Learn how to solve expert Sudoku level 5 game 6 quickly
The expert Sudoku game 6 solved using advanced Sudoku techniques and expert Sudoku strategy so that it is easy to learn how to solve expert Sudoku quickly.
- A few words on Expert Sudoku
- Expert Sudoku level 5 game 6
- Solving expert Sudoku level 5 game 6 by advanced Sudoku techniques and strategy
- Expert Sudoku Strategy for quick solution
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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.
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.
The 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 Expert Sudoku level 5 game 6 Stage 1: Breakthrough by Double 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 still—created in a spreadsheet.
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.
The very first valid cell by row column scan is in R2C3 2 by scan for 2 in R1, R3, C2.
Cycle of twins (1,2) in R8C5, R9C5 by double digit scan for [1,2] in R7, C6 on empty cells of bottom middle major square. Digits [1,2] cannot appear anywhere outside the two cells in parent zones C4 as well as central middle major square. The digits may cycle within these two cells only.
A double digit scan usually will result in a valuable puzzle solving resource such as a Cycle and is an advance Sudoku technique.
R9C6 7 by scan for 7 in R7 on empty cells of bottom middle major square -- Cycle of triplets (5,6,8) formed in R7C4, R7C5, R7C6 formed by leftover three digits in the major square. This Cycle of triplets will reduce the possible digit subsets in row R7.
Carry out a second double digit scan for [1,2] in C5 by Cycle of twins and C6 with [1,2] on empty cells of central middle major square to form the breakthrough Cycle of twins (1,2) in central middle major square.
This results in the breakthrough of R6C5 7 by scan for 7 in C6 on empty cells of central middle major square. It has been a hard-earned valid cell breakthrough.
This is followed by R5C5 9 by scan for 9 in C6 and thus forms another Cycle of triplets (3,4,8) in R4C6, R5C6, R6C6 in C6 and central middle major square.
We'll stop here to keep the Cycle of triplets undisturbed. But before closing we'll stop to form the single digit lock on digit 8 in R3C7, R3C9 by scan for 8 in R2 and C8 on the empty cells of top right major square.
The lock on digit 8 in these two cells can either be used for scan for 8 on empty cells R3C4, R3C5 in R3 or it can help to create a breakthrough by reduction of 8 in the possible digit subsets of R3C4, R4C5.
In essence, the single digit lock disallows any further incidence of digit 8 in empty cells of R3 as well as in top right major square.
We'll see its breakthrough effects next stage.
Result of the steps taken shown below.
Solving Expert Sudoku level 5 game 6 Stage 2: Parallel digit scan, Single digit lock, Double digit scan and DSA reduction
Highlight color of valid cells at this second stage is light blue.
First thing we'll do in this stage is to create the breakthrough R7C5 8 in C5 by parallel digit scan for 8 on empty cells of C5.
8 in R2 and single digit lock in R3 eliminate the two cells R2C5 and R3C5 for 8 leaving the single cell R7C5 for 8.
As a result Cycle of twins (4,6) is formed by the two leftover digits in C5.
This will result in further valid cells, but let's go down to bottom middle major square first.
With 8 in R7C5, R7C4 5 by reduction -- R7C6 6 by reduction -- R1C6 5 by exception in C6.
The possible digit subset of three empty cells in C4 and top middle major is reduced to [7,8,9].
With [7,8] in R2, R2C4 9 by reduction -- R3C4 7 by reduction of 8 by single digit lock in R3 from DS [7,8] -- R1C4 8 by exception in C4.
R1C3 7 by scan for 7 in R3, C1, C2.
We'll now convert the single digit lock on 8 to Cycle of twins (8,9) by double digit scan for [8,9] in R2 and C8. This is for future use.
R4C3 4 by DSA reduction of [5,6,9] from possible digit subset [4,5,6,9] in C3.
This helps to form Cycle of twins (5,6) in R3C3, R5C3 by reduction of 9 from reduced possible digit subset of [5,6,9] by Cycle (8,9) in R3 and 9 in R5 -- R6C3 9 by exclusion in C3.
