Last Remaining Cell

Beginner

Find the only possible position where a specific number can be placed within a row, column, or 3×3 box when all other positions are blocked.

What is Last Remaining Cell?

The Last Remaining Cell technique, also known as "Hidden Singles", involves finding the only possible position where a specific number can be placed within a row, column, or 3×3 box. This occurs when all other positions for that number are blocked by existing numbers.

Unlike Last Free Cell (which finds the only missing number in an almost-complete group), this technique focuses on finding the only available position for a specific number that hasn't been placed yet.

How Last Remaining Cell Works

When you're looking for where to place a specific number (1-9) in a row, column, or 3×3 box, sometimes only one cell is available because all other cells are either filled or would create conflicts with the Sudoku rules.

1

Choose a Number

Select a specific number (1-9) you want to place

2

Find the Group

Look at a row, column, or 3×3 box that needs this number

3

Identify the Cell

Find the only position where it can legally be placed

Example 1: Last Remaining Cell in a Row

We need to place the number 7 in the top row. Let's see where it can go:

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

1 Looking at the top row, we need to place a 7. Most cells are already filled.

2 The only empty cell in the top row is position 3 (highlighted in yellow).

3 Since this is the only available position for 7 in this row, we can place it there with confidence.

Example 2: Last Remaining Cell in a Column

We need to place the number 5 in the middle column. Notice how other 5s block most positions:

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

1 Looking at the middle column (column 3), we need to place a 5.

2 Other 5s in the grid (in rows 1, 2, 4, 6, 7, and 9) block those positions in column 3.

3 The only available position is row 3, column 3 (highlighted in yellow), so the 5 must go there.

Example 3: Last Remaining Cell in a 3×3 Box

We need to place the number 4 in the top-right 3×3 box:

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

1 The top-right 3×3 box contains: 2, 6, 6, 2, 4, 1, 7, 8, and one empty cell.

2 We need to place a 4 in this box, but there's already a 4 in position (2,9).

3 Therefore, the 4 must go in the only remaining empty cell: position (1,9) highlighted in yellow.

When to Use This Technique

Best Scenarios

  • Early solving: Look for numbers that appear frequently on the board
  • High-constraint areas: Focus on rows, columns, or boxes with many filled cells
  • After placing numbers: Each new number creates constraints for the remaining empty cells

Strategy Tips

  • Systematic approach: Go through each number 1-9 and find where each can be placed
  • Focus on constraints: Look for cells that are heavily constrained by existing numbers
  • Combine with other techniques: Use together with Last Free Cell for maximum efficiency

⚠️ Common Mistakes to Avoid

  • Missing constraints: Forgetting to check all three groups (row, column, and 3×3 box)
  • Overlooking existing numbers: Not noticing that a number already exists in the target group
  • Rushing the process: Not systematically checking all possibilities for each number
  • Confusing with Last Free Cell: Mixing up the two related but different techniques

💡 Practice Tips

Systematic Method

  • Number by number: Go through each digit 1-9 and find all possible placements
  • Visual scanning: Train your eye to quickly spot where numbers already exist

Verification

  • Triple check: Verify the cell is empty in its row, column, AND 3×3 box
  • Mark candidates: Use pencil marks to track possible numbers in each cell

Why This Technique Works

The Last Remaining Cell technique works because of Sudoku's fundamental constraint: each number 1-9 must appear exactly once in every row, column, and 3×3 box. When all but one position for a specific number are blocked by existing numbers, that remaining position is the only legal place to put the number.

This technique is completely logical and reliable - there's no guessing involved. When you identify a last remaining cell, you can place the number with absolute certainty.

Related Techniques

Related Beginner Techniques

Prerequisites

  • Basic Rules - Understanding Sudoku constraints
  • Pattern Recognition - Spotting filled and empty cells
  • Logical Deduction - Understanding constraint-based reasoning
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