The Math Crossword asks you to fill four shared variables — A, B, C, and D — so that three crossing multiplication equations all hold at the same time, and a clean way through the board is A = 3, B = 6, C = 2, and D = 6 for a 960-point finish. Choosing your next step is therefore not a guess between blank cells; it is a forced sequence dictated by which equations still need their last nonzero value. The keyboard-driven board shows 2 × A = B, A × C = D, and B × C = 12, and because the three equations share A, B, and C across them, every entry you make must agree with the previous one. The right way to choose your next step is to think of the three equations as a small crossing grid: pick the variable whose equation has only one remaining unknown, fill it, then move to the equation that has now narrowed to a single value.
This page walks through that reasoning in plain language, ties it to the exact controls on the Math Crossword page, and shows why four clean entries are enough to finish with 960 points. If you have already started and run into a warning, the same board logic still applies — every completed but false equation is fully repairable, and you can read the contrast in the contradictory-board guide.
What the Math Crossword Board Actually Asks of You
The board displays four labeled slots, one for each of the variables A, B, C, and D. The slot shows whatever digit you last entered, and below the slots the page renders three multiplication equations in fixed positions: 2 × A = B on the left, A × C = D on the right, and B × C = 12 at the bottom. The three equations share variables rather than sharing letters the way a printed crossword does — A appears in the first two equations, B in the first and third, C in the second and third, and D only in the second.
Choosing your next step starts with noticing which equation has only one unknown left. The first equation 2 × A = B ties A and B together directly. The third equation B × C = 12 ties B and C together. Once you fix one of those pairs, the other equations collapse toward a single answer. The point of the puzzle is to read the equations as a tiny grid rather than three independent math problems, and that single shift in framing is what removes the guesswork from every later entry.
How to Fill the Four Variables in Order
Use the arrow keys to slide the visible selection between A, B, C, and D. Press a number from 1 through 9 to set the selected variable, and use Backspace or Delete to clear it. Mouse and touch users can click a variable to cycle through the same 1–9 range. The validator only checks an equation once every variable it needs is nonzero, so a half-finished board never triggers a false alarm.
- Move to the A slot with the Left or Right arrow key. Press 3 to assign A = 3. The board now has a single nonzero value but no equation has every variable it needs, so the status stays neutral.
- Move to B and press 6. Now both variables in 2 × A = B are filled, the equation reads 2 × 3 = 6, and the validator accepts it as true. The other two equations still wait for C and D.
- Move to C and press 2. The third equation now has both B and C nonzero, so 6 × 2 = 12 is checked and accepted. The middle equation A × C = D still needs D, so it waits.
- Move to D and press 6. The middle equation closes as 3 × 2 = 6, all three equations are simultaneously true, and the status flips to complete. Your score settles at 960 because you used four clean entries.
If you overshoot at any step, just press the right digit again or Backspace to clear and try a different value. The score reflects total edits, so changing your mind is allowed but costs you ten points per extra entry, and the validator responds to the current board rather than remembering the mistake.
Why Incremental Validation Gives You Room to Rethink Your Next Move
The validator is deliberately patient. It only judges an equation once every variable used by that equation is nonzero. That means a board with A = 4 and the rest empty is not wrong — 2 × A = B cannot be checked yet because B is still empty. The moment you change A to 3 while B is still 8, the first equation becomes 2 × 3 = 8, the validator sees a fully populated equation that is false, and the status line reports a contradiction.
This is the central reason a "wrong" step is not a dead end. Restoring A to 4 makes the equation true again, the warning clears, and the board is back to a viable partial state. Choosing your next step therefore never costs you a fresh puzzle — you only lose ten points on the score for the entry you replaced. The constraint that always matters is the math; the warning is a description of the current board, not a lock on it, and that distinction is what makes the puzzle feel like a small decision tree rather than a maze cul-de-sac.
Reading the Three Equations Like a Crossing Grid
Treat the three equations as a small crossing diagram. The first equation crosses with the third through B, and the first equation crosses with the second through A. The middle equation crosses with the third through C. That sharing pattern is why picking the next variable is a constraint-satisfaction question, not a guess, and the table below shows how the board opens up after each clean entry.
| Step | Variable you set | Equation that becomes checkable | Status after the entry |
|---|---|---|---|
| 1 | A = 3 | None yet | Neutral, board still partial |
| 2 | B = 6 | 2 × A = B | First equation true |
| 3 | C = 2 | B × C = 12 | Third equation true |
| 4 | D = 6 | A × C = D | All three true, board complete |
Notice that the third equation never becomes checkable before the second — B and C are both required. Likewise, the middle equation waits for D, which is why the clean route naturally ends with D. If you filled D earlier, the equation would not yet be checkable, and you would have spent an edit without gaining any new information about whether the rest of the board holds together.
Score, Restart, and Boss Key Behavior
The score starts at 1,000 and the page subtracts ten points for every variable edit, so four clean entries settle the run at 960. Restart resets A, B, C, and D to empty, returns the selection to the first slot, restores the score to 1,000, and clears any warning line. Your best score lives only in the browser's localStorage — the page does not send it across the network and there is no account layer to maintain.
Double-press Escape to swap the puzzle for a simulated spreadsheet screen, and double-press Escape again to drop back to the same unfinished board with the same selection and the same nonzero entries intact. There is no timer, no audio, no canvas, and no download: the entire interaction is keyboard, mouse, or touch on a single semantic page, and the interface stays usable on a phone without a mouse because every variable is reachable through both clicks and physical key presses.
Where Most Players Trip Up on Their Next Entry
Three traps catch first-time players. First, entering C before B looks tempting because B × C = 12 is the equation with a known constant, but without B the validator cannot check it and your edit is wasted — the third equation only opens up once the first equation has already pinned B. Second, picking the same digit for every variable because the puzzle has only four slots misreads the equations; the board does not require uniqueness, and the clean answer uses 6 in both B and D because the shared multiplication forces that overlap rather than forbidding it.
Third, treating a contradiction warning as a permanent error makes the puzzle feel like a maze cul-de-sac, when in fact the warning reflects the current board and disappears the moment you restore a true equation. Choosing your next step on a Math Crossword is therefore a matter of reading the shared variables first, picking the slot that closes one equation, and letting the next equation narrow the value before you press it in. Four clean entries score 960, the validator stays patient between checks, and a Restart wipes everything except your stored best score.
Related reading: Choosing Your Next Step in Number Balance: A Walkthrough.