Sudoku

Sudoku rules at a glance

Classic Sudoku is played on a 9×9 grid divided into nine smaller 3×3 boxes. Some numbers are supplied as fixed clues. Your task is to fill every empty cell with a number from 1 to 9 while satisfying three rules:

1. Every row contains the numbers 1–9 exactly once.
2. Every column contains the numbers 1–9 exactly once.
3. Every 3×3 box contains the numbers 1–9 exactly once.

There is no addition or calculation. The numbers could be replaced with nine different symbols without changing the puzzle. What matters is eliminating impossible positions until only valid ones remain.

In Felt & Wood, select an empty cell and use the number pad or keyboard keys 1–9. Backspace, Delete, or the Clear button removes a player entry. Fixed clues are darker and cannot be changed; your entries appear in teal. Conflicting duplicates are highlighted, and Undo restores the previous move. Changing difficulty starts a fresh puzzle with fewer clues at higher levels.

Begin with a systematic scan

The easiest deductions are often visible before you write any candidates. Choose one number—say 7—and inspect each 3×3 box. Existing 7s in crossing rows and columns rule out cells in that box. If only one cell remains, that cell must be 7. Repeat for all nine numbers.

Then scan individual rows and columns. If a row already contains 1, 2, 3, 4, 5, 6, 8, 9, its empty cell must be 7. This is a naked single: the cell itself has only one legal candidate.

A hidden single is slightly less obvious. A row may have several empty cells, each with multiple candidates, but perhaps only one of those cells can hold 7. The 7 is “hidden” among other candidate marks, yet its position is forced. Hidden singles also occur in columns and boxes.

Work in a repeatable order instead of staring at the whole board:

• Scan each box for digits 1 through 9.
• Scan each row for missing digits.
• Scan each column for missing digits.
• After placing a number, rescan its row, column, and box.

One placement changes three units at once and often starts a chain of deductions.

Use candidates without creating clutter

When direct scanning stops, list the possible numbers for each empty cell. A candidate is valid only if it is absent from that cell’s row, column, and box. For example, if a cell’s row rules out 1, 2, and 5, its column rules out 3 and 8, and its box rules out 4 and 9, only 6 and 7 remain.

Candidates are temporary possibilities, not commitments. Update them whenever you place a number. Start in the most constrained area: a nearly complete row, column, or box.

Pairs and triples

Suppose two cells in one row can each contain only {2, 8}. Those two numbers must occupy those two cells in some order. Therefore, 2 and 8 can be removed from every other cell in that row. This is a naked pair.

The same logic applies to three cells sharing exactly three candidates. Pairs and triples work in rows, columns, and boxes.

A hidden pair reverses the observation. If 3 and 9 appear as candidates in only the same two cells of a box, those cells must contain 3 and 9—even if they currently show other candidates. Remove the other candidates from those two cells.

Do not identify a pair merely because two cells share two candidates. For a naked pair, both cells must be limited to those same two candidates. For a hidden pair, the two digits must occur nowhere else in that unit.

Box-line interactions

Boxes and straight lines overlap, creating useful deductions. Imagine that all possible positions for 5 in the upper-left box lie on its top row. The 5 must appear somewhere in those box cells, so no other cell in that row outside the box can be 5. This pattern is often called a pointing pair or pointing triple.

The reverse is also useful. If every candidate for 6 in a row lies within one 3×3 box, then 6 cannot appear in the other cells of that box. This is sometimes called claiming.

These deductions do not place a number immediately. Instead, they remove candidates, frequently exposing a single or pair on the next scan. Intermediate Sudoku is largely about making these small, certain eliminations and noticing what they unlock.

A reliable solving routine

When a puzzle feels stuck, use this cycle:

1. Check every cell with only one candidate.
2. Check every row, column, and box for a digit with only one position.
3. Look for naked pairs or triples in constrained units.
4. Look for digits confined to one line within a box, or one box within a line.
5. Update candidates and return to singles.

Start with the units containing the most filled cells, but do not ignore a sparse unit forever. A deduction elsewhere may have changed it. Rotating through rows, columns, boxes, and individual digits prevents tunnel vision.

If you think a placement is forced, state the reason before entering it: “This is the only place for 4 in the box,” or “This cell has no candidate except 9.” That brief check catches accidental guesses.

Common mistakes

Checking only the row and column. Every placement must also satisfy its 3×3 box. A number can look safe along both straight lines and still duplicate a box value.

Forgetting to update candidates. A correct placement can make old notes invalid in three different units. Remove those candidates immediately.

Misreading a pair. Two cells that both include 2 and 8 are not a naked pair if either cell also has another candidate. Verify the exact condition before eliminating anything.

Guessing when the board looks quiet. A stalled board usually needs a different scan. Search digit by digit, then inspect box-line interactions and pairs before branching.

Continuing after a contradiction. A duplicate highlight, a cell with no candidates, or a unit with no possible location for a missing digit signals an earlier mistake. Undo until the contradiction disappears and recheck the reasoning.

Difficulty and improvement

Difficulty is not determined only by the number of clues, but clue count strongly affects how much information is available at the start. Easy puzzles generally expose more singles. Normal puzzles require broader candidate scanning and simple interactions. Hard puzzles begin with fewer clues and may demand longer chains of eliminations.

To improve, prioritise accuracy over speed. Solve one unit carefully, keep candidate notes current, and use Undo as a learning tool rather than restarting at the first error. Over time, hidden singles, pairs, and pointing patterns become visually familiar. The goal is not to calculate faster; it is to recognise constraints more reliably.

Frequently asked questions

Do I need to be good at mathematics to solve Sudoku?

No. Sudoku uses the symbols 1–9, but it requires no arithmetic. You solve by tracking where each symbol can appear under the row, column, and 3×3 box rules.

Can a Sudoku have more than one solution?

A properly constructed classic Sudoku should have one solution. Felt & Wood generates a completed valid board first and removes clues while preserving a unique solution whenever possible.

What should I do when I cannot find another number?

Rescan systematically. Check each missing digit across every row, column, and box, then write down candidates and look for cells or units with only one possibility.

Is guessing allowed in Sudoku?

You can guess, but a well-formed puzzle can be solved through deduction. Before guessing, check for hidden singles, pairs, and interactions between boxes and lines.