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Solving Sudoku Expert Level 5 Game 10 Quickly

Solving Sudoku Expert Level 5 Game 10 Quickly

Learn solving Sudoku expert level 5 game 10 quickly

Challenge of solving Sudoku expert level 5 game 10 met by using advanced Sudoku techniques aggressively from the very start with easy to learn steps.

Sections are,

  1. A few words on Expert Sudoku
  2. Expert Sudoku level 5 game 10
  3. Solving expert Sudoku level 5 game 10 by advanced Sudoku techniques and strategy
  4. Expert Sudoku Strategy for quick solution

You may move directly to any of the above sections by clicking its link and return to previous position by clicking on browser back button.

To skip the following first section of "A few words on Expert Sudoku", Click here.


A few words on Expert Sudoku

This level of Sudoku we consider as equivalent to level 5 Sudoku, the hardest Sudoku.

An expert Sudoku will definitely be hard, but the most distinctive feature of an expert Sudoku is its numbers of digits filled initially. The number of filled digits in the 81 cells to start with will be in most cases 22 or 23, a very low figure.

But interestingly you may find even a 23 filled cell Sudoku easier to solve than a level 4 Sudoku with 25 filled cells. We won't assure that you will find any expert Sudoku solved here as extremely difficult for you.

But that won't be the norm. Generally an expert Sudoku will be really hard. As hardness of a Sudoku puzzle cannot be measured and is in reality a relative and changing attribute, you cannot point to a Sudoku classifying it with hardness level 5.

That's why we say at this point that distinctive feature of an expert Sudoku will be its number of filled digits as 22 or 23 in most cases. In a rare case, if we find a 24 cells filled Sudoku very very challenging we would include it here as an expert Sudoku.

To sum up, if you are after learning how to solve very challenging Sudoku puzzles, this should be the category for you.


Expert Sudoku level 5 game 10

The following is the Sudoku puzzle that should engage your mind for some time. The Rs are the row labels, Cs are the column labels.

Expert Sudoku level 5 game 10

The detailed strategy for quickly solving expert Sudoku is placed after the solution.

Following is the solution of the puzzle explained step by step in details. The techniques used should be understood from the detailed explanatory.

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


Solving Sudoku Expert level 5 game 10 Stage 1: Breakthrough by Double digit scan, Single digit lock, Parallel digit scan and Cycles of twins and triplets

We'll show the puzzle again for ease of understanding.

To follow the details accurately, you should better have the game actually with you written on paper, or better stillcreated in a spreadsheet.

Expert Sudoku level 5 game 10

Strategy adopted in brief: start with row column scan coupled with aggressive breakthroughs by advanced Sudoku techniques.

To skip the rest of the brief strategy click here.

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 or even a parallel scan also.

When possible valid cell by a row column scan is exhausted, we take up the next two patterns of possible digit analysis DSA technique and forming Cycles of twins or triplets (or of even larger number of cells).

A little later when more cells are filled with unique digits, we raise our alertness for more powerful breakthrough digit patterns such as an X wing.

On the whole, we are always ready to force a breakthrough using even an advanced Sudoku technique at the early stages if feasible.

On the other hand, we are always ready to look for the simplest method of row column scan even when facing a bottleneck.

Main focus is to either find a valid cell or forming a breakthrough pattern such as Single digit lock, Cycles of twins or triplets or X wing at the earliest.

In the process, avoiding enumeration of time-consuming and unnecessary evaluation of possible digit subsets in empty cells speeds up the solution considerably.

Highlight color of valid cells in this first stage is banana leaf green.

By row column scan we don't get any success except a single digit lock on 6 in R3C7, R3C9 by cross-scan for 6 in R2 and C9. It doesn't give us any breakthrough rightaway. So we preserve it for later use.

A single digit lock never fails to result in a breakthrough in our experience.

While still in scanning mode, now we look for the scan variant of double digit scan and actually get a valuable Cycle of twins (3,8) by double digit scan for [3,8] simultaneously in R5, C3 on empty cells of left middle major square.

And this gives us the first breakthrough in R4C3 4 by a simple scan for 4 in R5 on empty cells of left middle major square.

Leftover three digits form a valuable Cycle of triplets (1,6,7) in R5C1, R5C2, R5C3. This reduces the DS in R5 and creates another valuable Cycle of triplets (2,5,9) in right middle major square which reduces the possible digits in the cells of this parent major square.

Let's now get a difficult breakthrough valid cell R8C2 5 by possible digit analysis DSA reduction in promising cells and forming a Cycle of triplets.

