How to solve Sudoku Hard level 4 game 10 quickly by advanced Sudoku techniques
Know how to solve Sudoku hard level 4 game 10 quick and easy by the strategy of aggressive breakthroughs early by using advance Sudoku techniques.
The Sudoku hard level 4 Game 10
Before going through the solution solve the puzzle first.
How to solve Sudoku Hard level 4 Game 10 Stage 1: Breakthrough by Triple digit scan, Parallel digit scan and Cycles of twins and triplets
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 for a single digit lock by cross scan.
If we get one, we should get usually a breakthrough in one step or two.
Otherwise we know that the single digit lock might become useful later and we ignore it for the present.
Highlight color of valid cells in this first stage is banana leaf green.
Starting the solution process, R9C3 3 by scan for 3 in R7, R8 -- R3C1 8 by scan for 8 in R1, C3 -- R8C2 8 by scan in C1, C3 -- R5C3 5 by scan for 5 in C1, C2.
Now identify the special digit pattern of [3,6,9] in C2.
It reduces the possible digit subset in R4C2, R5C2, R6C2 from [1,3,4,6,7,9] to [1,4,7] and forms the breakthrough Cycle (1,4,7) of triplets in the three cells and a second Cycle (3,6,9) of triplets in the rest three cells of the left middle major square.
The actual breakthrough valid cell is R1C2 2 by reduction and exception in C2 because of the Cycle (1,4,7) of triplets in C2 -- R1C1 7 by reduction by 2 in R1C2 as well as the Cycle (3,6,9) in C1 -- R7C3 7 by scan for 7 in R8, C1 -- R8C3 9 by scan for 9 in Cycle (3,6,9) of triplets in C1.
A byproduct Cycle of (1,2) formed in R7C1, R8C1.
This is a case of Triple digit scan for [3,6,9] in C2 on empty cells of left middle major square.
This breakthrough causes a series of valid cells: R3C3 1 by scan for 1 in R1 -- R1C3 4 by exception in top left major square.
Still focusing on the most favorable zone R1, R1C7 5 by parallel scan for empty cells of R1 for digit 5 by elimination of cell R1C6 by 5 in C6 leaving R1C7 5 -- R1C6 3 by exception in R1.
Still remaining on the upper one-third zone, identify that possible digit subset in R2 as [1,2,4,7,9] whereas digit subset [1,7] exists in top right major square. By reduction then two Cycles are formed in R2: Cycle (1,7) of twins in R2C4, R2C6 and Cycle (2,4,9) of triplets in R2C7, R2C8, R2C9.
This results in formation of two other Cycles: Cycle (2,4,5) of triplets in top middle major square and Cycle (3,6) of twins in top right major square.
In the next stage our first action will be to break down the breakthrough Cycle (1,4,7) by 4 in R6C4. For now we preserve it for better understanding of the other breakthroughs.
Results of the actions taken shown.
How to solve Sudoku hard level 4 Game 10 Stage 2: Breakthrough by Double digit scan and Cycles of twins
Highlight color of valid cells at this second stage is light blue.
As mentioned earlier, with 4 in R6C4, R6C2 1 by reduction.
We'll create the next breakthrough by first forming the breakthrough Cycle of (6,9) of twins in R7C7, R7C9 by double digit scan for [6,9] in R9.
This Cycle participates in a scan for 6 on empty cells of bottom middle major square along with 6 in R9 and 6 in C4 to create the breakthrough R8C6 6.
R9C9 1 by scan for 1 in C7, C8.
A surprising breakthrough Cycle of twins (3,9) is formed in R4C4, R5C4 in central middle major square by double digit scan for [3,9] in both columns C4, C5 and none of [3,9] existing in central middle major square.
This Cycle enables R5C6 8 by scan for 8 in R6, C5.
In the same way a second breakthrough Cycle of (5,7) of twins formed in cells R9C4, R9C5 in bottom middle major square by double digit scan for [5,7] on empty cells of the major square by [5,7] in both R7 and R8 but none of [5,7] in the bottom middle major square.
Same way as before, this Cycle of (5,7) of twins enables breakthrough valid cell R7C4 8 by scan for 8 in R8, C5 and C8.
The new incidences on 8 create the last but one incidence of 8 in R4C8 8 by scan for 8 in R5, R6 and C9 followed by the last one R9C7 8 by scan for 8 in C8 -- R9C8 2 by exception in C9.
With 1 in R6C2, R6C6 2 by reduction of [1,6,7] from DS [1,2,6,7] -- R3C6 4 by reduction -- R7C6 1 by reduction -- R2C6 by reduction -- R2C4 1 by reduction -- R8C4 2 by reduction -- R7C5 4, R8C1 1 by reduction -- R7C1 2 by reduction.
With 2 in R8C4, R3C4 5 by reduction -- R3C5 2 by reduction.
First two stages are rich in extraordinary breakthroughs. This approach of early breakthroughs by advanced Sudoku techniques speeds up solution of this Sudoku hard puzzle.
Game status shown below.
How to solve Sudoku hard level 4 Game 10 Stage 3: Breakthrough by DSA and Cycles of Twins
Highlight color of valid cells at this third stage, which is not the last stage, is light grayish yellow.
First valid cell at this stage is an easy one by row column scan: R6C9 5 by scanning for 5 in R4, R5, C8.
A pending valid cell: with 5 in R3C4, R9C4 7 by reduction -- R9C5 5 by reduction.
Possible digit subset in R6 [3,6,9] reduced by [3,6] in C5 for valid cell R6C5 6 -- R6C8 9 by reduction of 3 in C8 -- R6C1 3 by exception.
R5C5 1 by scan for 1 in R4, C4 -- R4C5 7 by exception in C4 -- R4C2 4 by reduction -- R5C2 7 by reduction.
By reduction of 9 in right middle major square from DS [3,6,9] in R4 and hence in R4C9, the DS in the cell [3,6] forms a Cycle of (3,6) with [3.6] in R3C9. This Cycle creates the valid cell R7C9 9 by reduction of 6 by the Cycle -- R7C7 6 by reduction.
We'll move over to the last stage for the formality of putting the easy valid digits in their valid cells.
All breakthrough are taken care of.
How to solve Sudoku hard level 4 Game 10 Final Stage 4: No more challenges left
Highlight color of valid cells at this fourth and last stage is light cyan.
With 6 in R7C7, R3C7 3 by reduction -- R3C9 6 by reduction -- R4C9 3 by reduction -- R4C4 9 by reduction -- R4C1 6, R5C4 3 by reduction of 9 -- R5C1 9 by reduction.
R2C7 9 by scan for 9 in C7, C8 -- R5C7 2 by exception in C7 -- R2C8 4 by reduction -- R2C9 2 by reduction -- R5C8 6 by exception in C8, R5C9 4 by exception in whole game.
Final solution below.
Highlight background colors of valid cells are used for keeping track of stages in which the valid cells are obtained.
A series of early breakthroughs by advanced Sudoku techniques of Triple digit scan, parallel digit scan, Cycles in the form of twins and triplets and double digit scan ensured quick solution to this 10th Sudoku hard level 4 puzzle game.
Especially satisfying is the fact that there has been no need to enumerate the possible digit subsets in many empty cells that saved a lot of time.
Avoiding unnecessary enumeration of possible digit subsets in empty cells always speeds up up the solution.
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