Know how to solve hard Sudoku from solution to Sudoku level 3 game 11
Learn how to solve hard Sudoku level 3 game 11 quickly. Hard Sudoku tips and techniques used in solving the game including two types of X wing explained.
First the solution to the Sudoku hard level 3 game 11 explained in full details. It includes explanation on how a specific Sudoku technique works.
It is followed by a brief on Tips for solving a hard Sudoku puzzle game.
The contents are,
- Solution to the Hard Sudoku level 3 game 11 in three 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 breakthrough by X wing digit pattern - This is an advanced digit pattern of more power for creating a breakthrough.
- Solution stage 2: Sudoku technique of single digit lock- This is a powerful pattern that usually provides a breakthrough.
- 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 11 - 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 11 Stage 1: Breakthrough by a pair of X wing formations explained
We'll explain the solution in segments of stages so that from the game status at the end of each stage, how the valid cells are obtained using Sudoku techniques can be understood without any difficulty.
First valid cells are by row column scan, DSA reduction and by exception from the whole set of digits in a zone,
R7C4 1 scan C4, C5 -- R6C2 1 scan R5, C1, C3 -- R6C9 3 scan R4, R5, C7 -- R4C1 4 scan R5, R6, C3 -- Cycle of (5,8) in R1C4, R5C4 by DSA reduction from DS [5,7,8,9] -- R2C4 9 reduction of 7 in top middle major square -- R6C4 7 by exception.
DSA reduction of possible digit subset [7,9] occurs for both cells R1C4, R5C4 because of presence of [7,9] in both rows R1 and R5. The digits possible in the two cells of column C4 DS [5,7,8,9] thus reduces for both to [5,8] that forms a Cycle of (5,8) in C4.
No more immediate valid cell by scan but valid cell and Cycles by possible digit subset analysis or DSA.
R2C8 4 hidden single DSA reduction of [6,7,8] in the cell from DS [4,6,7,8] in R2. Cycle (6,8) in R2C1, R2C5 by reduction of 7 from DS [6,7,8] in R2 -- R2C7 7 by exception.
R4C9 7 scan C7, C8 -- Cycle (2,8) in R1C9, R8C9 by DSA reduction -- R9C9 1 reduction -- R7C9 4 reduction.
Cycle (6,8) in R2C1, R2C5 doesn't assure in which cell 6 or 8 will finally be placed, but it ascertains that these two digits will certainly appear in either of the two cells and in no other in R2. If you place 6 in R2C1, 8 must be placed in R3C5 and vice versa. The two digits Cycle between these two cells and being locked, these can't appear in any other cell of R2.
A Cycle reduces the degree of uncertainty in the game and is a valuable asset to have.
We'll now see how an extraordinary breakthrough happens. Two single digit locks forming one after the other followed by another pair of single digit locks. Together these form A PAIR OF X WING digit formation.
First: Single digit lock on 2 in R1C8, R1C9 formed by scan for 2 in R3.
Second: Single digit lock again on 2 in bottom right major square formed in R8C9, R9C8 by scan for 2 in R7.
These 4 numbers of same digit 2 in possible digit subsets of four cells form the powerful pattern of Deformed X wing.
The two pairs of locked 2s share the common columns C8 and C9 eliminating 2 in possible digit subset of any other cell in these two columns. In this game thus 2 is reduced from the DSs of R4C8, R6C8 creating a third single digit lock on 2 in C7 cells R4C7, R6C7.
The final link in this chain is provided by the 4th single digit lock on 2 in R4C5, R6C5 by scan for 2 in C4, C6.
This pair of locked 2s share both rows R4, R6 and columns C5, C7 thus eliminating 2 in DS of R6C1. This is a properly shaped X wing that disallows digit 2 in any of the shared rows R4, R6 and shared columns C5, C7.
Result is in the big breakthrough R5C2 2.
Effectively R5C2 2 is by scan of locked pair of 2s in R4 and R6 in the X wing on 2s.