First form the DS of [2,5] in R8C2 as rest seven digits [1,3,4,6,7,8,9] exist in the three parent zones of the cell, R8, C2 and bottom left major square. This is possible especially because of force-forming the Cycle of twins (3,8) in C2.

Next step is easy. The possible digit subset DS in C3 is [1,2,6,7,9] and with [1,7] in bottom left major square, the DS for the three cells R7C3, R8C3 and R9C3 reduces to [2,6,9].

With three digits left for three cells, a breakthrough Cycle of triplets (2,6,9) is formed in these three cells in the parent major square.

Finally, the Cycle (2,6,9) reduces [2] from DS [2,5] in R8C2 to give us the breakthrough R8C2 5.

As a bonus, the Cycle of triplets (2,6,9) gives us another breakthrough in R6C1 6.

This happens by scan for 6 in R2, lock on 6 in R3, and Cycle (2,6,9) lock on 6 in C3.

We ignore other breakthrough possibilities to preserve status for ease of explanation but will take the valid cell R7C2 4 by reduction of [1] by existing digit 1 in bottom left major square and [2,6] in Cycle (2,6,9) from DS [1,2,4,6] in C2.

Result of the steps taken shown below.

Expert Sudoku level 5 game 10 Stage 1

Solving Sudoku Expert level 5 game 10 Stage 2: Breakthrough preparation by Single digit lock

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

First valid cell at this stage we take R3C1 4 by scan for 4 in R2, C2, C3.

Followed by R2C1 5 by scan for 5 in C2, C3 -- R1C3 7 by scan for 7 in C2 -- R5C3 1 by reduction -- R5C2 6 by reduction -- R5C1 7 by reduction.

R1C5 4 by scan for 4 in R2, R3, C4, C6 -- R9C7 4 by scan for 4 in R7, R8, C8 -- and lastly R6C9 4 by scan for 4 in R5, C7, C8.

R2C5 8 by scan for 8 in R1, R3, C6.

We will close this stage by forming a single digit lock on 7 in R4C6, R6C6 by scan for 7 in C4. This will give us the first breakthrough next stage.

The game status shown below.

Expert Sudoku level 5 game 10 Stage 2

Solving Sudoku Expert level 5 game 10 Stage 3: Breakthrough by Single digit lock, DSA reduction, Parallel digit scan, Cycle of twins

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

First breakthrough at this stage is in R3C5 7 by scan for 7 in C4 and single digit lock on 7 in C6.

Possible digit subset reduced to [1,2,5] in C5 by DSA reduction -- R9C5 2 by reduction of [1,5] in R9 from [1,2,5] -- R8C5 1 by reduction -- R7C5 5 by exception in C5.

Next breakthrough is in naked single R9C8 8 by DSA reduction of [3,6,9] in bottom right major square and C8, from DS [3,6,8,9] in R9.

Followed by R4C9 8 by scan for 8 in R5, C7, C8 -- R4C2 3 by reduction of 8 -- R6C2 8 by reduction of 3.

A big breakthrough by parallel scan for 8 on empty cells of R7 in R7C1 8.

Cells R7C3 eliminated by 8 in C3, R7C6 eliminated by 8 in C6, R7C8, R7C9 eliminated by 8 in bottom right major square. The only cell left in R7 is R7C1 8.

This results in further valid cells:

R8C1 3 by reduction of 8 -- R7C9 3 by scan for 3 in R8, C8 -- R7C6 6 by reduction of 3 -- R7C3 2 by reduction of 6 -- R8C3 9 by reduction of 2 -- R9C3 6, R8C4 8 by reduction of 9.

R7C8 1 by reduction of 2 -- R6C8 7 by reduction of [1,8] -- R4C8 6 by reduction of [1,7,8].

Appreciate the importance of the critical breakthrough in R7C1 8.

All the rest will be routine valid cells that we will show next stage.

The puzzle game at this stage is shown below.

Expert Sudoku level 5 game 10 Stage 3

Solving Sudoku Expert Level 5 game 10 Final Stage 4: Rest are routine valid cells

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

With 7 in R6C8, R4C6 7 by scan for 7in R6, C4.

R4C7 1 by reduction of 5 by Cycle of triplets (2,5,9) from DS [1,5] in R4 -- R4C4 5 by reduction of 1.

With 6 in R4C8, R3C76 by scan for 6 in R1, R2, C8, C9.

R6C7 3 by scan for 3 in R5.

R8C7 7 by scan for 7 in C8 -- R8C8 2 by exception in R8 -- R3C8 5 by scan for 5 in R2, C9.

R2C9 7 by scan for 7 in R1, R3, C7 -- R3C9 9 by scan for 9 in R1, C7 -- R3C4 3, R5C9 2 by reduction of 9 -- R5C7 5 by reduction of 2 -- R5C8 9 by reduction of 5.

