Jun 04 - Very Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R3C4 can only be <6>

R5C5 can only be <1>

R5C7 can only be <3>

R7C5 can only be <8>

R4C4 can only be <4>

R4C6 can only be <9>

R5C3 can only be <6>

R3C5 can only be <9>

R3C6 can only be <8>

R6C4 can only be <7>

R4C8 can only be <8>

R6C6 can only be <6>

R4C7 can only be <2>

R4C2 can only be <3>

R4C3 can only be <1>

R7C1 is the only square in row 7 that can be <6>

R1C2 is the only square in row 1 that can be <6>

R9C8 is the only square in row 9 that can be <6>

R8C4 is the only square in column 4 that can be <2>

R7C6 is the only square in column 6 that can be <5>

Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R2C1 - removing <3> from <345> leaving <45>

R2C8 - removing <1> from <147> leaving <47>

Squares R8C1 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R8C8 - removing <1> from <179> leaving <79>

R8C9 - removing <3> from <389> leaving <89>

R1C8 is the only square in column 8 that can be <1>

Squares R2C8 and R3C7 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R2C9 - removing <4> from <458> leaving <58>

R3C9 - removing <4> from <245> leaving <25>

R7C9 is the only square in column 9 that can be <4>

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

Squares R2C2 and R2C9 in row 2 and R8C2 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 9 can be removed.

R1C9 - removing <8> from <289> leaving <29>

R9C2 - removing <8> from <258> leaving <25>

Squares R6C2 and R9C2 in column 2 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.

R2C2 - removing <5> from <578> leaving <78>

Squares R6C2, R6C3, R9C2 and R9C3 form a Type-1 Unique Rectangle on <25>.

R9C3 - removing <25> from <258> leaving <8>

R9C7 can only be <1>

R8C2 can only be <7>

R7C7 can only be <7>

R7C3 can only be <3>

R3C7 can only be <4>

R8C8 can only be <9>

R2C2 can only be <8>

R8C9 can only be <8>

R6C8 can only be <4>

R2C9 can only be <5>

R2C1 can only be <4>

R3C9 can only be <2>

R6C7 can only be <9>

R2C8 can only be <7>

R3C1 can only be <5>

R1C9 can only be <9>

R1C7 can only be <8>

R7C4 can only be <1>

R1C3 can only be <2>

R8C1 can only be <1>

R2C4 can only be <3>

R8C6 can only be <3>

R2C6 can only be <1>

R1C1 can only be <3>

R6C3 can only be <5>

R3C3 can only be <7>

R9C1 can only be <2>

R6C2 can only be <2>

R9C2 can only be <5>

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