Copyright © Kevin Stone

R1C9 is the only square in row 1 that can be <7>

R2C4 is the only square in row 2 that can be <6>

R7C5 is the only square in row 7 that can be <9>

R7C9 is the only square in row 7 that can be <5>

R7C3 is the only square in row 7 that can be <7>

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

R9C4 is the only square in row 9 that can be <7>

R1C4 is the only square in column 4 that can be <8>

R3C3 is the only square in column 3 that can be <8>

R4C4 is the only square in column 4 that can be <5>

R5C7 is the only square in column 7 that can be <9>

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

Squares R5C1 and R5C3 in block 4 form a simple locked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R4C1 - removing <1> from <1389> leaving <389>

R4C2 - removing <1> from <137> leaving <37>

R6C1 - removing <1> from <1389> leaving <389>

R6C2 - removing <1> from <137> leaving <37>

Squares R4C2 and R6C2 in column 2 form a simple locked 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 column.

R2C2 - removing <3> from <123> leaving <12>

R8C2 - removing <3> from <123> leaving <12>

Squares R4C2 and R6C2 in block 4 form a simple locked 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.

R4C1 - removing <3> from <389> leaving <89>

R6C1 - removing <3> from <389> leaving <89>

Intersection of row 8 with block 8. The value <4> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.

R9C6 - removing <4> from <1345> leaving <135>

Squares R3C1 and R3C7 in row 3 and R9C1 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 1 and 7 can be removed.

R1C1 - removing <2> from <1234> leaving <134>

R1C7 - removing <2> from <1234> leaving <134>

R1C6 is the only square in row 1 that can be <2>

R1C5 is the only square in row 1 that can be <5>

R9C6 is the only square in row 9 that can be <5>

Squares R2C6 and R2C8 in row 2 and R8C6 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 6 and 8 can be removed.

R4C8 - removing <3> from <137> leaving <17>

R6C8 - removing <3> from <137> leaving <17>

Squares R4C8 and R6C8 in column 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R2C8 - removing <1> from <123> leaving <23>

R8C8 - removing <1> from <123> leaving <23>

Squares R4C8 and R6C8 in block 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R4C9 - removing <1> from <138> leaving <38>

R6C9 - removing <1> from <138> leaving <38>

Squares R4C9 and R6C9 in column 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R3C9 - removing <3> from <134> leaving <14>

R9C9 - removing <3> from <134> leaving <14>

Squares R3C5 and R9C5 in column 5 and R3C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 3 and 9 can be removed.

R3C1 - removing <1> from <1234> leaving <234>

R9C1 - removing <1> from <1236> leaving <236>

R9C3 - removing <1> from <136> leaving <36>

R3C7 - removing <1> from <1234> leaving <234>

R9C7 - removing <1> from <1234> leaving <234>

Squares R6C4, R8C4, R6C6 and R8C6 form a Type-4 Unique Rectangle on <14>.

R6C6 - removing <1> from <149> leaving <49>

R8C6 - removing <1> from <134> leaving <34>

Squares R2C2 (XY), R1C3 (XZ) and R2C8 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.

R1C7 - removing <3> from <134> leaving <14>

Squares R1C7 and R3C9 in block 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R3C7 - removing <4> from <234> leaving <23>

Intersection of row 1 with block 1. The value <3> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.

R3C1 - removing <3> from <234> leaving <24>

Squares R7C1 (XY), R5C1 (XZ) and R9C3 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.

R9C1 - removing <6> from <236> leaving <23>

R5C3 - removing <6> from <16> leaving <1>

R5C1 can only be <6>

R1C3 can only be <3>

R9C3 can only be <6>

Squares R8C2 (XY), R7C1 (XZ) and R8C8 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.

R7C7 - removing <3> from <13> leaving <1>

R7C1 can only be <3>

R1C7 can only be <4>

R9C9 can only be <4>

R3C9 can only be <1>

R1C1 can only be <1>

R3C5 can only be <3>

R9C1 can only be <2>

R9C7 can only be <3>

R3C1 can only be <4>

R8C2 can only be <1>

R9C5 can only be <1>

R3C7 can only be <2>

R8C8 can only be <2>

R2C2 can only be <2>

R2C8 can only be <3>

R2C6 can only be <1>

R8C4 can only be <4>

R8C6 can only be <3>

R6C4 can only be <1>

R4C6 can only be <9>

R4C1 can only be <8>

R6C6 can only be <4>

R6C8 can only be <7>

R6C2 can only be <3>

R4C8 can only be <1>

R4C9 can only be <3>

R6C1 can only be <9>

R4C2 can only be <7>

R6C9 can only be <8>