The full reasoning can be found below the Sudoku.
Jun 15 - Super Hard
Puzzle Copyright © Kevin Stone
Share link:
Reasoning
R2C4 can only be <8>
R4C4 can only be <5>
R8C6 can only be <3>
R2C6 can only be <7>
R6C4 can only be <3>
R5C4 can only be <1>
R7C5 can only be <1>
R8C4 can only be <2>
R9C5 can only be <6>
R2C9 is the only square in row 2 that can be <2>
R4C8 is the only square in row 4 that can be <2>
R4C5 is the only square in row 4 that can be <7>
R5C7 is the only square in row 5 that can be <3>
R6C6 is the only square in row 6 that can be <8>
R6C5 is the only square in column 5 that can be <4>
R6C3 can only be <9>
R8C9 is the only square in column 9 that can be <1>
R8C3 is the only square in row 8 that can be <7>
R5C2 is the only square in row 5 that can be <7>
Squares R6C1 and R6C2 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C1 - removing <6> from <456> leaving <45>
Squares R5C1 and R5C3 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C8 - removing <4> from <489> leaving <89>
R5C9 - removing <4> from <4689> leaving <689>
Intersection of row 1 with block 3. The value <5> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <5> from <45789> leaving <4789>
Squares R2C7<46>, R4C7<469> and R8C7<49> in column 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <469>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <69> from <5689> leaving <58>
Squares R7C7<58>, R7C8<578> and R7C9<78> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <578>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <8> from <238> leaving <23>
Intersection of row 7 with block 9. The values <578> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R9C8 - removing <8> from <489> leaving <49>
Squares R3C2 and R9C2 in column 2 and R3C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 3 and 9 can be removed.
R3C1 - removing <4> from <345> leaving <35>
R9C1 - removing <4> from <149> leaving <19>
R3C3 - removing <4> from <458> leaving <58>
R9C3 - removing <4> from <148> leaving <18>
R3C9 - removing <4> from <4789> leaving <789>
R4C9 is the only square in column 9 that can be <4>
Squares R1C7, R7C7, R1C8 and R7C8 form a Type-4 Unique Rectangle on <58>.
R1C8 - removing <8> from <589> leaving <59>
R7C8 - removing <8> from <578> leaving <57>
Squares R1C8 (XY), R1C7 (XZ) and R5C8 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R3C8 - removing <8> from <4789> leaving <479>
R5C8 is the only square in column 8 that can be <8>
Squares R9C3 (XY), R2C3 (XZ) and R9C2 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C2 - removing <4> from <348> leaving <38>
R3C8 is the only square in row 3 that can be <4>
R9C8 can only be <9>
R2C7 can only be <6>
R9C1 can only be <1>
R1C8 can only be <5>
R8C7 can only be <4>
R1C7 can only be <8>
R7C8 can only be <7>
R4C7 can only be <9>
R4C6 can only be <6>
R5C9 can only be <6>
R5C6 can only be <9>
R7C9 can only be <8>
R7C7 can only be <5>
R1C9 can only be <9>
R8C1 can only be <9>
R9C3 can only be <8>
R2C1 can only be <4>
R9C2 can only be <4>
R3C3 can only be <5>
R1C5 can only be <3>
R3C9 can only be <7>
R2C3 can only be <1>
R5C1 can only be <5>
R3C1 can only be <3>
R5C3 can only be <4>
R1C2 can only be <6>
R3C5 can only be <9>
R3C2 can only be <8>
R7C1 can only be <2>
R7C2 can only be <3>
R6C1 can only be <6>
R6C2 can only be <2>
Today's Sudoku Puzzles
All daily items change at midnight GMT – set your local time zone.
Note: BrainBashers has a Dark Mode option. For BrainBashers, I'd recommend not using your browser's built-in dark mode, or any dark mode extensions (sometimes you can add an exception for a specific website).