Hidden Single Sudoku Technique Explained

Understanding the Hidden Single Pattern

In the displayed puzzle, we can observe several elements that demonstrate Hidden Singles in action:

Red Circled Numbers: Multiple numbers are marked with red circles throughout the grid:

• Row 1: 8 (column 1), 7 (column 3)
• Row 2: 5 (column 4), 7, 2, 8 (columns 7, 8, 9)
• Row 3: 2 (column 1), 3 (column 3)
• Row 6: 2 (column 2)
• Row 7: 7 (column 2)

These red circles indicate candidates being analysed across different units. When searching for Hidden Singles, you examine where each missing number can be placed in a row, column, or box. These marked numbers help track which candidates are being considered.

The Blue Cell (Row 2, Column 2): The prominent blue-highlighted 1 represents a Hidden Single that has been identified and solved. This is a key teaching moment in the puzzle. To understand why this is a Hidden Single:

1. Examine row 2: Where can the number 1 be placed?
2. Check each empty cell in row 2 for validity
3. The number 1 can only go in column 2 (the blue cell)
4. Therefore, despite potentially having other candidates, this cell must be 1

Green Background Cells with 1: Four cells contain the number 1 with green backgrounds:

• Row 3, Column 6
• Row 4, Column 1
• Row 5, Column 4
• Row 8, Column 3

These green cells show where the number 1 has already been placed in the puzzle. They serve multiple purposes:

• Constraint visualization: They show why 1 cannot appear in certain other positions
• Unit completion tracking: They help identify which rows, columns, and boxes still need a 1
• Hidden Single creation: Their presence often creates Hidden Singles in related units

How the Blue 1 Was Found

The blue 1 in row 2, column 2 was identified as a Hidden Single through this analysis:

1. Row analysis: Row 2 doesn't have a 1 yet, so we search for where it can go
2. Checking column 2: Can 1 go here? Check the column – no 1 present vertically
3. Checking the top-left box: Can 1 go in this position within the box? Verify no conflicts
4. Checking other cells in row 2: The other empty cells in row 2 are blocked by existing 1s in their columns or boxes
5. Conclusion: Column 2 is the ONLY place in row 2 where 1 can be placed – Hidden Single found!

1. Choose row 1 as your starting point
2. List missing numbers: e.g., {1, 4, 6, 9}
3. For each missing number:
   • Where can 1 go in this row? (check all empty cells)
   • Where can 4 go in this row?
   • Continue for all missing numbers
4. Move to row 2 and repeat
5. After all rows: scan all columns, then all boxes

1. Choose number 1 to track across entire grid
2. Check each row: Does this row need a 1? Where can it go?
3. Check each column: Does this column need a 1? Where can it go?
4. Check each box: Does this box need a 1? Where can it go?
5. Move to number 2 and repeat for the entire grid
6. Continue through all numbers 1-9

Example: A box has 6 numbers filled: {1,2,3,4,5,6}. Missing: {7,8,9}. Looking for 7: only one empty cell in the box can contain 7 (because 7 appears in the relevant row and column of the other empty cells). That's a box Hidden Single!

Example: Row 5 is missing only {3,7,9}. Looking for 3: it can only go in column 4 of that row because column positions 1,2,3,5,6,7,8,9 either already have 3 in their columns, or the cells belong to boxes that already have 3. That's a row Hidden Single!

Example Cascade:

1. You find a Hidden Single 6 in box 1 (row 3, column 2)
2. Placing 6 means row 3 now has a 6, eliminating 6 from other cells in row 3
3. This creates a Hidden Single 6 in box 3 (because row 3's 6 blocks positions)
4. Placing that 6 creates a Hidden Single 6 in column 8
5. And so on...

One Hidden Single can trigger a chain reaction that solves large portions of the puzzle!