Yes, you can correct a contradictory board in Math Crossword by replacing or clearing any variable, and validation recalculates all three equations on the next edit, so a mathematical deadlock is fully recoverable rather than a permanent fail. The puzzle asks you to fill four shared single-digit variables — A, B, C, and D — so the three displayed equations 2 × A = B, A × C = D, and B × C = 12 are true at the same time. Math Crossword only flags a contradiction after every variable needed by an equation is nonzero and that equation still evaluates false, which means a half-finished board never produces a false warning. As soon as you change or clear a value, the validator re-checks every completed equation against the current board, so a single wrong entry does not lock the run, which means every contradictory state in this four-variable grid can be resolved by a follow-up edit without restarting the puzzle.
That recovery loop is what makes Math Crossword forgiving even when the displayed equations look intimidating. The four variables are shared, the three equations are tied together, and the same digit can legitimately repeat. The verified clean answer uses A = 3, B = 6, C = 2, and D = 6, which yields 2 × 3 = 6, 3 × 2 = 6, and 6 × 2 = 12 — three true equations at once. Filling those four digits with no corrections scores 960 points from the initial 1,000, because each edit deducts 10 from the score and four edits total a 40-point cost.
How Math Crossword Detects a Contradiction
The validator in Math Crossword accepts exactly four integer slots in the range 0 through 9, with the browser input restricted to 1 through 9 and zero serving as the clear state. Validation is incremental rather than all-or-nothing. The first equation, 2 × A = B, is only checked once both A and B are nonzero. The second equation, A × C = D, only checks once A, C, and D are all nonzero. The third equation, B × C = 12, only checks once B and C are nonzero. As long as any needed variable is still empty, that equation stays out of the verification step and no warning appears.
The contradiction message appears the moment a completed equation is false. For example, entering A = 4 and B = 8 satisfies 2 × A = B, so the board remains viable while C and D are still empty. If you then change A to 3 while B stays 8, the validator immediately reports a contradiction because 2 × 3 is not 8. Restoring A to 4 clears the warning, which proves the validator reflects the current board rather than remembering an earlier mistake. This makes a contradiction a current-state problem, not a sticky penalty, and a half-correct board that you walk away from never triggers the warning on its own.
How to Recover From a Contradictory Board
- Read the contradiction message to confirm a completed equation is false; the warning tracks the live board.
- Pick any variable that participates in the failing equation and select it with Left or Right arrow until that slot is highlighted.
- Press a digit from 1 through 9 to overwrite the value, or press Backspace or Delete to clear the slot back to empty and reset that equation to "not yet validated."
- Watch the status text — replacing or clearing the offending variable forces an immediate re-check, and a corrected board clears the contradiction within one edit.
- Repeat the cycle on any other false equation until all three equations read true and every variable is nonzero, which closes the puzzle.
You can also use a mouse click or tap to cycle the selected variable through 1 through 9 if you do not want to switch back to the keyboard. Clicking advances the digit, and the validator re-runs after every change. There is no separate penalty for clearing a variable beyond the standard 10-point edit cost, and clearing resets that equation's contribution to "not yet checked," which removes the contradiction in many cases before you even choose a replacement value. If you would rather start over, the restart control wipes A through D, restores 1,000 points, and removes every warning while leaving your stored best score untouched.
The Clean 960-Point Solution Walked Through
The verified clean route is a four-edit finish. Start with A = 3, which makes 2 × 3 = 6 and forces B to be 6 to keep the first equation true. Enter B = 6; at this point the third equation 6 × C = 12 is already constrained, and C must be 2. Enter C = 2; the second equation becomes 3 × 2 = D, so D must equal 6. Enter D = 6 to close the puzzle. Substituting back gives 2 × 3 = 6, 3 × 2 = 6, and 6 × 2 = 12, all three true simultaneously. Starting from 1,000 and subtracting four edits at 10 points each gives the 960-point finish, and the variables are non-unique by design — B and D are both 6 because the equations only require them to satisfy the products, not to differ.
If you fill the variables in a different order, you may enter a contradiction that you then fix. For instance, entering A = 4 first and B = 8 second is internally consistent on the first equation. If you then type D = 7 while C is still empty, the second equation A × C = D is not validated yet because C — a needed variable — is still empty, so no warning appears at that step. Only once C is also filled does the validator check whether 4 × C = 7 holds, and since no integer digit in the 1 through 9 range makes that true, the warning fires. Clearing D back to empty removes the contradiction, and you can enter D = 8 once C = 2 is in place. The validator simply reports the truth of each equation with the current board; it does not lock past input, which is why the recovery steps above always work regardless of how many digits you have already typed.
Controls and Input Reference
The Math Crossword interface exposes a small, deterministic control set. Each variable has one editable button, and the equation display echoes the current shared value so you can read the live board without guessing what the validator is currently testing.
| Input | Action | Notes |
|---|---|---|
| Left / Right arrow | Move selection between A, B, C, and D | |
| 1 through 9 | Replace the selected variable with that digit | Each press counts as one edit and subtracts 10 points |
| Backspace or Delete | Clear the selected variable to empty | Resets the affected equation to "not yet validated" |
| Click or tap a variable | Select and cycle through 1 through 9 | Mouse and touch share the same input range as the keyboard |
| Double-press Escape | Toggle the simulated spreadsheet boss screen | Pressing it again resumes the same puzzle in progress |
| Restart control | Clear A through D, restore selection and 1,000 points | Removes every warning without touching the stored best score |
There is no canvas, no random generation, no timer, no audio, no account, no download, no hardware access, and no network request. The completed best score is stored only in localStorage, so it persists across refreshes on the same browser but does not sync between devices. The validator also rejects values outside 0 through 9, non-integers, and arrays of the wrong shape, so the only legal moves are the inputs in the table above — anything else simply does not register as a valid edit.
Score Mechanics and Best-Score Persistence
The score starts at 1,000 and follows a fixed formula: max(0, 1000 − 10 × number of variable edits). Every time you overwrite or clear a variable, the edit count rises by one and the displayed score drops by 10. The minimum is zero, but the clean four-edit finish lands at 960, which is the verified top score for this puzzle. Because the validator only marks an equation as wrong once every variable it needs is filled, you can leave a partially correct board in place while you think; it does not pay to rush a replacement digit because each one costs 10 points regardless of whether it was correct. Clearing a variable to escape a contradiction also counts as one edit, so if you clear once and then enter the right digit, that path costs 20 points beyond the four clean edits.
Restart returns the board to the initial empty state, restores the 1,000-point score, and clears every warning. It does not erase the locally saved best score, which keeps tracking your best Math Crossword run across sessions until you clear site data. If you want to compare strategies, finish the puzzle twice — once from scratch with no corrections and once after deliberately breaking an equation and recovering — to confirm the 960-point and 950-point results respectively. The difference of 10 points reflects exactly one extra edit on the corrected path, which is the entire cost of taking advantage of the recovery loop.
Related Number Puzzles
If you enjoy Math Crossword's mix of arithmetic and recovery, try Addition Maze.. Magic Square is another related number play option. Both share the same deterministic, keyboard-first feel as Math Crossword, which makes them natural next stops once you have the multiplication grid under control.