Jul 05 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <7>
R8C2 can only be <5>
R9C1 can only be <2>
R9C9 can only be <4>
R8C5 can only be <8>
R8C8 can only be <3>
R9C4 can only be <9>
R7C3 can only be <7>
R1C9 can only be <9>
R7C7 can only be <5>
Squares R3C6 and R7C6 in column 6 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 column.
R1C6 - removing <4> from <456> leaving <56>
R2C6 - removing <4> from <147> leaving <17>
Squares R3C7 and R6C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C7 - removing <4> from <469> leaving <69>
R5C7 - removing <8> from <689> leaving <69>
Squares R1C4<68>, R2C4<78> and R8C4<67> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <678>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C4 - removing <8> from <238> leaving <23>
Squares R6C1<478>, R6C2<34>, R6C7<48> and R6C9<37> in row 6 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3478>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C3 - removing <8> from <258> leaving <25>
R6C8 - removing <48> from <2458> leaving <25>
Squares R4C2<469>, R4C3<29>, R4C7<69> and R4C8<24> in row 4 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2469>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C1 - removing <4> from <147> leaving <17>
Squares R4C7, R5C7, R4C2 and R5C2 form a Type-3 Unique Rectangle on <69>. Upon close inspection, it is clear that:
(R4C2 or R5C2)<34> and R6C2<34> form a naked pair on <34> in block 4. No other squares in the block can contain these possibilities
R6C1 - removing <4> from <478> leaving <78>
(R4C2 or R5C2)<34>, R6C2<34>, R6C1<478>, R5C1<18> and R4C1<17> form a naked set on <13478> in block 4. No other squares in the block can contain these possibilities
R5C3 - removing <8> from <589> leaving <59>
(R4C2 or R5C2)<34> and R6C2<34> form a naked pair on <34> in column 2. No other squares in the column can contain these possibilities
R2C2 - removing <4> from <49> leaving <9>
R3C3 can only be <8>
R3C7 can only be <4>
R1C1 can only be <4>
R3C6 can only be <3>
R6C7 can only be <8>
R2C8 can only be <8>
R6C1 can only be <7>
R5C8 can only be <5>
R1C5 can only be <5>
R1C6 can only be <6>
R9C5 can only be <1>
R1C4 can only be <8>
R8C6 can only be <7>
R2C4 can only be <7>
R3C4 can only be <2>
R7C6 can only be <4>
R5C3 can only be <9>
R6C8 can only be <2>
R6C9 can only be <3>
R4C1 can only be <1>
R6C3 can only be <5>
R4C8 can only be <4>
R6C2 can only be <4>
R5C9 can only be <1>
R7C5 can only be <2>
R8C4 can only be <6>
R2C6 can only be <1>
R9C6 can only be <5>
R2C5 can only be <4>
R3C5 can only be <9>
R7C4 can only be <3>
R4C9 can only be <7>
R5C1 can only be <8>
R4C2 can only be <6>
R5C7 can only be <6>
R4C3 can only be <2>
R5C2 can only be <3>
R4C7 can only be <9>
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