Dec 03 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 is the only square in row 4 that can be <3>
R2C2 is the only square in row 2 that can be <3>
R6C5 is the only square in row 6 that can be <5>
R8C7 is the only square in row 8 that can be <3>
Intersection of row 1 with block 2. The value <5> 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.
R3C4 - removing <5> from <1256> leaving <126>
R3C6 - removing <5> from <1357> leaving <137>
Intersection of row 2 with block 3. The value <6> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C7 - removing <6> from <12568> leaving <1258>
R3C8 - removing <6> from <1678> leaving <178>
Intersection of row 8 with block 7. The values <28> 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 these values.
R7C2 - removing <8> from <189> leaving <19>
R7C3 - removing <8> from <14589> leaving <1459>
R9C2 - removing <2> from <129> leaving <19>
Squares R7C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <1> from <1278> leaving <278>
R3C2 - removing <1> from <1278> leaving <278>
Squares R7C2 and R9C2 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <19> from <1459> leaving <45>
Intersection of row 8 with block 9. The value <6> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <6> from <1569> leaving <159>
R7C8 - removing <6> from <1469> leaving <149>
Intersection of row 9 with block 8. The values <25> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C4 - removing <5> from <568> leaving <68>
R7C6 - removing <5> from <345> leaving <34>
Intersection of column 2 with block 1. The value <7> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C3 - removing <7> from <1257> leaving <125>
R3C3 - removing <7> from <12578> leaving <1258>
Intersection of row 2 with block 3. The values <67> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C8 - removing <7> from <178> leaving <18>
R3C8 - removing <7> from <178> leaving <18>
R2C8 is the only square in column 8 that can be <7>
R8C8 is the only square in column 8 that can be <6>
Squares R1C8 and R3C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C8 - removing <1> from <149> leaving <49>
R9C8 - removing <1> from <149> leaving <49>
R9C2 is the only square in row 9 that can be <1>
R7C2 can only be <9>
R7C8 can only be <4>
R7C3 can only be <5>
R7C6 can only be <3>
R9C8 can only be <9>
R8C9 can only be <5>
R7C7 can only be <1>
R4C7 can only be <8>
R6C7 can only be <9>
R5C7 can only be <6>
R2C9 is the only square in row 2 that can be <6>
R3C5 is the only square in row 3 that can be <3>
R3C7 is the only square in row 3 that can be <5>
R2C7 can only be <2>
R2C3 can only be <1>
R2C1 can only be <5>
R4C3 can only be <7>
R4C5 can only be <4>
R6C3 can only be <8>
R4C9 can only be <1>
R9C5 can only be <2>
R6C9 can only be <7>
R6C1 can only be <1>
R3C3 can only be <2>
R5C9 can only be <4>
R9C4 can only be <5>
R1C5 can only be <7>
R5C5 can only be <8>
R3C6 can only be <1>
R5C3 can only be <9>
R8C3 can only be <4>
R1C2 can only be <8>
R3C4 can only be <6>
R3C8 can only be <8>
R1C6 can only be <5>
R5C6 can only be <7>
R3C2 can only be <7>
R1C8 can only be <1>
R5C4 can only be <1>
R7C5 can only be <6>
R5C1 can only be <2>
R7C4 can only be <8>
R9C6 can only be <4>
R1C4 can only be <2>
R8C2 can only be <2>
R8C1 can only be <8>
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