Choosing your next step in a Number Fill-In Puzzle means deciding which of the six editable cells to commit to, and which digit to place there, based on the row and column that already surround it. The board is a compact 3 by 3 grid where three diagonal 1s are fixed givens; you fill the remaining six cells with 1, 2, or 3 so that every row and every column contains each of those digits exactly once. Every placement is checked immediately, and any repeated nonzero digit in a row or column triggers an instant contradiction, so the grid itself tells you when a step is wrong. The decision framework is therefore simpler than in larger logic puzzles: there are only six moves to make, the givens never change, and validation runs after every edit, so you can either commit, correct, or restart. Your next step is the cell that leaves you with the fewest contradictions and the cleanest path to a row that reads 1, 2, 3 and a column that reads 1, 2, 3.
How the Board Shapes Every Decision
The first decision you make on a Number Fill-In Puzzle is not where to move, it is what to look at. The grid is only nine cells, divided into two groups: three dark diagonal 1s that cannot change, and six editable cells that start empty. Zeros are treated as empty cells by the validator, so a fresh board shows six blank squares flanked by 1s along the main diagonal. Knowing which cells are givens, and which are open, collapses the entire board into a small set of possible lines: three rows, three columns, and six intersections. Your next-step question is always asked of one of those six intersections.
Every row and column must end with the multiset {1, 2, 3}. Each diagonal 1 already contributes a 1 to its row and a 1 to its column, which means every row and column still needs a 2 and a 3 to be complete. That observation narrows your choice before you press a number key: in any row or column with a 1 already placed, the two remaining cells can never both be 2 or both be 3, because doing so would leave a missing value. Looking at the diagonals first, then asking what each row and column still owes, is the structural shortcut that drives every next move.
Because the three givens are permanent, they cannot be changed during play; the validator requires them to remain intact. For a fuller explanation of why those three squares stay locked, the companion guide Number Fill-In Puzzle: Why the Given Cells Can't Change walks through the validator rule that protects them.
Reading a Row and Column Before You Press a Key
Before you commit to a move, look at both the row and the column of the cell you have selected. The validator checks six three-cell lines, three rows and three columns, and a placement is only safe if it satisfies both at once. A 2 placed in a row that already has a 1 and a 2 elsewhere will fail the moment the third cell is filled, because the line would contain two 2s. The same is true for a column. Treating each candidate cell as the intersection of two constraints is the fastest way to choose a step that does not need to be undone.
The grid exposes its state through contrasting surfaces. Given cells use a different background from editable cells, and a contradiction flag uses a visual warning so the offending row or column is obvious. Keyboard focus outlines also indicate which cell your arrow keys are about to edit, which keeps you from filling the wrong square by accident. The semantic CSS grid interface announces row, column, given status, current value, and selection to assistive technology, so the information you need to choose a next step is always visible.
Two practical shortcuts follow from that visibility. First, scan for any row or column that already contains two distinct nonzero digits; those lines can only accept the third value, so any cell in one of those lines must take the missing digit if it is to be filled safely. Second, when neither line contains two distinct nonzero digits, every digit is still available in that line, and your choice is governed by the perpendicular line, not the line you are scanning. This second pattern is where most strategic decisions actually live.
Choosing Your Next Fill in Number Fill-In Puzzle
The order in which you fill the six editable cells does not change the final grid, but it does change the number of edits you make and therefore the score. The fastest route uses six placements, one per editable cell, and scores 940 from a starting score of 1,000. Here is the concrete procedure for choosing each next fill.
- Use the arrow keys to move the visible selection to an editable cell whose row and column you can both read at a glance, ideally a corner adjacent to a diagonal 1.
- Check the row: if it already has a 1 and a 2 placed, the only safe value in that cell is 3, so press 3. If it has a 1 and a 3, press 2. If it has only blanks or only one nonzero, the row does not yet force the value.
- Check the column using the same forced-digit rule. If both the row and the column force the same digit, press that digit and move on.
- If only one of the two lines forces a digit, press that digit; the other line will be satisfied later by a neighbouring cell.
- If neither line forces a digit, choose any of 1, 2, or 3 that does not duplicate a placed value in either line. Press 1, 2, or 3 to place it, then watch for a contradiction flag on the cell or its row.
- If a contradiction appears, press Backspace or Delete to clear the cell, move to a different editable cell with the same logic, and continue. Use Restart if the board becomes tangled.
Mouse and touch users cycle through the same three values by clicking an editable cell, so the order of decisions is identical regardless of input method. The selection state, the editable markers, and the contradiction outline all update after every edit, which means your next step is always informed by the most recent board state.
