Solving Sudoku level 3 game 9: Know how solve a hard Sudoku
Learn how to solve hard Sudoku level 3 game 9 quickly. Hard Sudoku tips and techniques used in solving the game including single digit lock explained.
First the solution to the Sudoku hard level 3 game 9 explained in full details. It includes explanation on how a specific Sudoku technique works.
It is followed by a brief Tips for solving a hard Sudoku puzzle game.
The contents are,
- Solution to the Hard Sudoku level 3 game 9 in four stages.
- Solution stage 1: Sudoku technique of valid cell by possible digit analysis or DSA - This is the most frequently used multi-purpose Sudoku technique, used for finding a valid cell and also to form the possible digit subsets of empty cells.
- Solution stage 1: Sudoku technique of simplification by Cycles of digits - Forming a Cycle may directly result in a valid cell, but if not, even then a Cycle reduces the overall uncertainty in a game.
- Solution stage 1: Sudoku technique of single digit lock - This is a powerful pattern that usually provides a breakthrough.
- Solution stage 2: Sudoku technique of parallel digit scan - Instead of scanning for a valid cell in a major square in usual row column scan, in this variation, intersecting rows (or columns) are scanned for a specific digit against the empty cells of a column (or a row).
- Tips for solving hard Sudoku puzzle games.
First try to solve the game before before going through its solution.
How to solve hard Sudoku level 3 Game 9 - The puzzle game
The following is the Sudoku hard puzzle that should engage your mind for some time.
How to solve Hard Sudoku level 3 puzzle game 9 Stage 1: Breakthroughs by DSA, Cycle and Single digit lock explained
First valid cell by row column scan as per systematic valid cell scan strategy:
R7C3 3 by scan for 3 in R8, R9, C2.
And that's all by row column scan at this point of time.
It took a bit of an effort to get the breakthrough by possible digit analysis or DSA:
R2C8 8 by reduction of [1,2,3,4] from DS [1,2,3,4,8] in 5 empty cells of R2 by 1 in top right major square and [2,3,4] in second parent zone C8 of R2C8.
Form the single digit lock on 6 in R8C5, R9C5 by cross-scan for 6 in R7 and in C6.
This lock reduces 6 from possible digit subset [1,6,7] in R5C5 forming the Cycle (1,7) in R5C3 and R5C5 -- breakthrough R5C7 6 by reduction of 1 from DS [1,6] in the cell.
The digits [1,7] are locked in the Cycle in cells R5C3 and R5C5 reducing all occurrences of these two digits in row R5 containing the Cycle.
This gives another valid cell hit in R9C9 6 by scan for 6 in R7, C7.
And then R1C8 6 by scan for 6 in R3, C7, C9.
Breakthrough R6C8 1 by DSA reduction:
The possible digit subset in R6C8 is DS [1,5,7,9] which is the DS in four empty cells of C8. Analyzing next the effect of the two other parent zones right middle major square (with [5,7]) and R8 (with 9), we find existing digits in these two influencing zones is [5,7,9]. These 3 digits are then reduced from the DS [1,5,7,9] to leave the single digit 1 valid for cell R6C8.
This is how DSA reduction works.
Continuing in the same way,
R4C8 9 by DS reduction of [5,7] from reduced DS [5,7,9] in C8 -- R7C8 5 by reduction of 7 from further reduced DS [5,7] in C8 -- R3C8 7 by exception in C8.
Next we form a Cycle proactively by DSA technique,
DS in four empty cells in C9 [2,4,8,9] is reduced by [8,9] for both R1C9 and R2C9 to form the breakthrough Cycle (2,4) in these two cells of C9.
As a result we get two valid cells in C9 directly by reduction:
R4C9 8 -- R7C9 9 and also by reduction R6C7 2 -- R2C7 3 -- R1C7 5 -- R3C7 9 -- R9C7 1 by reduction and R8C7 8 by exception.
Game status at this stage shown below.
How to solve hard Sudoku level 3 puzzle game 9 Stage 2: Breakthrough by Parallel digit scan, Cycle and DSA
With 6 in R9C9 we'll now destroy the all important single digit lock in R8C5, R9C5 that started the series of breakthrough valid cells.
R8C5 6 by reduction of single digit lock -- R9C5 9 by scan for 9 in R7, C6 -- R8C2 9 by scan for 9 in R7, R9, C1, C3. Digit 9 fully filled.
