Jun 06 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C4 can only be <5>
R5C5 is the only square in row 5 that can be <7>
R5C6 is the only square in row 5 that can be <4>
R9C6 can only be <3>
R1C6 can only be <6>
R6C9 is the only square in row 6 that can be <8>
R5C2 is the only square in row 5 that can be <8>
R8C5 is the only square in row 8 that can be <8>
R9C2 is the only square in column 2 that can be <6>
R6C5 is the only square in column 5 that can be <6>
R6C1 can only be <1>
R4C1 can only be <5>
R8C3 is the only square in block 7 that can be <1>
Squares R2C1 and R2C9 in row 2 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C1 - removing <4> from <249> leaving <29>
R1C9 - removing <4> from <123459> leaving <12359>
R9C1 - removing <4> from <249> leaving <29>
R9C9 - removing <4> from <1249> leaving <129>
Squares R1C1 and R9C1 in column 1 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.
R2C1 - removing <9> from <469> leaving <46>
R8C1 - removing <2> from <234> leaving <34>
Intersection of row 8 with block 9. The value <2> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. 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 <2> from <2359> leaving <359>
R7C8 - removing <2> from <2459> leaving <459>
R9C8 - removing <2> from <1249> leaving <149>
R9C9 - removing <2> from <129> leaving <19>
Squares R4C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <19> from <12359> leaving <235>
R2C9 - removing <19> from <1459> leaving <45>
R5C9 - removing <19> from <1259> leaving <25>
Squares R2C1<46>, R2C3<56> and R2C9<45> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <456>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C5 - removing <5> from <159> leaving <19>
R2C7 - removing <5> from <159> leaving <19>
Squares R2C5 and R4C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <19> from <1359> leaving <35>
R3C5 - removing <19> from <1359> leaving <35>
Squares R2C7 and R5C4 form a remote naked pair. <19> can be removed from any square that is common to their groups.
R5C7 - removing <19> from <1259> leaving <25>
Squares R5C7 and R5C9 in row 5 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.
R5C8 - removing <25> from <1259> leaving <19>
Intersection of column 7 with block 3. The value <1> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <1> from <12459> leaving <2459>
R3C8 - removing <1> from <1259> leaving <259>
Intersection of column 8 with block 3. The value <2> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <2> from <235> leaving <35>
R3C7 - removing <2> from <12359> leaving <1359>
Squares R1C5 and R1C9 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C8 - removing <5> from <2459> leaving <249>
Squares R7C2 (XY), R7C5 (XZ) and R9C1 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R9C5 - removing <2> from <24> leaving <4>
R7C3 - removing <2> from <23> leaving <3>
R5C3 can only be <6>
R8C1 can only be <4>
R2C1 can only be <6>
R7C2 can only be <9>
R7C5 can only be <2>
R2C3 can only be <5>
R5C1 can only be <3>
R2C9 can only be <4>
R3C3 can only be <2>
R1C1 can only be <9>
R7C7 can only be <5>
R3C2 can only be <1>
R9C1 can only be <2>
R7C8 can only be <4>
R5C7 can only be <2>
R1C4 can only be <1>
R1C8 can only be <2>
R1C2 can only be <4>
R5C4 can only be <9>
R2C5 can only be <9>
R2C7 can only be <1>
R4C5 can only be <1>
R4C9 can only be <9>
R9C9 can only be <1>
R5C8 can only be <1>
R5C9 can only be <5>
R8C7 can only be <3>
R9C8 can only be <9>
R1C9 can only be <3>
R8C9 can only be <2>
R3C7 can only be <9>
R3C8 can only be <5>
R1C5 can only be <5>
R3C5 can only be <3>
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