Forced Moves, Free Moves, and What to Avoid
Every move on a Number Fill-In Puzzle is one of three types: a forced move, a free move, or a mistaken move. A forced move is a cell whose row and column together leave only one safe value; placing it cannot create a duplicate in either line. A free move is a cell whose row and column together still allow more than one value; you can place any digit that does not duplicate what is already in those lines, and the choice affects only your future freedom. A mistaken move is any placement that creates a duplicate in a row or column, which the validator flags immediately and which you should undo rather than build on.
Two practical heuristics reduce mistaken moves. First, prefer filling cells in lines that already have two distinct placed digits, because the value is forced and the placement cannot create a new duplicate. Second, when both a forced and a free move are available, take the forced move first; it locks in a row or column and shrinks the search space for the next step. Free moves are best saved for the last two or three cells, when most of the grid is already constrained and the free choices are obvious.
Two patterns are worth avoiding regardless of strategy. Do not treat a partial row that contains, for example, 1 and 3 as a guarantee that the third cell must be 2; it can also be left empty until the column forces a value, and the validator treats zeros as empty rather than as errors. Do not assume that a contradiction means the most recently edited cell is wrong; the duplicate may actually live in a different cell of the same row, so undoing the right cell sometimes requires scanning the whole line rather than the last edit.
Reading the Score and Validation Feedback
The score on a Number Fill-In Puzzle starts at 1,000 and is computed as max(0, 1000 − 10 × edit actions). The "edit actions" count is every change to an editable cell, including corrections with Backspace or Delete, so a clean six-fill route produces 1000 − 10 × 6 = 940. If you make two extra corrections along the way, the score drops to 1000 − 10 × 8 = 920. The formula is therefore a direct proxy for how many undo decisions you needed to make, and the cleanest path is one where every next step is correct on the first try.
| Edit actions | Calculation | Final score |
|---|---|---|
| 6 (clean route) | 1000 − 10 × 6 | 940 |
| 8 (two corrections) | 1000 − 10 × 8 | 920 |
| 10 (four corrections) | 1000 − 10 × 10 | 900 |
Validation, however, runs after every edit and is a separate signal from the score. An incomplete row with two distinct placed digits is still valid, so the absence of a contradiction flag does not mean the row is finished; it means only that no rule has been broken yet. Conversely, a contradiction flag is an immediate hard signal that a duplicate exists in that row or column, not a hint about which digit to try instead. The cleanest use of feedback is to treat the score as a measure of how decisively you are choosing your next step, and to treat the contradiction flag as a signal to clear the duplicate from the affected row or column.
| Cell state | Visual cue | What it means for your next step |
|---|---|---|
| Given diagonal 1 | Contrasting surface, not editable | Permanent; cannot be changed; counts toward row and column totals |
| Empty editable | Plain editable background, value 0 | Free to fill; the validator will check the placement |
| Filled editable (valid) | Editable background, nonzero value | Placement is consistent with the row and column so far |
| Filled editable (contradiction) | Warning indicator on the cell or line | A duplicate exists in the same row or column; clear with Delete |
The completed best score is stored only in your browser, so each session begins from 1,000 and your next-step discipline is measured fresh each time you start.
Restart, Boss Key, and End-of-Puzzle Checks
Three practical controls round out the decision workflow. Restart restores the three diagonal givens, clears all six editable cells, resets the selection and the score to 1,000, and removes any contradiction flag. Use it when more than one cell needs to change, because a series of undos can drift the score downward without restoring the board to a clean state.
The boss key is a double-press of Escape, which opens a shared simulated spreadsheet overlay; pressing Escape twice again returns you to the same puzzle state, with selection and filled values preserved. This lets you step away from the board without losing progress, so your next move on return is exactly where you left off.
Completion itself requires nine filled cells, the three givens unchanged, no duplicates in any row or column, and a total of 6 on every row and column, which is exactly the condition that each row and column contains one 1, one 2, and one 3. A valid solution reads 1-2-3, 3-1-2, or 2-3-1 across the rows, and the reverse orientation is also accepted when it satisfies the same disclosed constraints. The validator checks the rules rather than a hidden answer string, so any completed grid that preserves the givens and obeys the row and column rules is accepted.
Play the full grid in your browser on the Number Fill-In Puzzle page, where every input method, contradiction flag, score update, and restart gesture described above is wired into the same interface. Each step you choose is checked against the disclosed rules, and the next move you face is always the one with the fewest open decisions left.
Related reading: Easy One Line Draw Puzzles: Solve the 8-Node Graph.