Line Three: could this board occur in a legal game?
Check turns, stop-at-win rules, and a valid two-line finish. Edit seven examples in a position checker verified against every labeled board.
Before asking which square wins, ask whether the position could have occurred at all. A hand-copied diagram can give one side an extra turn, show both players already winning, or continue after the game should have ended. A tactical explanation built on that diagram can be wrong before its first suggested move.
This lesson checks ordinary Line Three rules: X starts, players alternate, marks never move, and play stops at the first completed row, column, or diagonal. The editable exercise below the lesson checks a position against those rules. It does not choose a move or load the diagram into the live computer game.
Start by counting turns
X plays first. After a completed O turn, both sides have the same number of marks. After a completed X turn, X has exactly one more. Those are the only possible counts: X = O, or X = O + 1. A dot in the diagrams is an empty square, not a third kind of mark.
X X · · · · · · ·
This board has two X marks and no O. It cannot occur in an alternating game: O had to place a mark between the first and second X. The absence of a winning line does not make the board valid.
If a valid unfinished board has equal counts, X is next. If X has one extra mark, O is next. Establish that before planning a threat; reversing the player to move changes the question.
A balanced count does not settle it
X X X O O O · · ·
Here the counts are balanced at three X and three O, but both players have completed a row. Someone had to finish a line first. That ended the game, leaving no legal turn on which the second player could complete another line. Reject the position rather than asking which of the two lines should count.
Check who was allowed to make the last move
X X X O O · · · O
This board also has three X and three O. Only X has a winning line, so the problem is subtler than two winners. A legal X victory occurs immediately after X moves, when X must have one more mark than O. The displayed equality means O took another turn after X already won.
You can expose the extra move with this attempted history: X at R1C1, O at R2C1, X at R1C2, O at R2C2, then X at R1C3. Stop there: X's top row wins with three X and two O. Adding O at R3C3 produces the printed diagram, but that sixth move was not allowed.
The opposite condition matters too. If O has won, the counts must be equal, because O just made the final move. Counting turns and checking the winner work together; neither step replaces the other.
Two winning lines can belong to one legal last move
X O X O X O X O X
X has five marks and O has four. X completes both diagonals through the center. This is not the same as both sides winning. A single final X at R2C2 can complete both diagonals at once.
To verify a real history, play X R1C1, O R1C2, X R1C3, O R2C1, X R3C1, O R2C3, X R3C3, O R3C2, and finally X R2C2. Before that last center mark, neither side has a completed line. The final move creates both X diagonals together, so the board is a legal X victory and the game is over.
Counting winning lines as if each required a different turn would wrongly reject it. What matters is whether one legal last move can produce the finished position without an earlier win.
Distinguish a legal next turn from a finished board
X O · · X · · · O
This position has two X and two O, no completed line, and empty squares. X is next. One legal history is X R1C1, O R1C2, X R2C2, O R3C3. This establishes that the board can occur; it does not say those were the best moves or that the live computer would choose them.
X O X X O O O X X
The full board has five X and four O, with no winning row, column, or diagonal. It is a completed draw. Equal counts are not required for a draw when X fills the ninth square. There is no next player after a win or a full-board draw.
Try the editable position check
Use Try the position check in the side panel. Choose a named example and Load example, or set the nine square controls to empty, X, or O. The labels R1C1 through R3C3 follow the diagrams. Choose Check position after editing.
Start with O moved after X won. Predict why it fails, then check it. Clear R3C3 and check again: the counts become three X and two O, and the top-row X victory is now valid. The missing O mark repairs the history rather than changing which line wins.
Next load Two lines, one last move. The checker should accept the finished X win and list both diagonals. Remove the center X: the board is now unfinished with four marks on each side, so X is next. Restoring that center X ends the game. Clear board returns all nine controls to empty; it does not change an ongoing live round.
| Example | Verdict |
|---|---|
| Empty board | Reachable; X is next |
| Too many X marks | Unreachable; turn counts fail |
| Both sides have a line | Unreachable; play had to stop at the first win |
| O moved after X won | Unreachable; X's win requires one extra X mark |
| X to move | Reachable; X is next |
| Two lines, one last move | Reachable; X won and play has ended |
| Full draw | Reachable; no next player |
How the check was verified
Each of nine squares has three possible labels: empty, X, or O. That gives 3 to the ninth power, or 19,683 labeled boards. An independent search started at the empty board, alternated players, and stopped expanding every win or full draw. It reached 5,478 distinct boards under these exact rules.
We compared the checker's answer with that reachable set for all 19,683 labelings, not just the seven examples. Every verdict agreed. Rotations and reflections were counted separately; these are labeled boards, not distinct strategic shapes. The count is not the number of complete games or move sequences, because different histories can reach the same board.
For this ordinary 3 × 3 game, the turn-count and winner conditions described above distinguish the reachable boards. That statement was checked against complete legal histories; a similar shortcut should not be assumed for a larger grid, a rule where O starts, or a game that continues after a win.
What a reachable board does not prove
Reachable means at least one permitted history exists. It does not prove that a screenshot is genuine, reconstruct the history actually played, identify optimal play, or promise that X can win next. The checker accepts a finished board as a valid position while still saying there is no next turn.
Use the check to repair a copied diagram or confirm whose turn your paper puzzle describes. Then return to reading immediate wins, blocks, and future threats. The live game already enforces alternating moves and locks a finished round; this separate exercise lets you inspect diagrams that the live controls correctly refuse to create.