Sudoku 4×4 – Easy

Sudoku 4×4

Sudoku 4×4 translates the well-known Sudoku principle onto a grid with 4 rows and 4 columns. The grid is further divided into 4 clearly outlined regions, each with 2×2 cells. Some digits are given; all others are completed by logical exclusion.

The puzzle type was originally published under the name Number Place. Despite the digits and letters, no calculations are performed: each symbol is simply a distinguishable sign. The only requirement is that each appears exactly once in every row, column, and region.

In this size, the digits 1 to 4 are used. The following setups are based on a fully verified solution grid. Each task shown has exactly one solution; candidates and eliminations have been recalculated for the visible state.

Basic Rules

• Each empty cell receives exactly one of the 4 allowed digits.
• Each row contains each allowed symbol exactly once.
• Each column contains each allowed symbol exactly once.
• Each 2×2 region contains each allowed symbol exactly once.
• Predefined entries cannot be changed.
• A candidate is allowed only if the symbol does not already appear in the corresponding row, column, or region.

Regions, Symbols, and Units

Row, column, and region are collectively called Units. Each unit contains 4 cells and ultimately the same full set of symbols. Two cells influence each other once they share at least one unit.

Regions at this size are 2×2 cells in size. Their shape is part of the rule: they are square. Always follow the bold boundary lines when scanning; an adjacent cell visually can already belong to another region.

The symbol set is small enough to compare missing digits directly in your head often. Nevertheless, row, column, and region are active simultaneously; a missing digit in a row might be forbidden by the column or region of a cell.

Coordinates and Candidates

Rows are numbered from top to bottom, columns from left to right. An indication like Row 2, Column 3 therefore refers to the third cell in the second row.

A Candidate is a symbol that may still fit in an empty cell based on current visible clues. The candidate set is created by removing all symbols already present in the row, column, and region.

Strategic Overview

Start with nearly complete units and cells with few candidates. Then search for a specific symbol across an entire unit. If direct placements are not possible, examine the interfaces between regions and lines and small candidate groups.

The illustrations use circled candidates for confirmed or reserved possibilities. Candidates marked in red are excluded by the corresponding deduction. A red result is not yet a placement as long as more than one candidate remains.

Each technique answers a different question: completing a unit for the last missing symbol, checking a cell with a single candidate, or tracking a hidden single. Pointing and Claiming utilize overlaps between region and line; pairs reserve two symbols for two cells.

1. The last missing symbol in a row

In the first intermediate state, row 1 is complete except for the cell in row 1, column 3. All allowed digits except 3 are already visible there. Therefore, this empty cell must be 3.

The conclusion does not require a lengthy candidate analysis: a complete row must contain each symbol exactly once. Since only 3 is missing, any other placement would violate the row rule.

The same pattern can occur in a column or region. Immediately check the crossing column and the associated 2×2 region after placement, as the new symbol may remove further candidates there.

2. Recognizing a Naked Single

Now consider row 3, column 2. All allowed symbols except 1 are already present across the visible row, column, and region. Although several cells are still empty in the three units, only one candidate remains for this specific cell.

This allows placing 1. A cell with exactly one possible symbol is called a naked single. The candidate is ‘naked’ because it is directly visible as the only note in the cell.

Always verify naked singles against all three units. Only considering row and column can overlook a digit excluded by the region, leading to an incorrect candidate list.

3. Finding a Hidden Single in a Unit

In row 2, the symbol 4 is missing. The cell in row 2, column 2 does have the candidates {1, 2, 3, 4} and is therefore not a naked single. However, in all other empty cells of this unit, 4 is blocked by crossing units.

Since row 2 must contain 4, only row 2, column 2 remains as the position. This is a hidden single: the certainty only becomes visible when following a specific symbol across the whole unit.

Scan for missing symbols one by one. A long candidate list in the target cell is not an argument against; what matters is whether the symbol remains possible somewhere else in the same unit.

4. Pointing: A Region shows on a Line

In region 1, 3 can only be in row 2, column 1, and row 2, column 2. All these possibilities are in row 2. Which one is correct is still unknown; but it is certain that the region places its 3 on this line.

