Oct 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 can only be <4>
R7C1 can only be <9>
R1C7 can only be <5>
R1C3 can only be <7>
R3C9 can only be <7>
R3C1 can only be <3>
R5C1 can only be <7>
R3C8 is the only square in row 3 that can be <6>
R3C2 is the only square in row 3 that can be <4>
R5C7 is the only square in row 5 that can be <3>
R6C8 is the only square in row 6 that can be <7>
R8C7 is the only square in row 8 that can be <9>
R7C5 is the only square in column 5 that can be <1>
R3C5 is the only square in column 5 that can be <9>
Squares R2C2 and R2C3 in row 2 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 row.
R2C4 - removing <25> from <2357> leaving <37>
R2C6 - removing <25> from <2357> leaving <37>
Squares R7C6 and R7C9 in row 7 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 row.
R7C2 - removing <2> from <268> leaving <68>
R7C4 - removing <25> from <2456> leaving <46>
R7C8 - removing <5> from <458> leaving <48>
Squares R3C6 and R7C6 in column 6 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.
R6C6 - removing <2> from <1239> leaving <139>
R8C6 - removing <25> from <257> leaving <7>
R2C6 can only be <3>
R2C4 can only be <7>
Squares R5C3 and R5C5 in row 5 and R9C3 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 5 can be removed.
R4C3 - removing <6> from <5689> leaving <589>
R6C3 - removing <6> from <69> leaving <9>
R6C6 can only be <1>
R4C6 can only be <9>
Squares R5C9 (XY), R6C7 (XZ) and R5C3 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R6C2 - removing <6> from <36> leaving <3>
R4C4 is the only square in row 4 that can be <3>
Squares R6C7 and R9C5 form a remote naked pair. <26> can be removed from any square that is common to their groups.
R9C7 - removing <2> from <24> leaving <4>
R2C7 can only be <1>
R7C8 can only be <8>
R2C8 can only be <4>
R4C7 can only be <6>
R6C7 can only be <2>
R6C4 can only be <6>
R5C9 can only be <5>
R7C2 can only be <6>
R8C8 can only be <5>
R4C8 can only be <1>
R7C9 can only be <2>
R5C3 can only be <6>
R7C4 can only be <4>
R5C5 can only be <2>
R9C3 can only be <2>
R8C4 can only be <2>
R7C6 can only be <5>
R8C2 can only be <8>
R3C4 can only be <5>
R9C5 can only be <6>
R2C3 can only be <5>
R2C2 can only be <2>
R4C3 can only be <8>
R3C6 can only be <2>
R4C2 can only be <5>
R8C3 can only be <4>
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