Sudoku: patterns to deduction
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Numbers as labels
Sudoku grew from Number Place puzzles and became widely known through Japanese publishing. Its rules do not require arithmetic. We begin on 4×4 boards, then transfer the same constraints to 9×9.
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1. Numbers as labels
Sudoku grew from Number Place puzzles and became widely known through Japanese publishing. Its rules do not require arithmetic. We begin on 4×4 boards, then transfer the same constraints to 9×9.
2. Three constraints, not one
Which units must contain each symbol exactly once?
Standard Sudoku checks rows, columns and boxes. Diagonals are not a standard constraint. In 4×4 use 1–4 and 2×2 boxes.
3. First deduction: a missing number
Find the empty cell in row 1. Which symbol is missing? Enter it.
R1C2 is 1. Check all three constraints before entering.
4. Read a column
Find the empty cell in column 3. Use its other three values.
R3C3 is 4. Check all three constraints before entering.
5. Use the small box
The lower-left 2×2 box lacks one symbol. Fill its empty cell.
R4C1 is 1. Check all three constraints before entering.
6. Two blanks, one constraint at a time
Row 1 has two blanks. Fill R1C1 by checking its column as well.
R1C1 is 3. Check all three constraints before entering.
7. Candidates are possibilities
Two symbols remain possible in a cell. What should you do?
A guess is not a deduction. Candidate notes help you keep possibilities distinct from filled values.
8. One possible place
A number is missing from a box and only one empty cell in that box can accept it. Is it forced, even if that cell has other candidates?
This is a hidden single: the uniqueness of a symbol’s location within a unit forces it.
9. A pair reserves two cells
Two cells in one row have exactly the same two candidates {1,4}. What follows?
Those two symbols must occupy those two cells in some order. This elimination applies only within a shared unit.
10. Move from mini to classic
A classic Sudoku uses which symbols and box size?
The same row, column and box exclusions scale up. Start with a single and build from there.
11. Build a solving routine
Scan missing symbols, write candidates when needed, seek singles, then inspect pairs. In practice you can generate a new unique-solution board or reveal the complete answer. If you get stuck, try a hint first; after finishing, compare the full answer and revisit the step that helped you.