Sudoku is a 9×9 grid puzzle divided into nine 3×3 subgrids (also known as boxes, blocks, or regions). The goal is to fill the grid with numbers from 1 to 9, ensuring that:
- Each row contains all the digits from 1 to 9, without repetition.
- Each column contains all the digits from 1 to 9, without repetition.
- Each 3×3 subgrid contains all the digits from 1 to 9, without repetition.
Some numbers in sudoku will already be placed in the grid to give you a starting point, and your job is to figure out the missing numbers using logic.
Steps to Solve Sudoku
Step 1: Start with Simple Scanning
Begin by looking for easy placements in this Sudoku tool. These are the cells where only one number can fit based on the existing numbers in the row, column, and subgrid. For example:
- Row scanning: If a number is missing in a row but appears elsewhere in the row’s subgrid or column, you can deduce where that number should go.
- Column scanning: Similarly, scan columns for numbers that are missing but are found in the corresponding rows or subgrids.
- Subgrid scanning: For each 3×3 subgrid, if a number can only fit in one place, it’s an easy fill.
Step 2: Use the Process of Elimination
Once you’ve filled in some easy numbers, move on to using elimination. This means identifying which numbers are impossible for a given cell based on the numbers already in its row, column, and subgrid.
- Cross-Hatching: Cross-hatching refers to the practice of scanning rows and columns within a subgrid to eliminate possible placements for certain numbers. Let’s say you’re trying to place a “5” in a 3×3 subgrid. Look at the rows and columns outside the subgrid—if “5” already appears in them, it cannot go in any cell in that row or column inside the subgrid.
- Candidates Technique: For each empty cell, write down the possible numbers (candidates) that can go in that cell based on what’s already filled in the row, column, and subgrid. This technique will help narrow down your options.
Step 3: Look for Naked Pairs and Triples
The naked pairs/triples technique in sudoku is another helpful strategy, especially when the puzzle becomes more complicated.
- Naked Pair: If two cells in the same row, column, or subgrid have exactly the same two possible candidates (like 3 and 8), then those two numbers must go in those cells, meaning no other numbers can go there.
- Naked Triple: This applies the same logic, but to three cells with the same three candidates.
Once you identify a naked pair or triple, you can eliminate those numbers from being candidates in other cells within the same row, column, or subgrid.
Step 4: Try the “Pencil Marks” Method
When the sudoku puzzle starts getting more challenging, you might want to use the pencil marks method, which is particularly useful in harder puzzles where the next move isn’t immediately obvious. Here’s how to apply this method:
- Write down all the possible numbers that could go in each empty cell, given the constraints of the row, column, and subgrid.
- As you solve more of the puzzle and eliminate possibilities, you can start erasing some of the pencil marks until only one number is left for a given cell.
Step 5: Use the “Hidden Singles” Technique
Sometimes, there is only one place a number can go, but it might not be immediately obvious. Hidden singles occur when a number is the only option for a cell in a row, column, or subgrid, even though other possible numbers are listed.
For example, if in a row, “7” can only go in one cell (even though that cell has other candidates like 2 or 5), “7” is a hidden single for that row.
Step 6: Apply Advanced Strategies
Once you’ve mastered the sudoku basics, you can start using more advanced techniques for harder puzzles.
- X-Wing: This technique involves looking for patterns in rows and columns where a number can only go in two possible spots. If these spots align in two rows and two columns, you can eliminate that number as a candidate from other cells in those rows and columns.
- Swordfish: Similar to X-Wing, Swordfish extends this pattern recognition across three rows and three columns.
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