Learn how to solve Sudoku expert level 5 game 7 quickly
Sudoku expert level 5 game 7 solved by advanced Sudoku techniques and expert strategy to make it suitable for learning how to solve expert Sudoku.
- A few words on Expert Sudoku
- Sudoku Expert level 5 game 7
- Solving Sudoku Expert level 5 game 7 by advanced Sudoku techniques and strategy
- Sudoku Expert 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 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.
You will find the detailed strategy for quickly solving expert Sudoku after the solution.
Following is the solution of the puzzle explained step by step in details. The techniques used should be easy to understand from the detailed explanation of the solution.
If you want more details on the techniques used, please go through the "Strategies and techniques" section of our first solution of Sudoku expert level 5 game 1.
Please spend your time fruitfully on the game trying to solve it before going through the solutions.
Solving Sudoku Expert level 5 game 7 Stage 1: Breakthrough by Double digit scan, Single digit lock, 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 highlight colors for cells involved in a Cycle of twins, triplets or quadruplets are primarily yellow and for two adjacent Cycles light orange.
The term names are all ours as we learned how to solve Sudoku and created all the term names (for labels to techniques) by actually solving easy to extremely hard Sudoku games. But that should be easy to relate to as we have kept the names FUNCTIONAL AND MEANINGFUL.
Only recently when referring to some Sudoku solution literature we liked a few term names and included it in our terminology.
First valid cell by row column scan is in R7C9 7 by scan for 7 in R8, C8 on empty cells of bottom lower major cell -- R8C9 8 by scan in C7, C8 -- R8C7 2 by scan in C8 -- R8C8 3 by scan for 3 in R7 -- R7C8 4 by exception in bottom lower major square.
Discover the breakthrough R4C5 6 as the naked single with all the three parent zones of the cell R4, C5 and central middle major square together having the rest 8 digits [1,2,3,4,5,7,8,9] already existing. Check for yourself.
Reduced possible digit subset DS in R4 [1,3,4,5] reduced by 3 in left middle major square to [1,4,5] for three cells R4C1, R4C2, R4C3 thus forming the Cycle of triplets (1,4,5) in these three cells in R4.
As a result we get another breakthrough R4C9 3 by reduction of [1,4,5] from DS [1,3,4,5].
A new Cycle of twins (3,7) in R2C7, R3C7 force-formed by double digit scan for [3,7] in R1, C8 and C9 just like a normal row column scan for a single digit on the empty cells of top right major square.
It produces another Cycle of triplets (1,4,9) by leftover digits in C7. Both of these Cycles have no immediate positive effect, but the single digit lock on 5 in R3C8, R3C9 formed by cross-scan for 5 in R2, C7 on empty cells of top right major square has breakthrough effect.
It participates in an important breakthrough of R1C4 5 by scan for 5 in R2, lock on 5 in R3 (as 5 cannot appear in any other empty cell of R3 by the lock) and 5 in C6. The possible digit subset [2,5,7,8,9] reduced by existing digit subset [2,5,9] in central middle major square to form the Cycle of twins (7,8) in R5C5 and R6C5.
Rest of the three digits [2,5,9] in C5 form a second byproduct Cycle of triplets (2,5,9).
Result of the steps taken shown below.
Solving Expert Sudoku level 5 game 7 Stage 2: Breakthrough by Single digt lock, Cycle of twins, Parallel digit scan
Highlight color of valid cells at this second stage is light blue.
We'll form first a breakthrough Cycle of twins (3,7) in R9C4, R9C6 by double digit scan for [3,7] just like single digit row column scan in R7, R8 and C5  because of Cycle of twins (7,8) and 3 in C5] on empty cells of bottom middle major square.
This enables us to discover the breakthrough valid cell R7C6 8 by scan for 8 in R8, C5 by lock on 8 by Cycle of twins (7,8) and C4 (as it has already been established that R9C4 and R9C6 can't have 8 because of the twins).
R7C4 2 by scan for 2 in R8. Again, because of Cycle of twins (3,7) in R9C4, R9C6 these two cells are to be considered already occupied by digits [3,7] together as a group and so cannot be occupied by any other digit.
