Jan 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 is the only square in row 4 that can be <1>
R4C4 is the only square in row 4 that can be <3>
R4C6 is the only square in row 4 that can be <4>
R5C2 is the only square in row 5 that can be <3>
R2C2 can only be <9>
R9C9 is the only square in row 9 that can be <3>
R1C3 is the only square in row 1 that can be <3>
R2C8 is the only square in row 2 that can be <3>
R2C7 is the only square in row 2 that can be <5>
R3C8 is the only square in column 8 that can be <8>
R7C8 is the only square in column 8 that can be <1>
Squares R5C6 and R5C8 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <5> from <258> leaving <28>
Squares R4C1 and R6C1 in column 1 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.
R3C1 - removing <2> from <1246> leaving <146>
R7C1 - removing <25> from <256> leaving <6>
R9C1 - removing <25> from <2458> leaving <48>
Squares R5C4 and R5C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C4 - removing <2> from <259> leaving <59>
R6C5 - removing <2> from <269> leaving <69>
Intersection of row 3 with block 3. The value <9> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <9> from <679> leaving <67>
R1C9 - removing <9> from <179> leaving <17>
Intersection of column 7 with block 9. The values <24> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R7C9 - removing <2> from <2579> leaving <579>
Intersection of block 8 with row 9. The value <5> only appears in one or more of squares R9C4, R9C5 and R9C6 of block 8. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C3 - removing <5> from <2589> leaving <289>
Squares R4C1, R4C9, R6C1 and R6C9 form a Type-1 Unique Rectangle on <25>.
R6C9 - removing <25> from <257> leaving <7>
R1C9 can only be <1>
R5C8 can only be <5>
R1C1 can only be <8>
R3C9 can only be <9>
R3C7 can only be <6>
R7C9 can only be <5>
R5C6 can only be <7>
R8C8 can only be <7>
R4C9 can only be <2>
R1C4 can only be <9>
R9C1 can only be <4>
R2C3 can only be <6>
R1C6 can only be <6>
R6C4 can only be <5>
R1C7 can only be <7>
R2C5 can only be <8>
R3C3 can only be <2>
R5C5 can only be <2>
R3C2 can only be <4>
R7C3 can only be <9>
R4C1 can only be <5>
R5C4 can only be <8>
R8C5 can only be <9>
R6C1 can only be <2>
R6C6 can only be <9>
R9C4 can only be <2>
R6C5 can only be <6>
R9C6 can only be <5>
R7C7 can only be <2>
R8C3 can only be <5>
R9C3 can only be <8>
R7C2 can only be <7>
R8C7 can only be <4>
R8C2 can only be <2>
R9C7 can only be <9>
R3C1 can only be <1>
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