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Daily Sudoku Answer 



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The full reasoning can be found below the Sudoku.

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Apr 04 - Super Hard
Puzzle Copyright © Kevin Stone

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Reasoning 



R5C1 can only be <9>

R5C2 can only be <4>

R5C5 can only be <8>

R5C9 can only be <2>

R5C8 can only be <5>

R2C3 is the only square in row 2 that can be <3>

R4C6 is the only square in row 4 that can be <2>

R8C8 is the only square in row 8 that can be <8>

R1C9 is the only square in row 1 that can be <8>

R9C5 is the only square in row 9 that can be <1>

R9C8 is the only square in row 9 that can be <3>

R7C5 is the only square in row 7 that can be <3>

R9C2 is the only square in row 9 that can be <8>

R9C3 is the only square in column 3 that can be <4>

R7C9 is the only square in column 9 that can be <6>

R7C7 is the only square in row 7 that can be <4>

R6C8 is the only square in block 6 that can be <1>

R7C8 is the only square in block 9 that can be <7>

Squares R8C7 and R9C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C7 - removing <29> from <1259> leaving <15>

R2C7 - removing <9> from <159> leaving <15>

Squares R4C9 and R6C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R2C9 - removing <9> from <479> leaving <47>

R3C9 - removing <9> from <479> leaving <47>

Intersection of row 3 with block 1. The value <1> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.

R1C2 - removing <1> from <12679> leaving <2679>

R2C2 - removing <1> from <179> leaving <79>

Intersection of row 7 with block 7. The value <2> 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.

R8C1 - removing <2> from <2567> leaving <567>

R9C1 - removing <2> from <26> leaving <6>

Intersection of column 5 with block 2. The value <5> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.

R1C6 - removing <5> from <1569> leaving <169>

R2C6 - removing <5> from <159> leaving <19>

R2C7 is the only square in row 2 that can be <5>

R1C7 can only be <1>

R2C6 is the only square in row 2 that can be <1>

Squares R1C3<579>, R2C2<79> and R3C3<579> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <579>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R1C2 - removing <79> from <2679> leaving <26>

R3C1 - removing <57> from <1257> leaving <12>

R3C2 - removing <79> from <12679> leaving <126>

Intersection of column 1 with block 7. The value <5> 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.

R8C3 - removing <5> from <579> leaving <79>

Squares R1C2<26>, R1C6<69> and R1C8<29> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <269>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R1C3 - removing <9> from <579> leaving <57>

R1C5 - removing <69> from <5679> leaving <57>

Squares R1C3, R1C5, R3C3 and R3C5 form a Type-3 Unique Rectangle on <57>. Upon close inspection, it is clear that:

(R3C3 or R3C5)<69>, R3C8<29>, R3C2<126> and R3C1<12> form a naked quad on <1269> in row 3. No other squares in the row can contain these possibilities

R3C4 - removing <69> from <4679> leaving <47>

Squares R3C4 and R3C9 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R3C3 - removing <7> from <579> leaving <59>

R3C5 - removing <7> from <5679> leaving <569>

Squares R3C4, R3C9, R2C4 and R2C9 form a Type-1 Unique Rectangle on <47>.

R2C4 - removing <47> from <479> leaving <9>

R2C2 can only be <7>

R9C4 can only be <2>

R1C6 can only be <6>

R9C7 can only be <9>

R8C4 can only be <6>

R8C7 can only be <2>

R1C2 can only be <2>

R3C5 can only be <5>

R2C9 can only be <4>

R4C2 can only be <1>

R1C3 can only be <5>

R3C9 can only be <7>

R3C3 can only be <9>

R1C5 can only be <7>

R3C4 can only be <4>

R6C4 can only be <7>

R1C8 can only be <9>

R3C2 can only be <6>

R7C2 can only be <9>

R3C1 can only be <1>

R4C5 can only be <9>

R3C8 can only be <2>

R8C3 can only be <7>

R4C9 can only be <3>

R6C5 can only be <6>

R4C1 can only be <7>

R6C9 can only be <9>

R6C1 can only be <3>

R7C6 can only be <5>

R7C1 can only be <2>

R8C6 can only be <9>

R8C1 can only be <5>



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