Sudoku 12×12 – Medium

Sudoku 12×12

Sudoku 12×12 transfers the well-known Sudoku principle to a grid with 12 rows and 12 columns. The grid is additionally divided into 12 clearly bordered regions, each with 3×4 cells. Some symbols 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 performed: Each symbol is merely a distinguishable icon. It is crucial only that it appears exactly once in each row, column, and region.

In this size, digits 1 to 9 and letters A to C are used.

Basic Rules

• Each empty cell receives exactly one of the 12 allowed symbols.
• Each row contains each allowed symbol exactly once.
• Each column contains each allowed symbol exactly once.
• Each 3×4 region contains each allowed symbol exactly once.
• Given entries may not be changed.
• A candidate is only allowed if the symbol does not already occur in the associated row, column, or region.

Regions, Symbols, and Units

Row, column, and region are collectively called units. Each unit contains 12 cells and, in the end, the same complete set of symbols. Two cells influence each other once they share at least one unit.

The regions at this size are 3×4 cells. Their shape is part of the rule: they are rectangular and encompass 3 rows and 4 columns. Always follow the bold boundary lines when scanning; an optically neighboring cell may already belong to another region.

Strategic Overview

Start with almost complete units and cells with few candidates. Then look for a specific symbol across an entire unit. If direct placements do not suffice, 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 excluded by the respective deduction. A red result is not yet a entry as long as more than one candidate remains.

Each technique answers a different question: completing a unit with the last missing symbol, verifying a single in a cell, or tracking a hidden single. 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 state, row 1 is complete except for the cell in row 1, column 11. All allowed symbols except B are already visible there. Therefore, the only empty cell must have the value B.

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

The same pattern may occur in a column or region. Immediately check the crossing column and the associated 3×4 region after placing a symbol, as the new symbol may eliminate further candidates there.

2. Recognizing a Naked Single

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

This results in 3 being entered. A cell with exactly one possible candidate is called a naked single. The candidate is "naked" because it is directly visible as the only note in the cell.

Always check naked singles against all three units. Considering only row and column may overlook a digit excluded by the region, leading to a false candidate list.

3. Finding a Hidden Single in a Unit

In row 1, the symbol 6 is missing. The cell in row 1, column 9, has candidates {6, B} and is not a naked single. However, in all other empty cells of this unit, 6 is blocked by their crossing units.

Since row 1 must contain the symbol 6, only position is row 1, column 9. This is a hidden single: the uniqueness only becomes visible when tracking a specific symbol across the entire unit.

Scan for missing symbols sequentially. A long candidate list in the target cell is no argument; what counts is whether the considered symbol remains possible elsewhere in the same unit.

4. Pointing: A Region Points to a Line

In region 4, 5 can only be in row 5, column 3, and row 5, column 4. All these possibilities are together in row 5. Which one is correct is still unknown; but it is certain that the region places its 5 on this line.

Outside the region, no other cell in row 5 can keep the candidate 5. It is removed from row 5, column 7. Only 9 remains there; the cell is directly solved.

This block-line interaction is called Pointing or Locked Candidates Type 1. The observation begins in a region and influences outwardly onto exactly one line or column.

5. Claiming: A Line Claims a Region

The reverse also works. In row 6, 5 can only be in row 6, column 7, and row 6, column 8. All possible positions of the line are within region 5.

Row 6 claims the symbol 5 within this region. Other cells of the region not in row 6 lose this candidate; in the example, that is row 5, column 7. After removing, only 9 remains as a single candidate.

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

6. Discovering a Naked Pair

In row 7, cells at row 7, column 3, and row 7, column 6 each have exactly the two candidates {4, 5}. No further possibilities are available in these two cells.

The two symbols must be distributed exactly into these two cells. It is not yet decided which cell gets which symbol; but it has already been proven that both symbols are bound there in the unit.

A naked pair consists of two cells in the same unit, whose common candidate set includes exactly two symbols. Only this precise restriction allows eliminating other candidates in the remaining cells of the unit.

7. Applying the Naked Pair

Now consider row 7, column 4 in the same unit. Before the pair deduction, this cell had candidates {5, 7}. The 5 is already fully reserved for these two pair cells.

The reserved candidates are removed from the target cell. Only 7 remains; this cell is now solved. The elimination only applies in units containing both pair cells and the target cell.

This second insight separates discovery from deduction cleanly: the pair itself does not solve its cells but can remove candidates outside the pair, producing a new single or a smaller candidate set.

8. Revealing a Hidden Pair

In row 12, 5 and C can only be in row 12, column 6, and row 12, column 8. At least one of these cells contains additional notes; hence, the pair is initially hidden in larger candidate lists.

The two pair symbols must be distributed to these two cells. Consequently, from row 12, column 6, no other candidates remain, and from row 12, column 8, 7 is removed. The order of the pair symbols remains open, but all foreign possibilities in the pair cells are eliminated.

For a hidden pair, you do not look for two already identical candidate lists. Instead, you track two symbols that occur only in the same two cells within a unit. Removing the foreign notes makes it a visible naked pair.

Proven Solution Procedure

1. Scan rows, columns, and regions with few gaps for the last missing symbol.
2. Calculate candidates for strongly restricted cells and place naked singles.
3. Track each missing symbol within a unit and look for hidden singles.
4. Check regions for candidates lying in a single line or column, and apply Pointing.
5. Check lines and columns for candidates confined entirely 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 looking for more complex patterns.

Common Mistakes

• Forget the region: A symbol can be missing in row and column but still forbidden by the 3×4 region.
• Read region boundaries incorrectly: Especially rectangular regions are easily confused with neighboring cells. Correct boundary lines are crucial.
• Insufficient candidate notes: A supposed pair is invalid if a third candidate is still possible in a pair cell.
• Mixing up Pointing and Claiming: In Pointing, candidates are eliminated outside the region along the same line; in Claiming, candidates are eliminated inside the region outside the line considered.
• Misunderstanding a reservation as order: A pair establishes which two symbols occupy the cells but not which symbol goes where.
• Retaining outdated notes: Candidate sets change after every new clue in the row, column, or region of a cell.
• Guessing: If no step is visible, a systematic scan is more reliable than unwarranted guesses.

Tips for Beginners

• Use a fixed order, such as regions, rows, columns, then individual symbols.
• Mark candidates small but complete. Record not just a favorite but all possibilities allowed by the three units.
• Formulate a brief proof before each entry: which unit enforces the symbol, or which pattern permits the elimination?
• After a result, check for new singles; a pair or interface elimination often prepares for simpler deductions.
• Verify completed units against the full symbol set and look for duplicates immediately.
• Work with the given symbol order in letter Sudoku without assigning a numeric value to the letters.

Conclusion

Sudoku 12×12 relies entirely on the interplay of rows, columns, and 3×4 regions. Last missing symbols and singles give direct entries; Pointing, Claiming, and pairs produce secure candidate eliminations.

The grid size changes 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 with simple techniques after each result can solve the puzzle step by step without guessing.