Sep 25 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C8 can only be <2>
R5C5 is the only square in row 5 that can be <4>
R5C4 is the only square in row 5 that can be <6>
R5C7 is the only square in row 5 that can be <8>
R4C9 can only be <9>
R6C9 can only be <3>
R5C6 is the only square in row 5 that can be <3>
R8C2 is the only square in row 8 that can be <8>
R8C7 is the only square in row 8 that can be <3>
R7C8 is the only square in column 8 that can be <7>
Squares R2C2 and R2C8 in row 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 row.
R2C3 - removing <59> from <24569> leaving <246>
R2C5 - removing <5> from <25> leaving <2>
R2C7 - removing <9> from <2469> leaving <246>
Squares R5C2 and R5C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <5> from <125> leaving <12>
Squares R4C1 and R6C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. 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 <245> leaving <45>
R3C1 - removing <2> from <2356> leaving <356>
R7C1 - removing <1> from <13456> leaving <3456>
R9C1 - removing <1> from <1456> leaving <456>
Squares R1C1<45>, R1C4<578>, R1C6<57> and R1C9<458> in row 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <4578>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C3 - removing <457> from <24579> leaving <29>
R1C7 - removing <4> from <249> leaving <29>
Intersection of row 1 with block 2. The value <7> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C5 - removing <7> from <578> leaving <58>
R6C5 is the only square in column 5 that can be <7>
R6C4 can only be <1>
R6C1 can only be <2>
R6C6 can only be <9>
R4C1 can only be <1>
R4C6 is the only square in row 4 that can be <2>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <5> from <456> leaving <46>
R9C3 - removing <5> from <14569> leaving <1469>
R9C9 - removing <5> from <456> leaving <46>
Squares R9C1 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C3 - removing <46> from <1469> leaving <19>
R9C7 - removing <46> from <1469> leaving <19>
Squares R3C5 and R4C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C5 - removing <5> from <159> leaving <19>
R8C5 - removing <5> from <159> leaving <19>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 1 and 9 can be removed.
R7C1 - removing <4> from <3456> leaving <356>
R7C9 - removing <4> from <456> leaving <56>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 7 can be removed.
R7C3 - removing <9> from <14569> leaving <1456>
R7C7 - removing <9> from <1469> leaving <146>
R8C3 - removing <9> from <159> leaving <15>
Squares R2C2 and R2C8 in row 2, R5C2 and R5C3 in row 5 and R8C3 and R8C8 in row 8 form a Swordfish pattern on possibility <5>. All other instances of this possibility in columns 2, 3 and 8 can be removed.
R3C2 - removing <5> from <357> leaving <37>
R3C3 - removing <5> from <2567> leaving <267>
R3C8 - removing <5> from <15> leaving <1>
R7C2 - removing <5> from <359> leaving <39>
R7C3 - removing <5> from <1456> leaving <146>
Squares R9C4, R9C6, R1C4 and R1C6 form a Type-1 Unique Rectangle on <57>.
R1C4 - removing <57> from <578> leaving <8>
R4C4 can only be <5>
R3C5 can only be <5>
R4C5 can only be <8>
R1C6 can only be <7>
R9C4 can only be <7>
R9C6 can only be <5>
R3C9 is the only square in row 3 that can be <8>
Intersection of column 9 with block 9. The value <6> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <6> from <146> leaving <14>
Squares R8C3 (XY), R9C3 (XZ) and R8C8 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R9C7 - removing <9> from <19> leaving <1>
R9C3 can only be <9>
R7C7 can only be <4>
R2C7 can only be <6>
R9C9 can only be <6>
R1C3 can only be <2>
R7C2 can only be <3>
R9C1 can only be <4>
R7C9 can only be <5>
R1C7 can only be <9>
R2C8 can only be <5>
R2C3 can only be <4>
R3C7 can only be <2>
R2C2 can only be <9>
R8C8 can only be <9>
R1C9 can only be <4>
R3C2 can only be <7>
R7C1 can only be <6>
R8C5 can only be <1>
R1C1 can only be <5>
R3C3 can only be <6>
R5C2 can only be <5>
R3C1 can only be <3>
R7C3 can only be <1>
R5C3 can only be <7>
R7C5 can only be <9>
R8C3 can only be <5>
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