With 2 in R5C9, R1C9 1 by reduction -- R1C4 2 by reduction -- R1C6 5 by exception in R1, R6C4 1 by reduction of 2 -- R6C6 2 by reduction of 1.

Pending R2C7 2 by exception in top right major square -- R2C2 1 by reduction -- R3C2 2 by reduction -- R3C6 1 by exception in R3 -- R2C6 9 by reduction of 1 -- R9C6 3 by reduction of 9 -- R9C4 9 by reduction of 3.

Final solution below.

Expert Sudoku hard level 5 game 10 final stage 4


Expert Sudoku Strategy for quick solution

As a strategy we always try first—the row-column scan to find the valid cell at any stage, because that is the most basic and easiest of all techniques.

Valid cells by row column scan occasionally are also called as hidden singles, but to us process is row column scan and outcome is valid cells with unique digits.

When easy breaks by row-column scan becomes hard to come by, the next technique is used.

Next easy to use technique used is—identification of single valid digit for a cell by Digit Subset Analysis or DSA in short.

For a specific promising cell, considering digits existing in three parent zones, the subset of possible digits is enumerated. If the subset consists of a single digit, it becomes a naked single and we get a breakthrough by possible digit analysis or DSA technique.

And wherever possible, Cycles of twins or triplets are formed that in any situation are a treasure to have and Cycles play a key role in quick solution.

In a Cycle (1,2) of twins say in R8C5 and R9C5, the two digits may appear in any one of only these two cells in the zone column C5 and the bottom middle major square. By this twin digit Cycle, it becomes a certainty that as a group the two digits, locked in these two cells, cannot appear in any other cell in the parent zones of the Cycle and thus possible digits in the corresponding empty cells are reduced in C5 and bottom middle major square.

You may wait for Cycles to form automatically in a column or row.

But a proactive approach of forming a Cycle by DS analysis speeds up the solution process considerably. This is what we call forced creation of Cycles.

The last resort of filling EACH EMPTY CELL with valid digit subsets is to be taken when it is absolutely necessary. Only with all empty cells filled with valid digit subsets, the possible breakthrough points in a hard puzzle can be discovered.

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

In hybrid strategy, a few of the cells of interest are filled with DS of shorter length and analyzed for a breakthrough such as forming a Cycle or a single digit lockdown.

One of the most powerful patterns that we have used for highly positive result each time is the lock on a single digit in a row or column inside a 9 cell major square so that the digit is eliminated from all other DSs in the locked row or column outside the 9 cell square.

The necessity of use of this digit lock technique indicates in a way the hardness of the puzzle.

In solving this Expert Sudoku, we have mentioned the use of a technique of Parallel scan for a single digit on the cells of a row or column. Occasionally this may provide a very critical difficult to get breakthrough.

Similarly an exceptional pattern and technique for breakthrough is double digit scan where instead of a single digit, a scan for two digits simultaneously is carried out on empty cells of a major square. This usually has a valuable outcome.

A powerful Sudoku digit pattern is 4 cell single digit lock that may be encountered in very hard or expert level Sudoku hard puzzles. Naturally, it is a superset of the more common single digit lock in 2 cells and so is much more effective.

This powerful digit pattern is the single digit rectangle or X wing. In solving this Expert level 5 Sudoku hard puzzle, X wing provided the most important breakthrough.

A basic part of overall strategy is,

Whether we search for a breakthrough of a bottleneck or a valid cell identification, our focus usually is on the promising zones, the zones (row, column and 9 cell square combined) that contain larger number of filled digits including Cycles.

The main strategy should always be to adopt the easier and faster technique looking for key patterns all the time. Parallel digit scan, Double digit scan, Single Digit lock, Cycles of twins or triplets, Valid cell by DSA are some of the key patterns. Occasionally you may need to use X wing for a difficult breakthrough.

Focus when solving a hard Sudoku puzzle should be on using the technique that would produce best results fastest. Easy to say, not so easy to do—comes with practice.


End note

Like the previous ninth expert Sudoku puzzle, finding valid cells has been tough at the start. This is natural for a very hard expert Sudoku. In this class of Sudoku puzzles, you will always find multiple barriers or bottlenecks that are difficult to overcome.

For this expert Sudoku, the first stage barriers are broken down by advanced Sudoku techniques of double digit scan, parallel digit scan and single digit lock.

The most critical barrier in the third stage is overcome again by a difficult to discover parallel digit scan, and this has been the last of the hurdles in this tough expert Sudoku puzzle.

It has been a fittingly challenging expert Sudoku game.


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