R9C6 5 by scan for 5 in R7.
A quick valid cell by parallel digit scan:
R7C2 8 by parallel scan for 8 on empty cells of R7 with 8 in bottom middle major square eliminating 3 of 4 empty cells in R7 for 8 -- R1C3 8 by scan for 8 in R2, C1, C2.
We get now a Cycle initiating a valid cell breakthrough.
With Cycle (1,5) in R8C1, R8C3, possible digit subset in R9C1, R9C2, R9C3 reduces to [2,4,7].
But with [2,7] in C2 we get the valid cell hit R9C2 4 by reduction of [2,7] from DS [2,4,7].
Game status at the end of stage 2 shown below.
How to solve hard Sudoku level 3 puzzle game 9 Stage 3: Challenges over - preparing to finish
R3C2 5 by DSA reduction of [1,5] from DS [1,5,6] in C2 -- R6C2 6 by reduction -- R4C2 1 by exception in C2 -- R5C3 7 by reduction -- R5C5 1 by exception in R5 and also by reduction.
With 7 in R5C3, R9C3 2 by reduction -- R9C1 7 by reduction.
R2C3 1 by parallel scan for 1 in C5 and top right major square -- R8C3 5 by reduction -- R8C1 1 by reduction -- R4C3 4 by reduction -- R6C1 5 by exception in left middle major square.
R4C5 5 by scan for 5 in R6, C4, C6 -- R4C6 2 by reduction of 6 -- R4C4 6 by exception in R4.
Game status shown below.
How to solve hard Sudoku level 3 puzzle game 9 Final Stage 4: Easy valid cell hits by reduction and exception
R1C4 1 by scan for 1 in R2, R3, C5 -- R1C5 7 by reduction caused by Cycle 92,4) in R1.
R7C5 2 by reduction -- R7C4 7 by reduction -- R7C6 1 by reduction -- R2C5 4 by reduction -- R2C9 2 by reduction -- R1C9 4 by reduction -- R1C1 2 by reduction -- R3C1 4 by reduction. R3C4 2 by scan for 2 in C5, C6 -- R6C4 4 by exception in C4.
R3C5 3 by scan for 3 in C6 -- R3C6 8 by exception in R3 -- R6C6 7 by exception in C6 -- R6C5 8 by exception in whole game.
Following is the final solution.
Hard Sudoku Tips for quick and easy solution
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.
Hardness level being higher now, easy breaks by row-column scan are not many in the beginning.
So the next easy to use technique used is—identification of single valid digit for a cell by Digit Subset Analysis or DSA in short.
And wherever possible, Cycles of digits are formed that in any situation are a treasure to have and Cycles play a key role in quick solution.
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. In this game we have done this once.
When the easier techniques are no longer applicable, short length of 2 to 3 digit long possible digit subsets or DSs are evaluated in favorable cells belonging to favorable zones (having a larger number of cells already filled) quickly.
Objective now is to identify and use the higher level advanced Sudoku techniques of Single digit lock, X wing or parallel digit scan for creating a breakthrough.
Usually an often prescribed method of evaluating DSs of all empty cells is avoided as it is more time-consuming compared to valid cell identification using special digit patterns first.
At this level 3 hard Sudoku, number of breakthroughs that are needed are not many and overall going is not hard at every step continuing till the end. After the few barriers are overcome, finding rest of valid cells is easy.
The main strategy for solving a hard Sudoku puzzle is to use the technique that would produce best results fastest. Easy to say, not so easy to do—comes with practice.
Any puzzle solving involves essentially problem solving. The general steps are,
- First stage analysis and breaking it down into smaller chunks if possible as well as adapt the strategy of solving this type of problem,
- Solving the easier component problems so that the main problem size and complexity is reduced,
- Detailed information collection, that is, defining the problem in more details as far as possible,
- Second stage analysis of structure of problem (in this case of Sudoku) and information content,
- Key pattern identification,
- Use of the key pattern to create the breakthrough,
- Repeating the last four steps (steps 4, 5, 6 and 7) for finally solving the problem.
This Sudoku level 3 game should give you a fair bit of hard Sudoku solving practice before graduating to solving more difficult level 4 Sudoku hard games.
We leave you here with a new game to solve.
Tenth game at Third level of hardness
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Enjoy solving Sudoku hard.
By the way, Sudoku hard solution techniques are included with many of the solutions.
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