Sudoku Puzzle © Kevin Stone

R1C7 is the only square in row 1 that can be <6>

R4C3 is the only square in row 4 that can be <8>

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

R6C4 is the only square in row 6 that can be <1>

R7C5 is the only square in column 5 that can be <4>

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

R7C9 is the only square in column 9 that can be <9>

Intersection of column 1 with block 1. The value <4> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.

R2C2 - removing <4> from <145> leaving <15>

R3C3 - removing <4> from <12457> leaving <1257>

Squares R1C8<57>, R2C9<457> and R3C9<457> in block 3 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <457>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R2C8 - removing <57> from <1578> leaving <18>

R3C7 - removing <57> from <1578> leaving <18>

Intersection of column 7 with block 6. The values <79> 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 these values.

R5C8 - removing <7> from <257> leaving <25>

Squares R3C3 and R3C7 in row 3 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 7 can be removed.

R9C3 - removing <1> from <145> leaving <45>

R9C7 - removing <1> from <158> leaving <58>

Squares R5C3<459>, R6C3<59> and R9C3<45> in column 3 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <459>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C3 - removing <59> from <579> leaving <7>

R3C3 - removing <5> from <1257> leaving <127>

R7C3 - removing <5> from <125> leaving <12>

R1C8 can only be <5>

R1C2 can only be <9>

R5C8 can only be <2>

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

R7C3 can only be <1>

R3C3 can only be <2>

R3C7 is the only square in row 3 that can be <1>

R2C8 can only be <8>

R8C8 can only be <7>

R9C8 can only be <1>

R8C9 can only be <5>

R8C2 can only be <8>

R9C7 can only be <8>

R7C7 can only be <2>

R8C5 can only be <6>

R7C4 can only be <5>

R7C1 can only be <6>

R7C6 can only be <8>

R4C4 can only be <7>

R3C6 can only be <5>

R3C1 can only be <4>

R2C5 can only be <7>

R4C7 can only be <5>

R3C4 can only be <6>

R5C5 can only be <5>

R6C7 can only be <9>

R5C2 can only be <4>

R6C3 can only be <5>

R5C7 can only be <7>

R2C9 can only be <4>

R3C5 can only be <8>

R2C1 can only be <5>

R3C9 can only be <7>

R5C3 can only be <9>

R9C2 can only be <5>

R9C3 can only be <4>

R2C2 can only be <1>