## How to solve very difficult Sudoku puzzle level 4 game 13 quickly by advanced Sudoku techniques

Solving very difficult Sudoku puzzles: Level 4 game 13 solved quickly 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.

### The very difficult Sudoku puzzle level 4 Game 13

Before going through the solution solve the puzzle first.

### Solving very difficult Sudoku puzzles: Level 4 Game 13 Stage 1: Breakthrough by Single digit lock, 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.

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,**

**R5C6 5** by scan for 5 in R4, R6, C4 -- **R2C5 5** by scan for 5 in C4, C6 -- **R9C9 5** by scan for 5 in R8, C7, C8 on empty cells of bottom right major square -- **R3C2 5** by scan for 5 in R1, R2, C3 on empty cells of top left major square -- **R7C1 5** by scan for 5 in R9, C2, C3 on empty cells of bottom left major square.

Digit 5 over.

**R6C4 6** by scan for 6 in R5, C4, C6.

**R1C1 6** by scan for 6 in R2, C2, C3 on empty cells of top left major square.

**R2C4 8** by scan for 8 in C4, C5 on empty cells of top middle major square.

** R5C5 7** by scan for 7 in R6, C4, C6 on empty cells of central middle major square.

With possible digit subset in top middle major square reduced to [1,3,4] and 3 in R1, a **Cycle of twins (1,4)** formed in R1C5, R1C6 by reduction of 3 and valid cell **R3C6 3** by reduction of [1,4].

**R5C3 7** by scan for 7 in R4, R6, C1 on empty cells of left middle major square.

Time for more advanced Sudoku techniques starting with a **single digit lock.**

A **single digit lock on 8** created in R3C7, R3C8 by cross-scan for 8 in R2 and C9.

With this lock on 8 in R3, the possible digit subset in R3C3 is reduced by [6,7,8] from the DS [4,6,7,8] to create the valid cell breakthrough of **R3C3 4** -- **R3C9 6** by reduction of [7,8] in C9 from DS [6,7,8] in R3C9.

Next advanced techniques we'll use is **Parallel digit scan and double digit scan.**

**A major breakthrough of R6C1 8** by **parallel digit scan for 8** on empty cells of C1 by elimination of cell R2C1 by 8 in R2, cell R5C1 by 8 in R5 and cell R9C1 by 8 in R9 leaving only the cell R6C1 for digit 8.

A **breakthrough Cycle (6,8)** of twins formed in R4C7, R4C8 by **double digit scan for [6,8]** in as many as three zone, namely, R5, R6, C9 on empty cells of right middle major square.

It's a powerful resource to have and a bit difficult to identify.

Though difficult, this type of possibilities are easy to spot if you are on the lookout for it.

Results of the actions taken shown.

### Solving very difficult Sudoku puzzles: Level 4 Game 13 Stage 2: Breakthrough by Parallel digit scan, Single digit lock and Cycles of twins

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

We'll start from where we left.

First **breakthrough by parallel digit scan for 1** on empty cells of R4: by elimination of cell R4C2 by 1 in C2 and cell R4C9 by 1 in C9, single cell left for 1 in R4 is** R4C6 1**.

This paves the way for more valid cells for 1 by simple row column scan: **R6C3 1** by scan for 1 in R4, C1, C2 -- **R5C7 1** by scan for 1 in R4, R6, C9 -- **R1C5 1** by scan for 1 in R2, R3, C6.

An opportunistic valid cell hit in **R5C5 9** by scan for 9 in single column C4 -- **R8C6 9** by scan for 9 in C4, C5. This creates the opportunity of another valid cell for digit 1 in **R7C4 1** by scan for 1 in R9 and C5.

And lastly, **R8C8 1** by scan for 1 in R7, R9, C7, C9. Digit 1 fully filled.

**R5C4 3** by exception in central middle major square -- **R9C4 2** by exception in C4.

**R1C5 4** by exception in top middle major square.

Next **breakthrough by a single digit lock on digit 9** formed in R4C9, R5C9 by scan for 9 in R6. This helps to create the valid cell **R1C9 2** **by reduction of [8,9] in C1** from possible digit subset of [2,8,9] in R1 and hence in R1C9.

A **byproduct is the Cycle (8,9)** of twins in R1C2, R1C3 that will have reducing effect on the empty cells of top left major square.

An immediate gain is in **R2C2 7** by scan for 7 in C1, C3 followed by **R2C3 2** by scan for 2 in C1 and **R2C1 3** as exception in top left major square.

Game status shown below.

### Solving very difficult Sudoku puzzles: Level 4 Game 13 Stage 3: Minor breakthrough by Cycle of twins and DSA or reduction by possible digit subset analysis

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

Notice that the empty cells are largely filled and we are very near to the last of the challenges.

We'll first use the **Cycles (3,4) of twins** formed as leftover digits first in R8C5 and then in R8C9. This twin reduces the possible digit subset in R8 to [2,6,8] leading to **R8C3 8** by reduction of [2,6] from [2,6,8] in C3.

This is followed by **R8C2 2** by reduction of 6 in C2 -- **R8C7 6** by exception in R8.

With 8 in R8C3, **R1C3 9** by reduction -- **R1C2 8** by reduction -- **R7C3 3** by exception in C3.

With 6 in R8C7,** R4C7 8** by reduction of 6 -- **R3C7 7** by reduction of 8 -- **R3C8 8** by reduction of 7 and **R2C8 6** by reduction of 8.

**R7C7 2** by scan for 2 in R9, C8, C9 -- **R9C8 7** by scan for 7 in R7, C7, C9.

In this penultimate stage it is easier and faster to get a valid cell by good old row column scan.

Now only a few cells are left to be resolved and the way is clear.

All breakthrough have been taken care of.

### Solving very difficult Sudoku puzzles: Level 4 Game 13 Final Stage 4: Rest few cells are easy to resolve

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

The deluge of valid cell at this last stage starts with **R8C9 3** by reduction of 4 from the Cycle of twins (4,9) formed with leftover cells in bottom right major square.

With 3 in R8C9, R8C5 4 -- R9C5 3 -- R4C9 9 -- R5C9 4 -- R6C8 3 -- R6C2 4 by reduction -- R7C2 9 by reduction -- R7C8 4 -- R2C8 9 -- R2C7 4 -- R9C7 9 -- R9C1 4 -- R5C1 9 -- R4C2 3.

Final solution below.

Highlight of background colors in 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 13th very hard Sudoku puzzle at level 4.

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

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