Aug 06 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 is the only square in row 2 that can be <6>
R3C3 is the only square in row 3 that can be <1>
R5C7 is the only square in row 5 that can be <6>
R4C6 is the only square in row 4 that can be <6>
R4C1 is the only square in row 4 that can be <4>
R6C6 is the only square in row 6 that can be <4>
R2C5 is the only square in row 2 that can be <4>
R7C9 is the only square in row 7 that can be <6>
R7C7 is the only square in row 7 that can be <8>
R3C9 is the only square in row 3 that can be <8>
R9C4 is the only square in row 9 that can be <3>
R9C3 is the only square in row 9 that can be <4>
R9C6 is the only square in row 9 that can be <8>
R9C9 is the only square in column 9 that can be <2>
Intersection of column 7 with block 3. The value <5> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <5> from <579> leaving <79>
Squares R2C4<259>, R4C4<25> and R6C4<59> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <259>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C4 - removing <259> from <12579> leaving <17>
R8C4 - removing <25> from <1257> leaving <17>
Squares R3C5 and R3C7 in row 3, R7C1 and R7C5 in row 7 and R9C1 and R9C7 in row 9 form a Swordfish pattern on possibility <7>. All other instances of this possibility in columns 1, 5 and 7 can be removed.
R1C7 - removing <7> from <579> leaving <59>
R6C1 - removing <7> from <357> leaving <35>
R8C5 - removing <7> from <257> leaving <25>
Intersection of column 1 with block 7. The value <7> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C2 - removing <7> from <2579> leaving <259>
Squares R5C2<25>, R5C3<235> and R6C1<35> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <235>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <25> from <2578> leaving <78>
R6C2 - removing <5> from <578> leaving <78>
R4C4 is the only square in row 4 that can be <2>
R4C9 is the only square in row 4 that can be <5>
Intersection of column 5 with block 8. The value <2> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C6 - removing <2> from <125> leaving <15>
Squares R4C2, R4C8, R6C2 and R6C8 form a Type-1 Unique Rectangle on <78>.
R6C8 - removing <78> from <3789> leaving <39>
R6C2 is the only square in row 6 that can be <8>
R4C2 can only be <7>
R4C8 can only be <8>
R6C9 is the only square in row 6 that can be <7>
R1C9 can only be <9>
R1C7 can only be <5>
R3C7 can only be <7>
R9C7 can only be <9>
R9C1 can only be <7>
R8C8 can only be <7>
R8C4 can only be <1>
R8C6 can only be <5>
R1C4 can only be <7>
R8C5 can only be <2>
R2C6 can only be <2>
R1C6 can only be <1>
R8C2 can only be <9>
R7C5 can only be <7>
R2C2 can only be <5>
R2C4 can only be <9>
R5C2 can only be <2>
R3C1 can only be <9>
R6C4 can only be <5>
R3C5 can only be <5>
R5C5 can only be <9>
R5C8 can only be <3>
R5C3 can only be <5>
R6C8 can only be <9>
R6C1 can only be <3>
R7C3 can only be <2>
R1C1 can only be <2>
R7C1 can only be <5>
R1C3 can only be <3>
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