Feb 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C6 can only be <9>
R2C7 is the only square in row 2 that can be <7>
R3C3 is the only square in row 3 that can be <8>
R4C2 is the only square in row 4 that can be <9>
R6C5 is the only square in row 6 that can be <7>
R7C7 is the only square in row 7 that can be <8>
Squares R9C5 and R9C7 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <4> from <1249> leaving <129>
R9C3 - removing <3> from <239> leaving <29>
R9C9 - removing <3> from <139> leaving <19>
Squares R1C5 and R5C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C5 - removing <6> from <346> leaving <34>
Intersection of row 7 with block 7. The value <4> 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.
R8C2 - removing <4> from <456> leaving <56>
Intersection of block 2 with row 2. The value <1> only appears in one or more of squares R2C4, R2C5 and R2C6 of block 2. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain this value.
R2C2 - removing <1> from <1256> leaving <256>
R2C8 - removing <1> from <12569> leaving <2569>
Intersection of block 6 with column 8. The value <3> only appears in one or more of squares R4C8, R5C8 and R6C8 of block 6. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R3C8 - removing <3> from <1236> leaving <126>
R7C8 - removing <3> from <1356> leaving <156>
R8C8 - removing <3> from <3569> leaving <569>
Squares R2C2<256>, R6C2<25> and R8C2<56> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <256>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C2 - removing <26> from <1246> leaving <14>
R7C2 - removing <56> from <1456> leaving <14>
Intersection of row 3 with block 3. The values <36> 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 these values.
R1C7 - removing <6> from <56> leaving <5>
R1C9 - removing <6> from <1569> leaving <159>
R2C8 - removing <6> from <2569> leaving <259>
Squares R1C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <1> from <136> leaving <36>
R7C9 - removing <1> from <1356> leaving <356>
Squares R3C7 and R3C9 in row 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 row.
R3C8 - removing <6> from <126> leaving <12>
Squares R5C1<25>, R5C5<26> and R5C9<56> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <256>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <25> from <1258> leaving <18>
R5C6 - removing <6> from <168> leaving <18>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C1 - removing <1> from <124> leaving <24>
R7C1 - removing <1> from <145> leaving <45>
Squares R3C1<24>, R5C1<25> and R7C1<45> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <245>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C1 - removing <2> from <129> leaving <19>
R9C1 - removing <2> from <129> leaving <19>
R9C3 is the only square in row 9 that can be <2>
R1C5 is the only square in row 1 that can be <2>
R5C5 can only be <6>
R2C4 can only be <1>
R2C6 can only be <6>
R5C4 can only be <8>
R4C6 can only be <4>
R4C5 can only be <3>
R8C6 can only be <8>
R5C6 can only be <1>
R8C4 can only be <3>
R5C9 can only be <5>
R5C1 can only be <2>
R6C8 can only be <3>
R4C8 can only be <6>
R4C4 can only be <5>
R9C5 can only be <4>
R9C7 can only be <3>
R3C7 can only be <6>
R7C9 can only be <6>
R3C9 can only be <3>
R8C7 can only be <4>
R6C4 can only be <2>
R3C1 can only be <4>
R6C2 can only be <5>
R2C2 can only be <2>
R8C2 can only be <6>
R2C8 can only be <9>
R2C3 can only be <5>
R8C8 can only be <5>
R1C9 can only be <1>
R3C2 can only be <1>
R7C1 can only be <5>
R3C8 can only be <2>
R7C2 can only be <4>
R1C1 can only be <9>
R7C3 can only be <3>
R7C8 can only be <1>
R8C3 can only be <9>
R9C9 can only be <9>
R1C3 can only be <6>
R9C1 can only be <1>
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