## Learn how to solve Expert Sudoku hard level 5 game 20 quickly simple way

Expert Sudoku hard level 5 game 20 solved simple way using Sudoku solving techniques of DSA, parallel scan, Cycles and double digit scan.

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**Expert Sudoku Hard level 5 game 20****How to solve Expert Sudoku Hard level 5 game 20 simple way by Sudoku solving techniques****Expert Sudoku Solving Techniques and How to Use Special Digit Patterns****.**.**Expert Sudoku solving techniques of single digit scan and double digit scan****Expert Sudoku Solving Technique of Possible Digit Subset Analysis (DSA) and how to find a naked single.**.**Special digit pattern of Cycle of twins or triplets and how to use it in solving an Expert Sudoku puzzle****Expert Sudoku solving technique of parallel scan for a single digit on a row or a column.**

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### Expert Sudoku Hard level 5 game 20

The following Expert Sudoku hard game 20 is solved using Sudoku Solving Techniques. The techniques used are separately explained after the solution, but you must first try your best to solve the puzzle that will enrich your mind.

The Rs are the row labels, Cs are the column labels.

Following is the **solution of the puzzle explained in simple way.**

*Please spend your time fruitfully on the game trying to solve it before going through the solutions.*

### How to Solve Expert Sudoku Hard level 5 game 20 Simple Way by Sudoku Solving Techniques Stage 1: Double digit scan, Parallel scan, DSA, Cycles

R1C4 5 scan R2, R3 -- R2C6 9 scan R3 -- Cycle (2,7,8) in R3C4, R3C5, R3C6 in R3.

**Cycle (1,4)** in R3C2, R3C8 in R3 -- R3C8 6 as residual single digit in R3.

R6C3 8 scan R4, R5 -- R2C1 8 scan C2, C3.

**Parallel scan for 4 on empty cells of C1** -- R4C1 4 : R5C1 eliminated by 4 in R5, R8C1, R9C1 eliminated by 4 in left bottom major square.

R4C5 6 scan C4, C6, R6. **Cycle (1,9)** on R4C4, R5C4 by **double digit scan [1,9] R6, C6.**

**Leftover Cycle (2,5,7)** in R4C6, R5C6, R6C5 in central middle major square by DSA -- R6C6 4 by reduction -- R6C4 3.

**Unexpected Cycle (2,7) by DSA** in R4C8, R5C8 in right middle major square by reduction of [3,5,9] in C8 from DS [2,3,5,7,9] in the major square -- R6C7 5 by reduction of [3,9] in R7 -- R5C9 9 by reduction of 3 in C9 -- R4C7 3 as residual digit.

Status Shown.

### How to Solve Expert Sudoku Hard level 5 game 20 Stage 2: DSA, Cycles

With 5 in R6C7, R6C5 7 -- R3C5 2.

**Cycle (2,7)** in R8C1, R8C4 as DS [2,4,7,8] in R8C4 in C4 reduces by [4,8] in R8 -- DS [1,5,6] in R8 reduces by [5,6] in C7 -- R8C7 1 -- R8C5 5 -- R7C5 9 -- R9C5 1 -- R8C9 6 as residual digit in R8.

R3C8 1 scan on 1 in C7, C9, R1 -- R3C2 4 reduction.

Cycle (2,7) in R1 by **double digit scan of Cycle [2,7] in R2.**

R1C2 7 reduction by 2 in C2 -- R1C3 2. Cycle (1,3) in R2.

R1C7 9 scan 9 in C8, C9, R2. Cycle (4,8) in top right major square. **Cycle (2,4,7,8)** formed in R9C4, R9C6, R9C7, R9C8 **by DSA.**

Status shown.

### How to Solve Expert Sudoku hard level 5 game 20 final Stage 3: Cycles, DSA

The **Cycle of (2,4,7,8) reduces [2,7] in DS [2,3,7] in R9C1 by DSA** -- R9C1 3 -- R5C1 7 -- R8C1 2 -- R8C4 7 -- R9C6 8 -- R9C8 4 -- R9C4 2 -- R9C7 7 -- R2C7 2 -- R7C7 8 -- R1C8 8 -- R1C9 4 -- R2C9 7.

R7C4 4 as residual digit in bottom middle major square.

R7C9 2 scan for 2 in R8, R9 -- R9C9 5 as residual digit in bottom right major square.

R7C3 7 scan R9, C2 -- R7C2 5. R9C2 9 scan C3 -- R9C3 6.

With 8 in R9C6, R3C6 7 -- R3C4 8.

