Sudoku 6×6 – Easy

Sudoku 6×6

Sudoku 6×6 translates the well-known Sudoku principle onto a grid with 6 rows and 6 columns. The grid is additionally divided into 6 clearly outlined regions, each with 2×3 cells. Some digits are given; all others are completed through logical exclusion.

The puzzle type was originally also published under the name Number Place. Despite the digits and letters, no calculations are made: each symbol is merely a distinguishable marker. It is solely important that it appears exactly once in every row, column, and region.

In this size, the digits used are 1 to 6. The following teaching examples are based on a fully verified solution grid. Each presented task has exactly one solution; candidates and eliminations have been recalculated for the visible state.

Basic Rules

• Each empty cell receives exactly one of the 6 allowed digits.
• Each row contains each allowed symbol exactly once.
• Each column contains each allowed symbol exactly once.
• Each 2×3 region contains each allowed symbol exactly once.
• Pre-given entries must not be changed.
• A candidate is only allowed if the symbol does not already occur in the relevant row, column, or region.

Regions, Symbols, and Units

Row, column, and region are collectively called units. Each unit contains 6 cells and ends up with the same complete set of symbols. Two cells influence each other if they share at least one unit.

The regions are 2×3 cells in size in this grid. Their shape is part of the rule: they are rectangular, encompassing 2 rows and 3 columns. Always scan along the bold boundary lines; a visually neighboring cell might already belong to another region.

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

Strategic Overview

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

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

Each technique answers a different question: the last missing symbol completes a unit; a naked single checks a cell; a hidden single traces a symbol. Pointing and Claiming utilize the overlap of region and line; pairs reserve two symbols for two cells.

1. The last missing symbol in a row

In the first intermediate step, row 1 is complete except for the cell in row 1, column 5. All allowed digits except 5 are already visible there. Therefore, the only empty cell must get the value 5.

No lengthy candidate analysis is necessary: a complete row must contain each symbol exactly once. Since only 5 is missing, placing any other digit would violate the row rule.

The same pattern can occur in a column or region. Immediately check the intersecting column and the associated 2×3 region after placing the digit, as the new symbol might eliminate further candidates there.

2. Recognizing a naked single

Now consider row 1, column 6. All allowed symbols except 2 are already present in 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 2. A cell with exactly one possible digit is called a naked single. The candidate is 'naked' because it is visible as the only note in the cell.

Always verify naked singles against all three units. Relying only on row and column might overlook a digit excluded by the region, leading to an incorrect candidate list.

3. Finding a hidden single within a unit

In row 1, the symbol 5 is missing. The cell in row 1, column 5 has candidates {1, 2, 5} and is not a naked single. However, in other empty cells of this unit, 5 is blocked by intersecting units.

Since row 1 must contain 5, only row 1, column 5 remains as a possible position. This is a hidden single: the uniqueness becomes visible only when considering the entire unit.

Scan the missing symbols one by one. A long candidate list in the cell is not an argument against it; the key is whether the symbol remains possible elsewhere in the same unit.

4. Pointing: A region points to a line

Within region 1, 2 can only be in row 2, column 1 or 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 a 2 on this line.

Outside the region, no other cell in row 2 can keep 2 as a candidate. It is eliminated from row 2, column 5. Only 1 remains there; that cell is immediately solved.

This interaction between block line and interaction is called Pointing or Locked Candidates Type 1. The observation starts in a region and extends outward to exactly one line or column.

5. Claiming: A line claims a region

The reverse also works. In row 3, 6 can only be in row 3, column 1 or row 3, column 3. All potential positions are in region 3.

Row 3 therefore claims the symbol 6 within this region. Other cells in the region not in row 3 lose this candidate; in the example, this affects row 4, column 1. The candidate list is thus shortened to {2, 4}.

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 row 4, cells in row 4, column 3 and row 4, column 5 each have exactly the two candidates {2, 6}. No other possibility exists in these two cells.

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

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

7. Applying the naked pair

Now consider row 4, column 1, within the same unit. Before the pair deduction, this cell had candidates {2, 4, 6}. Among these, 2 and 6 are already fully reserved for the pair cells.

Reserved candidates are removed from the cell. Only 4 remains; the cell is now solved. The elimination applies only within units that contain both pair cells and this cell.

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

8. Revealing a hidden pair

In row 3, 3 and 6 can only be in row 3, column 1 and row 3, column 3 respectively. At least one of these cells contains additional notes; thus the pair is initially hidden in larger candidate lists.

The two pair symbols must be distributed to these two cells. Consequently, no additional candidates are eliminated from row 3, column 1 (candidates 4 and 5) and row 3, column 3. The order of the pair symbols remains open, but all other possibilities in the pair cells are excluded.

In a hidden pair, you do not look for two identical candidate lists. Instead, you track two symbols that only occur together in exactly two cells within a unit. Removing other notes makes it a visible naked pair.

Proven Solving Procedure

1. Scan rows, columns, and regions with few gaps for the last missing symbol.
2. Compute candidates for highly restricted cells and place naked singles.
3. Trace each missing symbol within a unit and look for hidden singles.
4. Check regions for candidates that are confined to a single line or column, and apply Pointing.
5. Check rows and columns for candidates confined to a single region, and apply Claiming.
6. Compare candidate lists for naked pairs; additionally look for hidden pairs in larger grids.
7. After each placement or elimination, return to the singles before searching for more complex patterns.

Common Mistakes

• Forgetting the region: A symbol can be missing in row and column but still forbidden by the 2×3 region.
• Misreading region boundaries: Especially rectangular regions can be confused with neighboring cells. The bold lines are decisive.
• Incomplete candidate notes: A supposed pair is invalid if a third candidate is still possible in one of the pair cells.
• Mixing up Pointing and Claiming: Pointing eliminates outside a region along the same line; Claiming eliminates outside the line within a region.
• Misunderstanding a reservation as an order: A pair determines which two symbols occupy the cells but not which symbol goes where.
• Retaining outdated notes: After each new given, candidates in the cell's row, column, and region change.
• Guessing: When no step is visible, a systematic scan is more reliable than an unfounded attempt placement.

Tips for Beginners

• Use a fixed sequence, e.g., regions, rows, columns, then individual symbols.
• Mark candidates small but complete. Note not just a favorite but all possibilities permitted by the three units.
• Formulate a brief proof before each placement: which unit enforces the symbol or which pattern allows the elimination?
• Check for new singles immediately after any result; a pair or interface elimination usually facilitates simpler 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 6×6 is entirely based on the interaction of rows, columns, and 2×3 regions. Last missing symbols and singles provide direct placements; Pointing, Claiming, and pairs create safe candidate eliminations.

The grid size affects the number of symbols and the shape of regions, but not the logic. Those who update candidates carefully, base each deduction on a visible unit, and start again with simple techniques after each result can solve the puzzle step by step without guessing.