An easy valid cell by scan: R4C9 7 by scan for 7 in R5, R6, C7. Followed by R8C8 7 by scan for 7 in R7, R9, C7, C9.
Single digit lock on 5 formed in R8C2, R9C2 by scan for 5 in C1. These two are the only cells in C2 for 5. We'll see its breakthrough effect next stage.
For ease of understanding let's close at this point and show you the status below.
Solving Expert Sudoku level 5 game 6 Stage 3: Breakthrough by Single digit lock, Cycle of twins
Highlight color of valid cells at this third stage, which is not the last stage, is light grayish yellow.
First and important breakthrough by single digit lock on 5: R3C3 5 by scan for in C1 and C2 by single digit lock on the empty cells of top left major square.
With 5 in R3C3, R5C3 6 by reduction.
Form a second single digit lock this time on 3 in R2C8, R3C8 in top right major square by cross-scan for 3 in R1, C9. This has been possible because of the earlier formed Cycle (8,9) of twins in the major square.
Breakthrough in R7C8 4 by reduction of 3 by the single digit lock on 3 in C8 -- We'll not disturb the Cycle (8,9) now.
R2C9 4 by scan for 4 in C8 -- R2C5 6 by reduction -- R3C5 4 by reduction.
R6C7 6 by scan for 6 in R4, R5, C8.
R5C7 4 by scan for 4 in R4, C8, C9 -- R5C9 5 by scan for 5 in R4, R6.
As you may guess there is no further challenge left. With many possible valid cells waiting to be taken, finishing the game is just a formality.
We'll not though disturb this status to preserve the earlier breakthroughs.
The puzzle game at this stage is shown below.
Solving Expert Sudoku level 5 game 6 Final Stage 4: Easy valid cells
Highlight color of valid cells at this fourth and last stage is light cyan.
With 9 in R7C9, R3C9 8 by reduction -- R3C7 9 by reduction With 4 in R5C7, R5C6 3 by reduction -- R4C6 8 by reduction -- R6C6 4 by reduction -- R6C2 8 by scan for 8 in R4, R5.
R6C8 1 by scan for 1 in C7 -- R4C7 2 by exception in right middle major square.
With 1 in R6C8, R6C5 2 by reduction -- R5C5 1 by reduction -- R5C1 2 by exception.
in R5. R9C7 8 by parallel scan for 8 on empty cells of C7 by 8 in R8 -- R8C7 5 by exception in C7 -- R9C2 5 by reduction of possible 5 in single digit lock partner R8C2 R9C1 9 by scan for 9 in R8.
A Cycle of twins (4,6) formed by the leftover two digits in R8C1, R8C2 -- R9C9 6 by scan for 6 in R8 by Cycle (4,6) and by 6 in C8 -- R8C9 1 by exception in C9 -- R9C8 2 by exception in bottom right major square -- R9C5 1 by reduction -- R8C5 2 by reduction.
With 6 in R2C5, R2C2 3 by reduction -- R3C8 3 by reduction of possible 3 in R2C8 -- R2C8 5 by exception in C8.
R4C1 3 by scan for 3 in C2 -- R4C2 1 by exception in R4 -- R3C2 6 by reduction -- R3C1 1 and R8C2 4 by reduction of 6 -- R1C2 9 by reduction -- R1C1 4 by reduction -- R8C1 6by reduction.
Final solution below.
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 lock.
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.
Finding valid cells has been hard during the initial stages.
But an aggressive approach of finding early breakthroughs by advanced digit patterns and techniques ensured smooth progress to the solution of this expert Sudoku puzzle.
Overall, this is a very hard puzzle to solve.
Other Sudoku puzzles you may like to go through at leisure
Sudoku hard Expert level 5 puzzles
How to Solve Expert Sudoku level 5 game 6
Hard Sudoku level 4 puzzles
New York Times Hard Sudoku puzzles
Hard Sudoku level 3 puzzles
You may access all hard Sudoku level 3 solutions at Third level hard Sudoku.
Medium level 2 puzzles
You may read through all medium level 2 solutions at Second level medium Sudoku.
For beginners, Sudoku beginner puzzle solutions are at Beginner level Sudoku.