A big breakthrough of R9C1 2 by parallel scan for 2 on empty cells of C1.
R1C1, R4C1, R5C1, R6C1 are eliminated for 2 by existing digit 2 in top left major square and 2 in left middle major square. The last but one cell in C1, R8C1 is eliminated by 2 in R8 leaving only the cell R9C1 in C1 for 2.
Get another few valid cells for 2 first in R6C2 2 by scan for 2 in R4, R5, C1, C3 -- R2C5 2 by scan in C4, C6 -- R3C9 2 by scan in R2, C7, C8.
As we place digit 2 in R3C9 it reduces the single lock partner cell for 5 and we get another valid cell in R3C8 5.
The last digit 5 enables another valid digit of 5 in R6C9 5 by scan for 5 in R5, C7, C8.
Cycle of twins (5,9) formed in R8C5, R9C5 by leftover two digits in C5 and with 9 in R9, breakthrough R9C5 5 by reduction -- R8C5 9 by exception in C5.
Breakthrough Cycle of twins (4,6) formed in R8C4, R8C6 by the leftover two digits in bottom middle major square and an extra Cycle of twins (6,9) formed in bottom left major square in cells R7C2, R7C3.
For ease of understanding let's close at this point and show you the status below.
Solving Expert Sudoku level 5 game 7 Stage 3: Breakthrough by DSA reduction, Cycle of twins
Highlight color of valid cells at this third stage, which is not the last stage, is light grayish yellow.
First critical breakthrough at this stage is in R8C1 1 by DSA reduction of existing digit subset [4,6,7,9] in R8 ([4,6] contributed by Cycle group in R8) from possible digit subset of [1,4,6,7,9] in C1 -- R4C1 4 by reduction of 1 -- R1C1 6 by reduction of [1,4] -- R1C6 1 by reduction of 6 -- R1C7 4 by reduction of 1 -- R2C9 6 by reduction of 4 -- R2C8 1 by reduction of 6.
With 1 in R2C8, R6C8 6 by reduction -- R5C9 4 by reduction -- R5C4 1 by reduction of 4 -- R5C7 9 by reduction of 1 -- R6C7 1 by reduction of 9.
R5C2 6 by scan for 6 in R4, R6, C1 -- R7C3 6 by scan for 6 in R9, C2 -- R7C2 9 by exception in R7.
With 9 in R5C7, R5C1 7 by reduction of 9 from possible digit subset [7,9] in C1 -- R6C1 9 by exception in C1.
With 7 in R5C1, R5C5 8 by reduction of 7 -- R6C5 7 by reduction -- R6C3 8 by exception in R6 which has Cycle of twins (3,4) by leftover digits in central middle major square.
Rest next stage.
Game status is shown below.
Solving Expert Sudoku level 5 game 7 Final Stage 4: Easy valid cells
Highlight color of valid cells at this fourth and last stage is light cyan.
First valid cells, R8C2 5 by exception in R8 -- R4C2 1 by reduction of 5 -- R4C3 5 by reduction of 1 -- R9C2 8 by scan for 8 in C3 -- R9C3 4 by exception in bottom left major square.
R2C2 4 by scan for 4 in R3, C3 -- R3C2 3 by exception in C2.
R3C3 1 by scan for 3 in R2 -- R2C3 9 by exception in C3.
R3C6 9 by scan for 9 in R2, C4 -- R3C4 6 by scan for 6 in R2 -- R2C6 7 by exception in top middle major square -- R2C7 3 by exception in R2 -- R3C7 7 by exception in C7.
R9C4 7 by scan for 7 in R8, C6 -- R9C6 3 by exception in R9.
R6C4 3 by scan for 3 in C6 -- R6C6 4 by exception in R6 -- R8C6 6 by exception in C6 -- R8C4 4 by exception in whole game.
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 first two stages.
But an aggressive approach of creating early breakthroughs by advanced digit patterns and techniques ensured smooth progress to the solution of this expert Sudoku puzzle.
Overall, this is a hard puzzle to solve.
Other Sudoku puzzles you may like to go through at leisure
Sudoku hard Expert level 5 puzzles
Sudoku expert level 5 game 7 solved quick
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.