Therefore, no other cells outside the region in row 2 can keep the candidate 3. It is eliminated from row 2, column 3. Only 2 remains there; this cell is immediately resolved.

This interaction between block lines is called Pointing or Locked Candidates Type 1. The observation starts within a region and projects externally onto exactly one line or column.

5. Claiming: A Line claims a Region

The opposite direction also works. In row 1, 1 can only be in row 1, column 1, or row 1, column 2. All potential positions of this line are within region 1.

Row 1 thus claims the symbol 1 within this region. Other cells of the region not in row 1 lose this candidate; in the example, it affects row 2, column 1. After elimination, 3 remains as the only candidate.

This technique is called Claiming, line-region interaction or Locked Candidates Type 2. Remember the direction: Pointing starts in a region, claiming starts in a line or column.

6. Discovering a Naked Pair

In region 1, row 1, column 1, and row 2, column 1, each have exactly the two candidates {1, 3}. No other options are available in these two cells.

The two symbols must therefore be distributed precisely in these two cells. It has not yet been decided which cell gets which symbol; but it is already proven that both symbols are bound within this unit.

A naked pair consists of two cells in the same unit, whose shared candidate set includes exactly two symbols. Only this precise restriction allows for eliminations in the other cells of the unit.

7. Applying the Naked Pair

Now consider row 1, column 2 in the same unit. Before the pair deduction, this cell had candidates {1, 2, 3}. It contains 1 and 3, which are already fully reserved for the pair cells.

The reserved candidates are removed from the target cell. Only 2 remains; this cell is solved. The elimination only applies within units that contain both pair cells and the target cell.

This second view clearly separates discovery and consequence: the pair itself does not solve its cells, but outside the pair, it can remove candidates and potentially create a new single or smaller candidate set.

At the 4×4 size, pair eliminations quickly lead to singles. A hidden pair with additional candidates to remove would only repeat the same information here, so it is not imposed as a separate diagram.

Proven Solution Process

1. Scan rows, columns, and regions with few missing cells for the last missing symbol.
2. Calculate candidates for severely restricted cells and place naked singles.
3. Follow each missing symbol within a unit and look for hidden singles.
4. Check regions for candidates that lie in a single line or column and apply Pointing.
5. Check rows and columns for candidates that fully lie within a region and apply Claiming.
6. Compare candidate lists for naked pairs; additionally look for hidden pairs in larger grids.
7. Return to singles after each placement or elimination before seeking more complex patterns.

Common Mistakes

• Forget the region: a symbol can be missing in row and column but still be forbidden in the 2×2 region.
• Misread region boundaries: especially rectangular regions can be confused with adjacent cells. Bold lines are decisive.
• Inaccurate candidate notes: an apparent pair is invalid if a third candidate is possible in a pair cell.
• Mix up Pointing and Claiming: in Pointing, elimination occurs outside a region on the same line; in Claiming, outside the line within the region.
• Misinterpret a reservation: a pair determines which two symbols occupy the cells, not which symbol belongs where.
• Keep outdated notes: candidates change after each new clue in the row, column, or region of the cell.
• Guessing: if no step is visible, a re-scan is more reliable than an unfounded attempt placement.

Tips for Beginners

• Use a fixed order, for example regions, rows, columns, then individual symbols.
• Mark candidates small but complete. Note not just a favorite, but all possibilities allowed by the three units.
• Formulate a short proof before each placement: which unit forces the symbol or which pattern allows the elimination?
• Check for new singles immediately after a result; pair or interface eliminations usually prepare for easier deductions.
• Verify completed units against the full symbol set and look for duplicates immediately.
• Use the small symbol set: consciously consider missing digits in a unit before making extensive notes.

Conclusion

Sudoku 4×4 relies entirely on the interplay of rows, columns, and 2×2 regions. Last missing symbols and singles give direct entries; Pointing, Claiming, and pairs produce safe candidate eliminations.

The grid size changes the number of symbols and region shape, but not the logic. Properly updating candidates, basing deductions on a visible unit, and resuming at simple techniques after each result enables step-by-step solving without guessing.