How to solve quickly the hard Sudoku puzzle level 4 game 18
Breakthroughs by advanced Sudoku techniques and each valid cell details explained in the four stage solution to the hard Sudoku puzzle level 4 game 18.
Solution to this difficult Sudoku puzzle will give you an idea on the techniques and strategy for solving a difficult Sudoku puzzle quickly.
The hard Sudoku puzzle level 4 Game 18
Before going through the solution solve the puzzle first.
Solving hard Sudoku puzzles: Level 4 Game 18 Stage 1: Breakthrough by Parallel digit scan, Double digit scan and Cycles of twins
Strategy adopted: start with row column scan coupled with aggressive breakthroughs by advanced Sudoku techniques.
As a strategy we always start row column scan from digit 1 and continue till digit 9. In the process we may get valid cells, but otherwise our lookout is for identifying a single digit lock by cross scan.
If we get one, we should get usually a breakthrough in one step or two.
In addition, at this early stage while carrying on row column scan, we remain alert for the possibility of a double digit scan also.
Highlight color of valid cells in this first stage is banana leaf green.
The very first valid cell by row column scan is in R3C3 8 by scan for 8 in R2, C1, C2.
And then, R5C1 9 by scan for 9 in R6, C3.
With these new valid cells, a valid cell for 4 is feasible in R6C1 4 by scan in C2, C3.
First major breakthrough R2C3 3 by parallel digit scan for 3 on empty cells of C3 by elimination of cells R7C3, R9C3 by 3 in R7 and R9 and elimination of R4C3, R5C3 by 3 in left middle major square leaving only R2C3 for 3 in C3 (shown by red arrows).
Cycle (3,4) of twins in R3C4, R3C6 by double digit scan of [3,4] in R1, R2 on empty cells of top middle major square (shown by blue arrows).
Possible digit subset [1,2,5,7] in C1 is reduced by [5,7] in R1, R3 forming Cycle of twins (1,2) in R1C1, R3C1 -- R3C2 9 by reduction of [1,2] from DS [1,2,9].
R1C2 6 by reduction of [5,7] in R1 from DS [5,6,7] in rest of the three cells in top left major square.
R2C9 6 by scan for 6 in R1, R3, C8.
R2C4 9 by parallel digit scan for 9 on empty cells of R2 by elimination of R2C5 by 9 in C5 and R2C8 by 9 in C8.
Results of the actions shown.
Solving hard Sudoku puzzles: Level 4 Game 18 Stage 2: Breakthrough by DSA reduction, Cycle of twins and triplets
Highlight color of valid cells at this second stage is light blue.
With 9 in R2C2, R3C7 2 by reduction -- R3C1 1 by reduction -- R1C1 2 by reduction -- R1C6 1 by reduction -- R2C5 2 by reduction -- R2C8 1 by reduction.
R1C7 9 by scan for 9 in C8 -- R1C8 8 by exception in R1.
Cycle of triplets (2,4,5) formed in C8 by DSA reduction from possible digit subset of [2,3,4,5] in C8 -- R8C8 3 by reduction of [2,4,5].
R4C6 9 by scan for 9 in R5, R6, C4, C5.
R9C9 8 by scan for 8 in R7, R8, C8 -- R6C7 8 by scan in R5, C8, C9 -- R4C5 8 by scan for 8 in R5, R6, C4.
R6C5 7 by reduction of [2,3,6] in C5 from DS [2,3,6,7] in R6 -- R6C2 2 by reduction.
Cycle of twins (1,7) formed in C3 and left middle major square -- Cycle of twins (2,6) formed from leftover two digits in R7C3, R9C3 reducing the DS in rest three cells of bottom left major square to [1,5,7] -- R9C2 5 by reduction of [1,7] from [1,5,7] in R9 -- R2C2 7 by reduction -- R2C1 5 by reduction -- R8C1 7 by reduction -- R8C2 1 by exception in C2.
Game status shown below.
Solving hard Sudoku puzzles: Level 4 Game 18 Stage 3: Breakthrough by DSA reduction
Highlight color of valid cells at this third stage, which is not the last stage, is light grayish yellow.
R7C8 5 by scan for 5 in R9, C7, C9.
DS in C5 [1,4] reduced by 1 in R8 to R8C5 4 -- R5C5 1 by exception in C5.
Reduced DS [2,5,6] in R8 and in R8C7 reduced by [2,5] in C7 to create the valid cell R8C7 6 -- R8C9 2 by reduction of 5 in C9 -- R8C6 5 by exception in R8.
With 2 in R8C9, R9C8 4 by reduction -- R4C8 2 by reduction.
R7C7 7 by reduction of 3 from DS [3,7] in C7 -- R5C7 3 by exception in C7 -- R7C9 9 by exception in bottom right major square.
With 1 in R5C5, R5C3 7 by reduction -- R4C3 1 by reduction.
Solving hard Sudoku puzzles: Level 4 Game 18 Final Stage 4: Rest are easy pickings
Highlight color of valid cells at this fourth and last stage is light cyan.
R4C9 7 by scan for 7 in R5 -- R5C9 4 by exception in C9 -- R4C4 4 by exception.
R3C4 3 by reduction -- R3C6 4 by reduction. R6C6 3 by scan for 3 in R5, C4 -- R6C4 6 by reduction -- R9C4 2 by reduction -- R9C3 2 by reduction -- R7C4 1 by reduction of [2,6] -- R7C6 6 by reduction of [1,2] -- R5C6 2 by exception in C6 -- R5C4 5 by exception in whole game.
Final solution below.
Breakthroughs by advanced Sudoku techniques of Difficult Parallel digit scan, Double digit scan, Cycles of twins and triplets ensured quick solution to this 18th Sudoku hard puzzle at level 4.
Unnecessary enumeration of possible digit subsets for empty cells avoided as far as possible.
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