Jan 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <2>
R9C6 can only be <9>
R1C2 is the only square in row 1 that can be <4>
R2C5 is the only square in row 2 that can be <9>
R2C1 is the only square in column 1 that can be <7>
R3C2 is the only square in block 1 that can be <8>
Squares R7C3 and R7C8 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <59> from <259> leaving <2>
R7C4 - removing <5> from <2578> leaving <278>
R7C7 - removing <59> from <459> leaving <4>
R8C6 is the only square in row 8 that can be <4>
R8C4 is the only square in row 8 that can be <2>
R2C6 is the only square in row 2 that can be <2>
R2C4 is the only square in row 2 that can be <8>
R7C4 can only be <7>
R7C6 can only be <8>
R3C4 is the only square in block 2 that can be <5>
Squares R1C4 and R1C5 in row 1 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.
R1C8 - removing <16> from <1367> leaving <37>
Squares R2C3 and R3C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C3 - removing <6> from <1469> leaving <149>
R6C3 - removing <3> from <1345> leaving <145>
R8C3 - removing <36> from <3569> leaving <59>
Squares R7C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C3 - removing <9> from <149> leaving <14>
R6C3 - removing <5> from <145> leaving <14>
Squares R4C3 and R4C9 in row 4 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 row.
R4C7 - removing <1> from <1679> leaving <679>
R4C8 - removing <1> from <12679> leaving <2679>
Squares R7C3 and R8C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C2 - removing <5> from <356> leaving <36>
Squares R4C9<14>, R5C9<58>, R6C7<15> and R6C9<1458> in block 6 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C8 - removing <5> from <569> leaving <69>
R6C8 - removing <15> from <125> leaving <2>
R4C1 is the only square in row 4 that can be <2>
Intersection of column 8 with block 9. The value <5> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. 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 <5> from <159> leaving <19>
R8C9 - removing <5> from <135> leaving <13>
Squares R1C4, R1C5, R9C4 and R9C5 form a Type-1 Unique Rectangle on <16>.
R9C5 - removing <16> from <156> leaving <5>
R8C3 is the only square in row 8 that can be <5>
R7C3 can only be <9>
R7C8 can only be <5>
R8C7 is the only square in row 8 that can be <9>
Squares R1C6, R1C8, R3C6 and R3C8 form a Type-1 Unique Rectangle on <37>.
R3C8 - removing <37> from <1367> leaving <16>
Squares R4C3, R4C9, R6C3 and R6C9 form a Type-1 Unique Rectangle on <14>.
R6C9 - removing <14> from <1458> leaving <58>
R6C3 is the only square in row 6 that can be <4>
R4C3 can only be <1>
R4C9 can only be <4>
R6C7 is the only square in row 6 that can be <1>
R3C8 is the only square in row 3 that can be <1>
R9C8 can only be <3>
R9C2 can only be <6>
R1C8 can only be <7>
R8C9 can only be <1>
R1C6 can only be <3>
R3C7 can only be <6>
R3C3 can only be <3>
R2C7 can only be <5>
R4C7 can only be <7>
R8C5 can only be <6>
R9C4 can only be <1>
R4C2 can only be <9>
R8C1 can only be <3>
R1C4 can only be <6>
R1C5 can only be <1>
R3C6 can only be <7>
R2C9 can only be <3>
R2C3 can only be <6>
R4C8 can only be <6>
R5C2 can only be <5>
R5C8 can only be <9>
R5C9 can only be <8>
R6C2 can only be <3>
R5C1 can only be <6>
R6C9 can only be <5>
R6C1 can only be <8>
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