R4C8 7 scan 7 in R5 -- R5C8 2 residual -- R5C6 5 reduction.

R4C4 9 scan for 9 in C6, R5 -- R4C6 2 by scan for 2 in R5 -- R5C4 1 residual in central middle major square.

R4C3 5 scan for 5 in R5, C2 -- R4C2 1 residual in R4.

R2C3 1 scan for 1 in R3C2 -- R2C2 3 residual in R2 -- R5C2 6 -- R5C3 3.

Final solution shown.

Check for the validity of the solution if you need.

### Expert Sudoku Solving Techniques and How to Use Special Digit Patterns

As a strategy * always try first—the row-column single digit scan to find the valid cell *at any stage, because that is the

**most basic and easiest of all techniques.**

While doing the single digit scan, look out for possible breakthroughs by double digit scan and even triple digit scan. Wherever possible, **Cycles** are formed that in any situation are valuable digit patterns to have and Cycles play a key role in quick solution.

Possible **Digit Subset Analysis** or **DSA** is a general technique that is the basis of finding a unique valid digit for a cell by Reduction, a Cycle or even the valuable digit pattern of a single digit lock. Whenever possible, short length possible digit subsets of 2 or 3 digits are to be formed in vacant cells by DSA.

A **Single digit lock** and an **X wing** are comparatively more powerful digit patterns that usually create important breakthroughs.

The **last resort of filling EACH EMPTY CELL with valid possible digit subsets** by DSA is to be taken when it is absolutely necessary. But,

Strategically for faster solution, it is better to delay this time consuming task as much as possible.

A **basic part of overall strategy** is,

Whether we search for a

breakthrough of a bottleneckor avalid cell identification, our focus usually is on thepromising zones,the zones (row, column or a major square) that contain larger number of filled digits including Cycles.

The main strategy should always be to adopt the easier and faster technique and path to the solution by looking for key patterns all the time. Digit lock, Cycles, Valid cell by DSA are some of the key patterns.

The four Sudoku solving techniques and special digit patterns used in solving the puzzle are explained now.

#### Expert Sudoku solving techniques of single digit scan and double digit scan

Let us use the following Sudoku game as the startiing point to explain the two techniques of single digit and double digit scan.

This is an initial stage of the Sudoku puzzle solution.

The result of breakthroughs by single digit scan and double digit scan are shown.

Digit scans are done on the cells of a major square. Single digit scan for 8 in R9C9 in C9 and in R5C3 in R5 blocks all other cells in the target right middle major square except R4C8. This is then the only cell in the major square where digit 8 can be placed. Single digit scan blocks then all other cells in the target major square except ONE cell to be occupied by the scanned digit.

This is the most used and most basic technique to find a unique cell for a digit.

In the same way, digits [1,9] appear in R6 and the pair of digits blocks R6C1, R6C2 and R6C3 for both the digits [1,9] in the target left middle major square. This is the **double digit scan**.

This leaves ONLY TWO VACANT CELLS for the two scanned digits [1,9] in the major square as well as in column C3.

This digit structure of two possible digits for only two cells in a column, row or a major square is termed as a two-cell Cycle.

Every opportunity of forming Cycles are utilized because, Cycles play a very important role in solving very hard to extremely hard Sudoku Puzzles.

Just as single digit scan on the cells of a major square is done searching for suitably affecting digit in multiple rows and columns, double digit scan can also be done with same two digits appearing in more than one row or column affecting the cells of a specific major square.

Double digit scan invariably provides an important breakthrough. Always look out for an opportunity for a double digit scan.

The concept of double digit scan can be extended to triple digit scan as well though it is rare. In this case a three digit long Cycle is formed.

#### Expert Sudoku Solving Technique of Possible Digit Subset Analysis (DSA) and how to find a naked single

The following is an initial stage of the Sudoku puzzle solution.

The result of finding a unique valid cell or naked cell by digit subset analysis technique applied on the above game stage shown now.

Digit Subset Analysis or DSA is a concept as well as a technique. By DSA, digits that can occupy a particular cell are identified.

This is an essential and very important function for identifying all other digit patterns possible in a target cell. When no easy unique possible digit in any cell can be identified, the only way to move ahead in solving the puzzle is to carry out DSA for PROMISING CELLS. The simplest type of promising cell is the cell with smallest number of possible digits DS of 2 or 3 digits (not 4 digits at first).

To identify a promising cell, identify first a row, column or major square with maximum number of already occupying digits. In the example above, row R4 is such a row with possible digit subset in the four empty cells [1,2,7,9].

