Solving Sudoku level 3 game 10: Know how solve a hard Sudoku
Learn how to solve hard Sudoku level 3 game 10 quickly. Hard Sudoku tips and techniques used in solving the game including parallel digit scan explained.
First the solution to the Sudoku hard level 3 game 10 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 10 in three stages.
- Solution stage 2: 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 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 10 - 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 10 Stage 1: All valid cells are by row column scan
First valid cells are for 3 by row column scan:
R4C9 3 by scan for 3 in C7, C8 -- R5C6 3 by scan for 3 in R4, R6, C4. For 5 next: R3C3 5 by scan in C1, C2 -- R9C1 6 by scan in R7, R8 -- R5C2 8 by scan in R4, C1, C3.
With more cells filled up a new valid cell for 3 by scan: R7C1 3 by scan in R8, C2, C3 -- followed by R9C5 3 by scan in R7, R8, C6. Digit 3 fully filled.
Opportunistic valid cell in favorable zone bottom left major square:
R7C2 9 by scan for 9 in R8, C3 -- R6C1 9 by scan in C2, C3 -- R5C8 9 by scan in R6, C7.
Attempting scan success for smaller incomplete digits, success for 7:
R6C8 7 by scan in C7 -- R3C7 6 by scan in C8, C9 -- R6C7 2 by scan for 2 in R4, R5 -- R4C7 5 by scan for 5 in R5 -- R5C7 1 by exception in right middle major square.
R7C7 8 by exception in C7 -- R4C2 1 by scan for 1 in C3 -- R6C5 1 by scan in R4, R5, C4, C6.
Game status at this stage shown below.
How to solve hard Sudoku level 3 puzzle game 10 Stage 2: Breakthroughs by Parallel digit scan and DSA
First breakthrough is by parallel scan for 2 on empty cells of C3.
R7C3 2 by parallel scan elimination of three cells R4C3, R5C3 and R6C3 for 2 by the presence of 2 in left middle major square. This is shown by red-colored arrows.
Possible digit subset DS in C3 [4,6,7] is reduced by [6,7] in R6 giving R6C7 4.
This is a hit by DSA technique.
Opportunistic scan hit: R3C9 8 by scan for 8 in R1, R2, C8.
R2C9 9 by scan in R1, C8 -- R3C6 9 by scan in R1, R2, C5 -- and lastly R4C4 9 by scan in R5, R6, C5, C6. Digit 9 fully filled.
A valid cell R7C9 1 by parallel scan for 1 on empty cells of C9 eliminating cells R8C9 by 1 in R8 and R1C9 by 1 in R1.
A not so easy valid cell hit by parallel scan for 7 on empty cells of C6: R4C6 7 by elimination of R9C6 by 7 in R9, elimination of R8C6 by Cycle (4,7) in R8, elimination of R6C6 by 7 in R6 and elimination of R3C6 by 7 in R3. Only R4C6 is left for 7 in C6.
Elimination of empty cells for 7 are shown by red-colored arrows.
Observe that a Cycle of (2,4,5,8) exists automatically in rest four empty cells of C6. If you decided to identify this Cycle instead, you would have been able to obtain the valid cell by reduction. But that would have been more time-consuming. That's why we prefer to go in for a parallel digit scan that avoids DS evaluatiin in empty cells.
R5C3 7 by scan for 7 in R4 -- R4C3 6 by exception in C3 -- R4C5 4 by exception in R4 -- R5C4 6 by exception in R5.
Game status at the end of stage 2 shown below.
How to solve hard Sudoku level 3 puzzle game 10 Final Stage 3: Challenges over - easy valid cells now
Possible digit subset in R3 [1,2,4,7] is reduced by [1,2,4] in C5 giving R3C5 7, a valid cell hit by DSA technique -- R1C2 7 by scan in R2, R3 -- R8C2 4 by reduction -- R8C1 7 by reduction -- R7C4 7 by scan for 7 in R8, R9, C5.
R7C5 5 by reduction -- R7C8 4 by reduction -- R9C8 2 by reduction -- R8C9 5 by reduction -- R1C9 2 by reduction.
R1C4 5 by reduction 6 by 6 in C4 from DS [5,6] in R1 -- R1C5 6 by exception.
With 5 in C4, R6C4 8 by reduction of 5 -- R6C6 5 by reduction of 8.
R9C6 4 by exception in R9 -- R2C6 2 by reduction of 4 from DS [2,4] in R2 -- R2C4 4 by reduction.
R8C4 2 by exception in C4 -- R8C6 8 by exception in C6.
R3C1 4 by scan for 4 in R2, C2 -- R2C1 1 by exception in C1 -- R3C2 2 by exception in C2 -- R3C8 1 by exception in R3 -- R2C8 5 by exception in whole game.
Game status 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. 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.
Eleventh game at Third level of hardness
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.