 Nov 25 - Super Hard

## Reasoning

R1C3 is the only square in row 1 that can be <2>

R1C7 is the only square in row 1 that can be <7>

R5C8 is the only square in row 5 that can be <1>

R7C4 is the only square in row 7 that can be <7>

R6C5 is the only square in row 6 that can be <7>

R7C8 is the only square in row 7 that can be <2>

R8C8 can only be <5>

R1C8 can only be <6>

R9C9 is the only square in row 9 that can be <9>

R9C3 is the only square in row 9 that can be <8>

R9C1 is the only square in row 9 that can be <6>

Squares R3C4 and R9C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R2C4 - removing <15> from <1258> leaving <28>

R4C4 - removing <5> from <45689> leaving <4689>

R6C4 - removing <5> from <245689> leaving <24689>

R8C4 - removing <1> from <124> leaving <24>

Intersection of row 3 with block 1. The value <9> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.

R2C1 - removing <9> from <3459> leaving <345>

R2C2 - removing <9> from <134569> leaving <13456>

Intersection of row 7 with block 7. The value <4> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.

R8C2 - removing <4> from <134> leaving <13>

Intersection of row 9 with block 8. The values <135> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.

R8C5 - removing <13> from <1234> leaving <24>

Intersection of column 3 with block 1. The values <17> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.

R1C2 - removing <1> from <15> leaving <5>

R2C2 - removing <1> from <13456> leaving <3456>

R3C2 - removing <1> from <13459> leaving <3459>

R1C9 can only be <1>

R6C1 is the only square in row 6 that can be <5>

R6C4 is the only square in row 6 that can be <2>

R2C4 can only be <8>

R8C4 can only be <4>

R8C5 can only be <2>

R2C6 is the only square in row 2 that can be <2>

R2C3 is the only square in row 2 that can be <7>

R2C5 is the only square in row 2 that can be <1>

R3C4 can only be <5>

R3C6 can only be <7>

R9C4 can only be <1>

R2C9 is the only square in row 2 that can be <5>

R2C2 is the only square in row 2 that can be <6>

R3C3 is the only square in row 3 that can be <1>

R5C1 is the only square in row 5 that can be <2>

R3C1 is the only square in column 1 that can be <9>

Intersection of column 3 with block 4. The values <346> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.

R5C2 - removing <34> from <3489> leaving <89>

R6C2 - removing <4> from <489> leaving <89>

Squares R3C9 and R7C1 form a remote naked pair. <34> can be removed from any square that is common to their groups.

R7C9 - removing <3> from <36> leaving <6>

Squares R9C5, R9C6, R4C5 and R4C6 form a Type-3 Unique Rectangle on <35>. Upon close inspection, it is clear that:

(R4C5 or R4C6)<48>, R4C8<49>, R4C7<689> and R4C4<69> form a naked quad on <4689> in row 4. No other squares in the row can contain these possibilities

R4C3 - removing <46> from <346> leaving <3>

Squares R6C9 (XY), R4C8 (XZ) and R6C2 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.

R6C7 - removing <9> from <689> leaving <68>

R6C2 is the only square in row 6 that can be <9>

R5C2 can only be <8>

R5C6 can only be <3>

R5C5 can only be <4>

R9C6 can only be <5>

R9C5 can only be <3>

R4C6 can only be <8>

R5C3 can only be <6>

R4C5 can only be <5>

R5C4 can only be <9>

R6C3 can only be <4>

R4C4 can only be <6>

R6C9 can only be <8>

R6C7 can only be <6>

R8C9 can only be <3>

R8C2 can only be <1>

R3C9 can only be <4>

R7C7 can only be <1>

R3C2 can only be <3>

R2C8 can only be <9>

R4C7 can only be <9>

R4C8 can only be <4>

R2C7 can only be <3>

R8C7 can only be <8>

R2C1 can only be <4>

R7C2 can only be <4>

R7C1 can only be <3>

## Today's Sudoku Puzzles

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