Jul 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <2>
R5C4 is the only square in row 5 that can be <3>
Squares R8C1 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <59> from <3589> leaving <38>
R8C5 - removing <5> from <258> leaving <28>
R8C9 - removing <9> from <239> leaving <23>
Squares R1C2 and R5C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <5> from <15> leaving <1>
R9C2 - removing <5> from <1358> leaving <138>
R2C9 can only be <7>
R1C3 is the only square in row 1 that can be <7>
R9C3 is the only square in row 9 that can be <1>
R5C1 is the only square in column 1 that can be <7>
R9C8 is the only square in column 8 that can be <7>
Squares R1C7 and R2C8 in block 3 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.
R3C7 - removing <45> from <1345> leaving <13>
Intersection of block 6 with row 5. The value <9> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C2 - removing <9> from <59> leaving <5>
R5C5 - removing <9> from <14569> leaving <1456>
R1C2 can only be <9>
R3C4 is the only square in row 3 that can be <9>
R4C4 can only be <8>
R7C7 is the only square in row 7 that can be <8>
Squares R4C3 and R6C3 in column 3 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.
R7C3 - removing <9> from <569> leaving <56>
Squares R1C5 and R1C7 in row 1 and R9C5 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 5 and 7 can be removed.
R2C5 - removing <5> from <456> leaving <46>
R6C5 - removing <5> from <2459> leaving <249>
Squares R2C1 and R2C8 in row 2 and R8C1 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 8 can be removed.
R3C1 - removing <5> from <456> leaving <46>
R7C1 - removing <5> from <569> leaving <69>
Squares R4C3, R6C3, R4C5 and R6C5 form a Type-3 Unique Rectangle on <29>. Upon close inspection, it is clear that:
(R4C5 or R6C5)<14>, R5C6<46> and R5C5<146> form a naked triplet on <146> in block 5. No other squares in the block can contain these possibilities
R6C4 - removing <4> from <45> leaving <5>
R6C6 - removing <4> from <2457> leaving <257>
(R4C5 or R6C5)<14>, R6C4<45>, R5C6<46> and R5C5<146> form a naked quad on <1456> in block 5. No other squares in the block can contain these possibilities
R6C6 - removing <5> from <257> leaving <27>
(R4C5 or R6C5)<14>, R5C5<146> and R2C5<46> form a naked triplet on <146> in column 5. No other squares in the column can contain these possibilities
R1C5 - removing <4> from <45> leaving <5>
(R4C5 or R6C5)<14>, R5C5<146>, R2C5<46> and R1C5<45> form a naked quad on <1456> in column 5. No other squares in the column can contain these possibilities
R9C5 - removing <5> from <58> leaving <8>
(R4C5 or R6C5)<14>, R9C5<58>, R5C5<146>, R2C5<46> and R1C5<45> form a naked set on <14568> in column 5. No other squares in the column can contain these possibilities
R8C5 - removing <8> from <28> leaving <2>
R1C7 can only be <4>
R6C7 can only be <7>
R2C8 can only be <5>
R8C8 can only be <9>
R7C4 can only be <4>
R6C6 can only be <2>
R4C7 can only be <1>
R8C9 can only be <3>
R7C6 can only be <5>
R8C1 can only be <5>
R5C8 can only be <4>
R7C9 can only be <2>
R8C2 can only be <8>
R3C9 can only be <1>
R9C7 can only be <5>
R9C2 can only be <3>
R3C7 can only be <3>
R5C9 can only be <9>
R4C5 can only be <9>
R5C6 can only be <6>
R6C3 can only be <9>
R4C6 can only be <7>
R7C3 can only be <6>
R4C3 can only be <2>
R6C5 can only be <4>
R5C5 can only be <1>
R3C6 can only be <4>
R2C5 can only be <6>
R7C1 can only be <9>
R3C3 can only be <5>
R2C1 can only be <4>
R3C1 can only be <6>
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