Dec 02 - Very Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R1C2 can only be <5>

R8C7 can only be <9>

R7C6 is the only square in row 7 that can be <1>

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

Squares R2C3 and R4C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R6C3 - removing <49> from <1479> leaving <17>

Intersection of row 1 with block 2. The value <6> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.

R2C4 - removing <6> from <245679> leaving <24579>

R2C5 - removing <6> from <45678> leaving <4578>

R2C6 - removing <6> from <245689> leaving <24589>

Intersection of block 1 with row 2. The value <4> only appears in one or more of squares R2C1, R2C2 and R2C3 of block 1. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain this value.

R2C4 - removing <4> from <24579> leaving <2579>

R2C5 - removing <4> from <4578> leaving <578>

R2C6 - removing <4> from <24589> leaving <2589>

R2C7 - removing <4> from <246> leaving <26>

Intersection of column 7 with block 6. The value <4> 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 this value.

R4C8 - removing <4> from <2489> leaving <289>

R5C8 - removing <4> from <1479> leaving <179>

R6C8 - removing <4> from <12479> leaving <1279>

Intersection of block 5 with row 5. The value <9> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.

R5C2 - removing <9> from <3679> leaving <367>

R5C8 - removing <9> from <179> leaving <17>

Intersection of block 5 with column 5. The value <5> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.

R2C5 - removing <5> from <578> leaving <78>

R8C5 - removing <5> from <578> leaving <78>

Squares R2C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R9C5 - removing <78> from <4678> leaving <46>

Squares R2C1 and R8C1 in column 1 and R2C5 and R8C5 in column 5 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 2 and 8 can be removed.

R2C6 - removing <8> from <2589> leaving <259>

R8C6 - removing <8> from <258> leaving <25>

R8C9 - removing <8> from <578> leaving <57>

R4C9 is the only square in column 9 that can be <8>

R5C9 is the only square in column 9 that can be <3>

Squares R6C3 and R8C3 in column 3 and R6C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 6 and 8 can be removed.

R6C2 - removing <7> from <2679> leaving <269>

R8C4 - removing <7> from <2357> leaving <235>

R8C5 - removing <7> from <78> leaving <8>

R6C8 - removing <7> from <1279> leaving <129>

R2C5 can only be <7>

R2C1 is the only square in row 2 that can be <8>

R3C2 can only be <9>

R2C3 can only be <4>

R4C3 can only be <9>

R4C8 can only be <2>

R1C8 can only be <4>

R3C8 can only be <5>

R3C4 can only be <4>

R2C9 can only be <6>

R2C7 can only be <2>

R6C9 can only be <7>

R3C6 can only be <8>

R6C3 can only be <1>

R8C9 can only be <5>

R5C8 can only be <1>

R8C6 can only be <2>

R5C1 can only be <4>

R6C8 can only be <9>

R8C3 can only be <7>

R7C2 can only be <8>

R8C4 can only be <3>

R1C6 can only be <6>

R1C4 can only be <2>

R9C6 can only be <4>

R5C6 can only be <9>

R6C1 can only be <5>

R5C4 can only be <6>

R2C6 can only be <5>

R4C1 can only be <3>

R7C8 can only be <7>

R9C2 can only be <3>

R7C4 can only be <5>

R9C8 can only be <8>

R8C1 can only be <1>

R4C2 can only be <6>

R9C5 can only be <6>

R2C4 can only be <9>

R4C7 can only be <4>

R5C2 can only be <7>

R6C2 can only be <2>

R4C5 can only be <5>

R6C7 can only be <6>

R9C4 can only be <7>

R6C5 can only be <4>

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