## How to solve very hard Sudoku puzzle level 4 game 14 quickly

Solving very hard Sudoku puzzles: Level 4 game 14 quick solution by aggressive early breakthroughs using advanced Sudoku techniques. Steps explained.

Solution of this very difficult Sudoku puzzle will give you a good idea on the techniques and strategy of solving a very difficult Sudoku puzzle using your basic reasoning skills and pattern identification abilities created by experience of solving hard Sudoku puzzles.

### The very hard Sudoku puzzle level 4 Game 14

Before going through the solution solve the puzzle first.

### Solving very hard Sudoku puzzles: Level 4 Game 14 Stage 1: Breakthrough by difficult to form Cycles of triplets and twins and Single digit lock

**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.

First valid cell by row column scan **R6C7 8** by scan for 8 in R4, C8, C9. And that's all for the moment by row column scan or possible digit subset analysis of empty cells at the moment.

At least let's form the **Cycle of twins (3,8)** in R5C4, R5C6 in central middle major square by the leftover digits in the row. It would be used when we concentrate on analyzing the possible digit subsets of the central middle major square.

Seriously searching for short length *two or three digit possible digit subsets in favorable zones*,** Cycle (1,2,9) of triplets** discovered in C5 -- **R8C5 3**. And this is an important not so easy to find breakthrough.

In favorable column C2 with 4 digits filled, the **possible digit subset DS [1,4,5,6,9]** gets reduced by **existing digits [4,5,6]** in both cell R7C2 and R9C2 forming the **Cycle of twins (1,9)** in the two cells and **R8C2 4** by further reduction of [1,9] from DS [1,4,9 in the cell.

This is the **second similar breakthrough.**

A **Cycle of twins (5,6)** formed in rest of the two cells R3C2 and R6C2 in C2 by leftover two digits.

**R2C1 4** by scan for 4 in R1, C2, C3 -- R2C3 8 by scan for 8 in R1, R3.

**R9C1 8** by scan for 8 in R8, C2, C3.

**R9C3 3** by scan for 3 in R7, R8. R7C3 2 by scan for 2 in C1 -- **R8C1 7** by exception in bottom left major square.

**Single digit lock on 3** formed in R4C7, R4C8 by scan for 3 in C9.

This lock on 3 in R4 debars any other empty cell in R4 to have digit 3.

That creates the **next breakthrough in R6C1 3** by scan for 3 in R4 by lock on 3, and 3 in C2, C3.

**R1C3 7** by scan for 7 in R3, C1.

Results of the actions taken shown.

### Solving very hard Sudoku puzzles: Level 4 Game 14 Stage 2: Breakthrough by Parallel digit scan, Single digit lock, Cycles of twins and DSA technique

**Highlight color** of **valid cells** at this **second stage** is light blue.

First **breakthrough at this stage is at R2C9 7** by **parallel digit scan for 7** on **empty cells of R2** by elimination of R2C4, R2C5, R2C6 for 7 by 7 in top middle major square and by elimination of R2C8 for 7 by 7 in C8.

A **single digit lock on 6** is formed in R3C2, R3C3 by scan for 6 in C1.

This helps to get the **next breakthrough in R2C4 6** by scan for 6 in R3 lock on 6, C4, C5.

**A big breakthrough created in R3C8 3** by reduction of [5,9] because of **Cycle (5,9) of twins** formed in R2C8 and R7C8. The first cell DS was earlier formed naturally from rest of the digits [1,5,9] in R2.

We'll explain in more details the possible digit analysis in R7C8, the formation of the Cycle of (5,9) and the breakthrough of R3C8 3. This is **application of DSA technique.**

The possible digit subset DS in R7 [1,5,7,8,9] reduced by [1,7,8] in C8, creating thus the possible digit subset DS [5,9} also in R7C8. This cell DS joined with the [5,9] in R2C8 in the same column C8 forms the Cycle of breakthrough twins (5,9).

As a result, we get the **important breakthrough in R3C8 3 by DSA reduction**: the possible digit subset in R3C8 first reduces by 6 of the single digit lock on 6, by 2 in top right major square and by [5,9] from Cycle (5,9), that is, by [2,5,6,9] as a whole from the possible digit subset DS in C8 of [2,3,5,6,9] leaving single naked digit 3 for R3C8.

**R1C6 3** by scan for 3 in R2, R3 -- **R4C7 3** by scan for 3 in C8, C9.

**R3C7 4** by **parallel digit scan for 4 on empty cells of C7:** eliminating bottom three cells in C7 by 4 in bottom right major square and eliminating R1C7 by 4 in R1.

**R1C8 6** by reduction of [1,5,9] from possible digit subset [1,5,6,9] in R1 by [1,5,9] in C8 -- **R4C8 2** by exception in C8.

Game status shown below.

### Solving very hard Sudoku puzzles: Level 4 Game 14 Stage 3: Breakthrough by Parallel digit scan and Cycle of twins

**Highlight color of valid cells** at this **third stage**, which is not the last stage, is light grayish yellow.

**R1C9 9** by **parallel scan for 9 on empty cells of R1:** eliminating R1C1 for 9 by 9 in C1, eliminating R1C7 for 9 by 9 in C7.

This is followed by **R2C8 5** by reduction -- **R1C7 1** by reduction -- **R1C1 5** by reduction -- R4C1 1 by reduction.

With 5 in R1C1, **R3C2 6** by reduction -- **R3C3 1** by reduction -- **R6C2 5** by reduction.

With 1 in R1C7, **R8C7 6, R9C7 7, R7C7 5, R7C8 9** by reduction -- **R7C2 1** by reduction -- **R9C2 9** by reduction.

**Cycle (4,6) of twins** formed by leftover two digits in left middle major square and C9.

All breakthrough have been taken care of.

Results shown.

### Solving very hard Sudoku puzzles: Level 4 Game 14 Final Stage 4: Rest are easy

**Highlight color of valid cells** at this **fourth and last stage** is light cyan.

With 2 in R4C8, R4C5 9 by reduction of 2 -- R2C5 1 by reduction of 9 -- R2C6 9 by reduction of 1 -- R6C5 2 by reduction of [1,9].

With 9 in R4C5, R4C3 6 by reduction of 9 -- R6C3 9 by reduction of 6, R4C9 4 by reduction of 6 -- R6C9 6 by reduction of 4.

R8C4 9 by scan for 9 in R7, R9, C6.

R5C4 3 by scan for 3 in R4, R6, C6 -- R5C6 8 by reduction of 3.

R7C4 8 by scan for 8 in R9, C6 -- R7C6 7 by exception in R7 as the only digit left.

R4C4 7 by cross-scan for 7 in R6, C6 -- R4C6 5 by exception in R4 -- R3C4 5 by scan for 5 in C6 -- R3C6 2 by exception in R3 -- R8C6 1 by reduction of 2 -- R9C4 2 by exception in bottom middle major square.

With 1 in R8C6, R8C9 2 by reduction of 1 -- R9C9 1 by exception in C9.

R6C6 4 by exception in C6 -- R6C4 1 by exception in C4, and 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.

Aggressive breakthroughs by advanced Sudoku techniques of Parallel digit scan, Single digit lock, Cycles of twins and triplets ensured quick solution to this 14th very hard Sudoku puzzle at level 4.

There has been no need to unnecessarily enumerate the possible digit subsets in many empty cells thus speeding up the solution.

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