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Mar 19 - Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R1C7 can only be <5>

R6C5 is the only square in row 6 that can be <5>

R6C2 is the only square in row 6 that can be <9>

R2C3 is the only square in row 2 that can be <9>

R1C9 is the only square in row 1 that can be <9>

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

R5C4 is the only square in row 5 that can be <9>

R8C8 is the only square in row 8 that can be <5>

Intersection of row 7 with block 9. The value <3> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.

R8C7 - removing <3> from <1346> leaving <146>

R9C7 - removing <3> from <1346> leaving <146>

R9C9 - removing <3> from <136> leaving <16>

R2C7 is the only square in column 7 that can be <3>

R3C9 can only be <2>

R3C8 can only be <8>

R2C8 can only be <6>

R3C5 is the only square in row 3 that can be <3>

R1C6 is the only square in block 2 that can be <4>

Squares R3C1 and R3C2 in block 1 form a simple naked 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.

R2C2 - removing <1> from <1278> leaving <278>

Intersection of row 1 with block 1. The value <2> 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.

R2C2 - removing <2> from <278> leaving <78>

Intersection of row 8 with block 7. The value <7> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.

R7C1 - removing <7> from <167> leaving <16>

R7C2 - removing <7> from <167> leaving <16>

Squares R7C1 and R7C2 in row 7 form a simple naked 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 row.

R7C9 - removing <16> from <1367> leaving <37>

Squares R7C1 and R7C2 in block 7 form a simple naked 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.

R8C2 - removing <16> from <12467> leaving <247>

R8C3 - removing <1> from <1237> leaving <237>

R9C1 - removing <16> from <1246> leaving <24>

R9C3 - removing <1> from <123> leaving <23>

R5C3 is the only square in column 3 that can be <1>

R5C6 can only be <8>

R5C5 can only be <4>

R5C7 can only be <6>

R4C5 can only be <1>

R4C9 can only be <3>

R8C5 can only be <2>

R4C8 can only be <4>

R7C9 can only be <7>

R7C8 can only be <3>

R6C9 can only be <1>

R2C5 can only be <8>

R2C2 can only be <7>

R1C4 can only be <7>

R9C9 can only be <6>

R9C6 can only be <1>

R1C3 can only be <2>

R2C4 can only be <1>

R5C2 can only be <2>

R8C2 can only be <4>

R2C6 can only be <2>

R8C4 can only be <3>

R5C8 can only be <7>

R6C1 can only be <7>

R6C8 can only be <2>

R8C7 can only be <1>

R3C2 can only be <1>

R9C1 can only be <2>

R8C3 can only be <7>

R9C4 can only be <8>

R8C6 can only be <6>

R9C7 can only be <4>

R9C3 can only be <3>

R1C1 can only be <8>

R4C1 can only be <6>

R3C1 can only be <4>

R7C2 can only be <6>

R4C2 can only be <8>

R7C1 can only be <1>

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