Copyright © Kevin Stone

R2C2 is the only square in row 2 that can be <8>

R1C5 is the only square in row 1 that can be <8>

R2C8 is the only square in row 2 that can be <9>

R3C6 is the only square in row 3 that can be <2>

R4C2 is the only square in row 4 that can be <2>

R5C9 is the only square in row 5 that can be <2>

R5C5 is the only square in row 5 that can be <9>

R7C4 is the only square in row 7 that can be <9>

R8C1 is the only square in row 8 that can be <2>

R9C9 is the only square in row 9 that can be <3>

R5C1 is the only square in column 1 that can be <3>

R1C2 is the only square in column 2 that can be <4>

Intersection of column 9 with block 3. The value <5> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.

R1C8 - removing <5> from <156> leaving <16>

R3C7 - removing <5> from <1456> leaving <146>

Squares R3C5 and R7C5 in column 5 and R3C7 and R7C7 in column 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 3 and 7 can be removed.

R3C4 - removing <4> from <1456> leaving <156>

R7C6 - removing <4> from <46> leaving <6>

R3C3 is the only square in column 3 that can be <6>

R3C4 is the only square in row 3 that can be <5>

R9C1 is the only square in column 1 that can be <6>

R2C4 is the only square in column 4 that can be <6>

R6C7 is the only square in column 7 that can be <6>

R4C7 is the only square in column 7 that can be <3>

Intersection of column 3 with block 4. The values <18> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.

R6C2 - removing <1> from <157> leaving <57>

Squares R5C3 and R5C7 in row 5 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.

R4C3 - removing <5> from <158> leaving <18>

R6C3 - removing <5> from <1578> leaving <178>

Squares R7C7 (XY), R7C5 (XZ) and R9C8 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.

R9C5 - removing <7> from <17> leaving <1>

R3C5 can only be <4>

R3C7 can only be <1>

R7C5 can only be <7>

R2C6 can only be <1>

R5C7 can only be <5>

R1C8 can only be <6>

R5C3 can only be <1>

R7C7 can only be <4>

R7C3 can only be <5>

R8C9 can only be <6>

R8C8 can only be <7>

R1C9 can only be <5>

R1C1 can only be <1>

R2C9 can only be <4>

R2C1 can only be <5>

R4C3 can only be <8>

R9C2 can only be <7>

R8C2 can only be <1>

R9C8 can only be <5>

R6C2 can only be <5>

R4C8 can only be <1>

R6C3 can only be <7>

R4C4 can only be <4>

R6C8 can only be <8>

R6C6 can only be <3>

R6C4 can only be <1>

R8C6 can only be <4>

R8C4 can only be <3>

R4C6 can only be <5>