Next, the cell R4C4 is easily identified as a promising cell as, [2,9] in Column C4 affecting the cell REDUCES the possible digit subset or DS for the cell to just [1,7]. Moving ahead, the third cell R4C6 gets DS [1,7,9].

And finally, for the fourth empty cell in the row R4C9, [1,9] in its parent major square and 7 in parent column C9 combine to form [1,7,9] to be reduced from the DS [1,2,7,9]. Result is, **R4C9 2**, a valid unique digit for a cell.

REDUCTION is a fundamental process in solving Sudoku puzzles.

**Naked Single:** By definition, a naked single is a digit that only can occupy a specific cell. If you analyze possible digits in R4C9 ignoring the earlier process of reduction from DS [1,2,7,9] in row R4, you will find only digit 2 can occupy the cell.

You may adopt this process of identifying a naked single **WITHOUT taking help of smaller possible digit subsets in vacant cells**, but this process is easier only occasionally.

#### Special digit pattern of Cycle of twins or triplets and how to use it in solving an Expert Sudoku puzzle

The following is an initial stage of the Sudoku puzzle solution.

The result of a breakthrough unique valid digit by forming 2 digit (twin) and 3 digit (triplet) Cycles is shown.

The digits [1,9] in R6 affect the possible digit subsets or DSs of vacant cells of left middle major square leaving only two cells of the square R4C2, R5C2 for the two digits [1,9]. It is not certain which of these two cells will finally be occupied by 1 or 9 but we can confidently say none other than these two digits are the **only eligible candidates** for occupying these two cells.

Thus a **Cycle (1,9)** is formed in these two cells restricting any other cell in the parent column and major square from having any of these two digits.

If we place 1 in R4C2, automatically R5C2 must have 9 and if we place 9 in R4C2 the cell R5C2 must have 1. Potentially these two digits Cycle between these two cells till their final positions are determined. That is why we can place the DS [1,2] in both the cells blocking any other cell of parent major square and column C2 from having these two digits.

This is a two digit Cycle and is the most frequently occurring one.

The direct positive result is formation of a second Cycle (3,5,7) in the three remaining vacant cells by exactly three remaining digits in the major square. This is a three-digit Cycle debarring all other vacant cells of parent row R6 to have these three digits. Result is formation of a third Cycle (4,8) in R6C5, R6C6 and a unique valid digit 6 in R6C9 as the REDUCED DS [4,6,8] in R6C9 is further reduced by [4,8] in C9 and right middle major square combined.

This breakthrough won't have been possible without the Cycle (3,5,7) in R6.

The main function of a Cycle is to REDUCE the length of possible digit subsets or DSs in affected parent zones and with each DS length reduction, certainty of getting a unique valid cell in the whole set of 81 squares increases.

#### Expert Sudoku solving technique of parallel scan for a single digit on a row or a column

The following is an initial stage of the Sudoku puzzle solution.

Result of carrying out parallel scan for digit 2 on the vacant cells of row R8 is shown.

In the relatively empty 81 square puzzle, digit 2 in left bottom major square and right bottom major square debar every vacant cell in the squares from having digit 2. With keen interest we observe, out of six vacant cells in row R8, four cells cannot have digit 2. If we can debar any of the two other remaining cells R8C5, R8C6 from having digit 2, we will get a unique valid digit breakthrough.

This actually happens, as 2 in R1C6 in C6 eliminates the fifth vacant cell R8C6 from having digit 2. We have achieved the breakthrough of unique valid digit 2 in R8C5 as if out of thin air.

In essence, a PARALLEL DIGIT SCAN for digit 2 is done on the empty cells of row R8. Even if digit 2 in R9C3 were in R2C3 or R3C3, the result would have been the same.

A parallel digit scan is done on vacant cells of a row or column (and NOT on vacant cells of a major square). Fortuitous presence of the digit scanned in other cells, all except one cell of the target row or column scanned are debarred from having the digit scanned for. This is an advanced and powerful Sudoku Solving Technique often providing a major unexpected breakthrough.

Observe, you could also have achieved the breakthrough by forming the five-cell long Cycle (1,3,4,6,8) in R8. But that would have been laborious. If you are aware of the possibility, a parallel scan will give you a quick and clean breakthrough.

*To go through the solution of this Expert Sudoku puzzle once more, click here.*

### More Expert Sudoku puzzles you may like to solve and learn how to solve

The **updated list** of **Solutions to Expert Sudoku **puzzle games:

**How to solve Expert Sudoku puzzle games full list****.**

Expert Sudoku solving strategy and techniques are included in many of the solutions.

*Enjoy solving and learning to solve Expert Sudoku puzzles.*