Jan 07 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 is the only square in row 2 that can be <8>
R3C8 is the only square in row 3 that can be <7>
R7C5 is the only square in row 7 that can be <8>
R3C6 is the only square in column 6 that can be <1>
R3C2 can only be <3>
R1C2 is the only square in row 1 that can be <1>
R2C9 is the only square in column 9 that can be <4>
Squares R7C8 and R9C8 in column 8 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.
R1C8 - removing <5> from <356> leaving <36>
R5C8 - removing <5> from <356> leaving <36>
Squares R3C4 and R3C5 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C5 - removing <5> from <3569> leaving <369>
R2C4 - removing <5> from <2356> leaving <236>
R2C5 - removing <5> from <3569> leaving <369>
R2C6 - removing <5> from <2359> leaving <239>
Squares R7C8 and R9C8 in block 9 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 block.
R8C9 - removing <2> from <1269> leaving <169>
R9C9 - removing <25> from <259> leaving <9>
R9C2 can only be <2>
R9C8 can only be <5>
R7C8 can only be <2>
Squares R3C4 and R7C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C4 - removing <5> from <356> leaving <36>
R8C4 - removing <4> from <234> leaving <23>
Squares R5C4 and R5C8 in row 5 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 row.
R5C1 - removing <3> from <34579> leaving <4579>
R5C6 - removing <3> from <35> leaving <5>
R5C9 - removing <6> from <567> leaving <57>
R5C9 can only be <7>
R7C6 can only be <9>
R7C2 can only be <4>
R7C4 can only be <5>
R5C2 can only be <9>
R3C4 can only be <4>
R3C5 can only be <5>
R5C1 can only be <4>
R8C5 is the only square in row 8 that can be <4>
R9C5 is the only square in column 5 that can be <7>
R9C1 can only be <3>
Squares R8C4, R8C6, R2C4 and R2C6 form a Type-1 Unique Rectangle on <23>.
R2C4 - removing <23> from <236> leaving <6>
R5C4 can only be <3>
R5C8 can only be <6>
R8C4 can only be <2>
R4C5 can only be <1>
R1C8 can only be <3>
R8C6 can only be <3>
R2C6 can only be <2>
R1C5 can only be <9>
R2C7 can only be <5>
R2C3 can only be <9>
R1C9 can only be <6>
R4C7 can only be <3>
R6C5 can only be <6>
R6C7 can only be <1>
R8C7 can only be <6>
R8C9 can only be <1>
R1C1 can only be <5>
R2C5 can only be <3>
R8C3 can only be <7>
R8C1 can only be <9>
R4C3 can only be <5>
R6C1 can only be <2>
R4C9 can only be <2>
R6C3 can only be <3>
R4C1 can only be <7>
R6C9 can only be <5>
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