May 24 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 is the only square in row 3 that can be <1>
R3C6 is the only square in row 3 that can be <2>
R5C9 is the only square in row 5 that can be <3>
R1C7 is the only square in row 1 that can be <3>
R6C6 is the only square in row 6 that can be <6>
R8C3 is the only square in row 8 that can be <3>
R4C4 is the only square in column 4 that can be <9>
R4C6 is the only square in row 4 that can be <3>
R7C6 can only be <5>
R7C4 can only be <3>
Squares R5C5 and R5C8 in row 5 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 row.
R5C1 - removing <5> from <569> leaving <69>
R5C2 - removing <5> from <569> leaving <69>
Squares R4C3 and R6C3 in column 3 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.
R1C3 - removing <5> from <459> leaving <49>
R2C3 - removing <5> from <457> leaving <47>
R9C3 - removing <25> from <2579> leaving <79>
Intersection of column 7 with block 9. The value <9> 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 this value.
R9C9 - removing <9> from <569> leaving <56>
Intersection of column 8 with block 9. The values <27> 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 these values.
R8C7 - removing <2> from <259> leaving <59>
R9C7 - removing <2> from <2569> leaving <569>
Squares R8C7<59>, R9C7<569> and R9C9<56> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <569>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <6> from <46> leaving <4>
R8C8 - removing <5> from <257> leaving <27>
Squares R8C5 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <7> from <579> leaving <59>
Intersection of row 7 with block 7. The value <6> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <6> from <2569> leaving <259>
Squares R3C4 and R5C8 form a remote naked pair. <45> can be removed from any square that is common to their groups.
R3C8 - removing <45> from <458> leaving <8>
R2C2 is the only square in row 2 that can be <8>
R2C3 is the only square in row 2 that can be <7>
R9C3 can only be <9>
R1C3 can only be <4>
R8C2 can only be <5>
R8C7 can only be <9>
R3C2 can only be <9>
R9C1 can only be <2>
R9C5 can only be <7>
R7C1 can only be <6>
R8C5 can only be <2>
R3C9 can only be <5>
R5C2 can only be <6>
R1C1 can only be <5>
R3C4 can only be <4>
R9C9 can only be <6>
R2C8 can only be <4>
R5C1 can only be <9>
R7C2 can only be <7>
R7C8 can only be <2>
R8C8 can only be <7>
R9C7 can only be <5>
R1C9 can only be <9>
R1C5 can only be <6>
R2C5 can only be <5>
R2C7 can only be <6>
R5C8 can only be <5>
R6C4 can only be <5>
R5C5 can only be <4>
R4C7 can only be <2>
R6C3 can only be <2>
R4C3 can only be <5>
R6C7 can only be <4>
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