The two pairs of the same digit sharing a pair of rows or both rows and columns is called X wing which is a very potent Sudoku digit pattern to identify. It invariably produces an important breakthrough.
Game status at this stage shown below.
How to solve hard Sudoku level 3 puzzle game 11 Stage 2: Breakthrough by single digit lock explained
Starting from where we left, let's recall the last valid cell, R5C2 2.
This immediately participates in finding a new valid digit R9C1 2 by scan in C2, C3 -- R8C9 2 by reduction of its partner locked 2 in R9C8 by the 2 in R9 -- R1C9 8 by reduction of 2 -- R1C8 2 by reduction of its partner 2 of X wing in R1C9 -- R3C7 1 by reduction of 8 -- R3C8 3 by reduction of 1.
Cycle (2,5) formed in R4C7, R6C7 reducing 5 in R7C7 to the unique digit, R7C7 8.
Observe that this is equivalent to a parallel digit scan for 8 on empty cells of C7 with R4C7 and R6C7 eliminated for 8 by digit 8 in R4 and R6.
With reduced DS [1,6] in two cells of right middle major square and 1 in R5, R5C8 6 by reduction -- R4C8 1 by exception in right middle major square.
Now we'll have a breakthrough by a single digit lock on 6.
A single digit lock on 6 is formed in R1C5, R2C5 by cross-scan for 6 in R3, C4.
Effect of this single digit lock is - digit 6 cannot appear in any other cell of the lock column C5 and it behaves as if digit 6 already exists in C5. This single digit lock can be used thus in a scan for 6 also.
Indeed the breakthrough by the single digit lock is created by scan only.
Breakthrough R4C6 6 by scan in R5 by the lock on 6 and 6 in R5.
With 8 in R1C9, R1C4 5 by reduction -- R5C4 8 by reduction -- R5C6 5 by exception in R5.
With the last breakthrough no challenges remain in the rest of the game.
Game status at the end of stage 2 shown below.
How to solve hard Sudoku level 3 puzzle game 11 Stage 3: Finding valid cells is straightforward
With 5 in R1C4 R1C1 6 by reduction -- R2C1 8 by reduction -- R1C2 4 by reduction -- R2C5 6 by reduction of partner lock 6 -- R1C5 3 by exception in R1.
R3C5 4 by scan for 4 in C6 -- R3C6 8 by exception in top middle major square.
R6C3 6 by scan for 6 in R4, C1.
R7C2 6 by scan in R8, R9, C3. R9C6 9 by reduction of 3 from DS [3,9] in C6 -- R8C6 3 by exception.
With 9 in R9C6, R9C8 5 by reduction -- R7C8 9 by reduction.
With DS [7,8] in R9 and 8 in C2, R9C2 7 by reduction -- R7C3 5 by reduction -- R8C2 9 by reduction -- R8C3 8 by reduction -- R8C5 5 by reduction -- R7C5 7 by reduction -- R9C5 8 by reduction.
With 5 in R7C3, R4C3 9 by reduction -- R6C1 5 by reduction -- R6C7 2 by exception -- R4C7 5 by reduction -- R6C5 9 by reduction -- R4C5 2 by reduction.
The last three are by exception in C1, C2 and C3 respectively: R3C1 9, R3C2 5, R3C3 7.
Final solution shown below.
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.
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 is with a relatively larger number of 27 cells already filled with digits. But still it poses a series of hurdles that needed use of advanced Sudoku techniques of X wing and parallel scan.
This gives you a good Sudoku hard solving practice before graduating soon to solving level 4 Sudoku hard games.
A new game for you to solve at hard Sudoku level 3
We leave you here with a new hard Sudoku level 3 game to solve.
More Sudoku hard puzzles you may like to solve and learn how to solve
The updated list of Solutions to level 3, level 4 and NYTimes Sudoku hard puzzle games:
Enjoy solving Sudoku hard.
By the way, Sudoku hard solution techniques are included with many of the solutions.
Enjoy also learning how to solve Sudoku hard in easy steps.