How to solve hard Sudoku level 4 puzzle game 11 quickly by advanced Sudoku techniques
How to solve hard Sudoku puzzle: level 4 game 11 explains how every breakthrough valid cell is achieved. It's a glimpse into hard Sudoku solving.
The hard Sudoku level 4 puzzle Game 11
Before going through the solution solve the puzzle first.
How to solve hard Sudoku level 4 puzzle Game 11 Stage 1: Breakthrough by Parallel digit scan, Cycle of twins and Double digit scan
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.
First few valid digits are all by row column scan,
R1C2 1 by scan for 1 in R2, R3, C1 -- R4C5 1 by scan for 1 in R6, C4, C6.
R5C6 2 by scan for 2 in R4, R6, C4 -- R7C5 2 by scan for 2 in R9, C4, C6.
R5C9 1 by scan for 1 in R4, R6, C8 -- R8C7 1 by scan for 1 in R7, C8, C9 -- R9C3 1 by scan for 1 in R7, R8, C2. R5C2 2 by scan for 2 in R4, R6, C4 -- R7C5 2 by scan for 2 in R9, C4, C6 -- R8C9 2 by scan for 2 in R7, R9, C8.
R7C4 3 by scan for 3 in R8, R9.
R9C8 6 by scan for 6 in R7, R8, C9 -- R6C4 6 by scan for 6 in R4, R5, C5.
R6C9 7 by scan for 7 in R4, R5.
Breakthrough of R9C4 7 by parallel scan for 7 on empty cells of R9 eliminating R9C2 by 7 in C2, R9C5 by 7 in C5 and R9C9 by 7 in C9, altogether an elimination of three cells out of four.
It's an important breakthrough.
Breakthrough Cycle of twins (2,7) formed by double digit scan for [2,7] in R1 and C9 on empty cells of top right major square that doesn't contain digit 2 or 7.
Last breakthrough valid cell at this stage is R1C7 6 by parallel scan for 6 on empty cells of C7 by eliminating cell R4C7 by 6 in R4 and cell R7C7 by 6 in R7.
This leaves the single cell R1C7 in C7 for digit 6.
Results of the actions taken shown.
How to solve hard Sudoku level 4 puzzle Game 11 Stage 2: Breakthrough by Cycle of twins and DSA or Possible digit analysis
Highlight color of valid cells at this second stage is light blue.
First valid cell at this stage is R4C7 4 by scan for 4 in C8 on empty cells of right middle major square -- R7C7 8 by reduction.
Cycle (3,8) in R4C8, R5C8 in C8.
A breakthrough Cycle (4,5) of twins formed in R1C6 and R8C6 by possible digit analysis by reduction of [3,6,7] for both the cells from possible digit subset of [3,4,5,6,7] in column C6.
This twins causes R4C6 3 by reduction of [6,7] from possible digit subset [3,6,7] in C6.
R5C8 3 by scan for 3 in R4 on empty cells of right middle major square -- R4C8 8 by exception of only digit left in the right middle major square.
That creates valid cell R4C1 5 by exception in R4 as the only digit left in R4.
R5C4 5 by scan for 5 in R4, R6 on empty cells of central middle major square -- R6C5 4 by exception as the only digit left in central middle major square.
R6C3 3 by scan for 3 in R5, C2 -- R6C2 9 by exception in R6.
Game status shown below.
How to solve hard Sudoku level 4 puzzle Game 11 Stage 3: Breakthrough by Parallel digit scan, Single digit lock and Cycle of twins
Highlight color of valid cells at this third stage, which is not the last stage, is light grayish yellow.
A breakthrough in R3C5 3 by parallel digit scan for 3 on empty cells of C5 eliminating R1C5 for 3 by 3 in R1 and R9C5 by 3 in R9 leaving only R3C5 for 3.
R2C1 3 by scan for 3 in R1, R3, C2, C3.
R3C1 6 by scan for 6 in R1, C2, C3 -- R3C6 7 by reduction of 6 -- R2C6 6 by reduction of 7 -- R3C7 2 by reduction of 7 -- R2C7 7 by reduction of 2.
R2C2 2 by scan for 2 in R1, R3, C3.
Breakthrough single digit lock on 5 formed in R1C5, R1C6 by single column C4 -- scan for 5 in C5 -- actual breakthrough in R1C8 9 by elimination of [5,7] from possible digit subset [5,7,9] in C8.
Apart from participating in a row column scan for a valid cell, this is the second way a valid cell is created by a single digit lock.
R3C3 9 by scan for 9 in R1, R2, C2.
Also Cycle of twins (5,8) formed by the leftover two digits [5,8] in R2C9, R3C9 of right middle major square and also in C9.
This causes breakthrough R9C9 4 by reduction of 5 in DS by the Cycle (5,8) in C9.
All breakthrough have been taken care of.
How to solve hard Sudoku level 4 puzzle Game 11 Final Stage 4: No more challenges left
Highlight color of valid cells at this fourth and last stage is light cyan.
With 4 in R9C9, R7C9 9 by reduction of [4,5] -- R7C1 7 by reduction -- R8C1 9 by reduction -- R8C8 7 by scan for 7 in R7 -- R7C8 5 by exception in C8 -- R7C3 4 by exception in R7.
R1C1 4 by scan for 4 in C3 -- R5C1 8 by reduction -- R5C2 4 by reduction of 8.
With 4 in R1C1, R1C6 5 by reduction -- R8C6 4 by reduction of 5 and R1C5 8 by exception in R1.
R2C4 4 by exception in top middle major square -- R8C4 8 by exception in C4 -- R9C5 5 by exception in C5 -- R9C2 8 by exception in C9 -- R3C2 5 by exception in C2 -- R3C9 8 by exception in R3 -- R2C9 5 by exception in R2.
Final solution below.
Highlight background colors of valid cells are used for keeping track of stages in which the valid cells are obtained.
Early breakthroughs by advanced Sudoku techniques of Parallel digit scan, Single digit lock, Double digit scan, Cycle of twins ensured quick solution to this 11th Sudoku hard level 4 puzzle game.
It is satisfying that there has been no need to unnecessarily enumerate the possible digit subsets in many empty cells that saved a lot of time.
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