

R2C9 can only be <5>

R8C6 can only be <2>

R3C5 can only be <5>

R8C9 can only be <3>

R3C7 can only be <8>

R7C3 can only be <5>

R3C8 can only be <7>

R6C7 can only be <2>

R5C8 can only be <6>

R5C1 can only be <9>

R6C8 can only be <8>

R6C2 can only be <7>

R6C5 can only be <1>

R4C8 can only be <5>

R7C8 can only be <2>

R8C7 can only be <5>

R5C9 can only be <7>

R9C1 can only be <2>

R8C5 can only be <7>

R4C2 can only be <2>

R5C7 can only be <3>

R5C3 can only be <1>

R8C1 can only be <6>

R5C5 can only be <2>

R6C3 can only be <6>

R5C2 can only be <5>

R8C3 can only be <9>

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