Last Possible Number Technique

Beginner

The Last Possible Number technique, also known as "Naked Singles," involves systematically eliminating possible numbers for a cell until only one candidate remains. This is a process of elimination that focuses on individual cells rather than groups.

How It Works

For any empty cell, start with all possible numbers (1-9) and eliminate those that already appear in the same row, column, or 3×3 box. When only one number remains possible, that's the answer for that cell.

Example 1: Basic Elimination Process

Let's find what number goes in the highlighted cell:

Before: Initial Candidates

5
3
7
8
1
9
2
6
4
8
1
9
3
7
5
6
2
4
2
6
4
9
2
3
1
7
8
1
7
2
5
8
4
9
3
6
3
9
6
1
4
7
8
5
2
6
2
8
7
3
1
4
9
5
4
5
1
2
9
6
3
8
7
7
8
3
4
5
2
1
1
9
9
4
5
6
1
2
3
4
5
6
7
8
9
8
7
4
3

After: Final Answer

5
3
7
8
1
9
2
6
4
8
1
9
3
7
5
6
2
4
2
6
4
9
2
3
1
7
8
1
7
2
5
8
4
9
3
6
3
9
6
1
4
7
8
5
2
6
2
8
7
3
1
4
9
5
4
5
1
2
9
6
3
8
7
7
8
3
4
5
2
1
1
9
9
4
5
6
1
8
7
4
3

Step-by-Step Elimination Process

For the cell at row 9, column 5 (highlighted in yellow):

1Check Row 9: Contains 9, 4, 5, 6, 8, 7, 4, 3

  • 3, 4, 5, 6, 7, 8, 9 - eliminated by row
  • 1, 2 - still possible

2Check Column 5: Contains 1, 7, 2, 8, 4, 3, 9, 5

  • 1, 2, 3, 4, 5, 7, 8, 9 - eliminated by column
  • 6 - still possible from our previous list

3Check Bottom-Center Box: Contains 4, 5, 1, 2, 9, 6, 7, 8, 3

  • Wait, column 5 already has 1, 2, 3, 4, 5, 7, 8, 9
  • From row elimination: only 1, 2 were possible
  • From column elimination: 2 is eliminated (present in column)
  • 1 - the only remaining possibility!

4Final Answer: Only 1 can go in this cell

Example 2: Multiple Eliminations

Here's a cell with more complex elimination:

5
3
7
8
1
9
2
6
4
8
1
9
3
7
5
6
2
4
2
6
4
9
2
3
1
7
8
1
7
2
5
8
4
9
3
6
3
9
6
1
4
7
8
5
2
6
2
8
7
3
1
4
9
5
4
5
1
2
9
6
3
8
7
7
8
3
4
5
2
1
1
9
9
4
5
6
1
8
7
4
3

The elimination cells (highlighted in red) show all the numbers that block our target cell:

Step-by-Step Process

  1. 1Select an empty cell to analyze
  2. 2List all possibilities (1, 2, 3, 4, 5, 6, 7, 8, 9)
  3. 3Check the row - eliminate numbers already present
  4. 4Check the column - eliminate numbers already present
  5. 5Check the 3×3 box - eliminate numbers already present
  6. 6Count remaining candidates - if only one remains, that's your answer!

When to Use This Technique

⚠️ Common Mistakes to Avoid

Advanced Applications

This technique becomes the foundation for more advanced strategies:

Practice Tips

  1. Start simple: Pick cells with the most filled neighbors
  2. Be systematic: Always check row, then column, then box
  3. Double-check: Verify your eliminations before concluding
  4. Use pencil marks: Write small candidate numbers to track possibilities
  5. Practice pattern recognition: Learn to quickly spot which numbers are blocked