Math Grid Tips: Solve Every Row and Column Like a Small Equation (2026)

1. Six small equations, not one big one

The board looks like arithmetic and is really a matching problem. Each of the three rows reads left to right as a op b = c, and each of the three columns reads top to bottom as a op b = c. Six lines, six operators, all printed for you before you place a single digit.

Because every line holds one operator, there is nothing to evaluate in order. You never have to decide whether 2 + 3 × 4 means 14 or 20, because the build never puts two operators in one line. Whatever worries you brought from school arithmetic, drop them at the door: this is six independent statements that happen to share cells.

That sharing is the whole puzzle. The three cells of the bottom row are the results of the three row equations and the last cell of the three column equations. Change one digit in the bottom row and you have changed two equations at once. Once you see the grid as six overlapping constraints instead of nine numbers, the solve order stops being a mystery.

2. The one rule that fills most cells: the third number from two

Inside a single line, if you know two of the three cells, the third is forced. You can invert every operator this build ships:

• +: c = a + b, so a = c − b and b = c − a.
• −: c = a − b, so a = b + c and b = a − c.
• ×: c = a × b, so a = c ÷ b and b = c ÷ a.
• ÷: c = a ÷ b, so a = b × c and b = a ÷ c.

Two guards come with the rule. The answer has to be a digit from 1 to 9, and a division has to come out exact. If inverting an operator gives you 0, 12, or 7 ÷ 2, then one of the two numbers you trusted is wrong — which is itself useful information, because it eliminates an assumption without costing a guess.

The board will not confirm a line for you until all three of its cells are filled. A line is marked green when its equation is true and red when it is false, so a half-filled line stays neutral. That is deliberate: you have to commit a digit before the board judges the line, and the judgement is about the whole line, not the cell you just typed.

3. What each tier actually hands you

The 28 puzzles are not the same puzzle with more blanks. Read the book by tier:

Across the whole book there are 62 given cells, so the average puzzle hands you 2.2 numbers and expects you to derive the other 6.8. Easy is the only tier where four givens are enough to keep the "third from two" rule running from the first move: in all 8 easy puzzles the four givens sit so that at least one line already holds two of them.

That is the line you should hunt for on any board. In this book only 10 of the 28 puzzles open with a line holding two givens — the 8 easy ones plus medium #12 and medium #15. On the other 18, no line starts with two numbers, so the technique in section 2 has nothing to grip at move one. Those puzzles are not harder because they are bigger; they are harder because the easiest rule is unavailable at the start.

4. How far pure logic gets you — measured

It helps to know how much of each tier is deduction and how much is search, because the two feel completely different when you are staring at the board. This session ran both techniques on all 28 puzzles.

The "complete the third" chain — repeatedly find a line with two numbers and fill its third — solves all 8 easy puzzles in exactly 5 placements each, no guessing, no dead ends. Four givens plus five forced cells is nine. That is the whole easy tier: a five-step chain.

The same chain adds nothing on 7 of the 10 medium puzzles (it adds 1 placement on #12 and 2 on #15) and nothing at all on any hard puzzle. So the technique that carries easy is worth roughly one move per medium puzzle. It is not that players are doing it wrong; after easy the book stops offering lines with two givens, and that is a deliberate design choice.

The next tool up is per-line candidate elimination. For one line, list every triple of digits 1-9 that satisfies its operator, then delete any value that no surviving triple allows. The raw sizes are small: of the 729 ordered triples of digits 1-9, only 36 satisfy a + b = c, 36 satisfy a − b = c, 23 satisfy a × b = c and 23 satisfy a ÷ b = c. Running that elimination to a fixed point pins every cell to a single value on 22 of the 28 puzzles.

Six puzzles survive it: medium #14, and hard #21, #23, #24, #26, #27. On those the per-line reasoning runs out with cells still holding two or more candidates, and you have to branch — pick a two-candidate cell, commit, and see whether a line breaks. That is the honest shape of the hard tier: a handful of forced cells, then a decision.

One last measurement, because it changes how you guess. Across the 28 solutions, the 252 filled cells use the digit 1 in 101 cells, 2 in 77, 3 in 27, 4 in 24, 5 in 6, 6 in 11, 7 in 2, 8 in 4 — and 9 in none at all. The largest digit anywhere in the book is 8. That is a property of this puzzle book, not a rule of cross math: 1 is the cheapest digit to place, because it is the identity for × and ÷ and a one-step neighbour for + and −. When you are down to two candidates and nothing else separates them, try the smaller one first.

5. × and ÷ lines are the narrowest — use the tables

A multiplication line has 23 valid triples instead of 36, and a division line has 23 as well. That is a third fewer possibilities per line, which makes those two lines the best place to start cutting. The complete tables for this build:

Multiplication — result on the left, the two input pairs on the right:

• 1 → (1,1)
• 2 → (1,2)
• 3 → (1,3)
• 4 → (1,4), (2,2)
• 5 → (1,5)
• 6 → (1,6), (2,3)
• 7 → (1,7)
• 8 → (1,8), (2,4)
• 9 → (1,9), (3,3)

Three readings follow immediately. A prime result (2, 3, 5, 7) forces a 1 on one of the two input cells — there is no other way to reach it. A result of 1 forces both inputs to 1. And a result of 4 or 8 is the wide case, with three and four pairs respectively, so those lines tell you the least per digit you spend.

Division — quotient on the left, the two input pairs on the right:

• 1 → (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9)
• 2 → (2,1), (4,2), (6,3), (8,4)
• 3 → (3,1), (6,2), (9,3)
• 4 → (4,1), (8,2)
• 5, 6, 7, 8, 9 → (5,1), (6,1), (7,1), (8,1), (9,1)

The quotient-1 row is the one people misread. It does not say "any digit"; it says the two cells are equal — nine pairs, all of them a digit and itself. That is a real constraint and it is the strongest equality the board can hand you. Every other quotient behaves the other way: a quotient of c ≥ 2 forces the divisor cell to be at most 9 ÷ c, and a quotient of 5 or more pins the divisor to 1 and the dividend to exactly the quotient. Eight of the ten hard puzzles contain a ÷ line, so this table is what makes the hard tier tractable rather than a coin flip.

6. Reading the board

• A line turns green only when all three of its cells are filled and its equation is true; red when all three are filled and it is false. Two filled cells never produce a colour, so you cannot use the board to confirm a partial guess.
• When a line goes red, every cell in it goes red too — except the given cells, which stay in their own style. The red is a marker of the line, not an accusation about one cell.
• Because each puzzle has exactly one solution, a red line means at least one of its three digits is wrong. It never means the operator changed. Re-check your last placement before you start rewriting the line.
• Digits may repeat, anywhere — inside a row, inside a column, in every cell at once. There is no sudoku habit worth carrying over: the only rule is that the six equations hold.
• After you place a digit, the selection jumps to the next empty cell in reading order. Typing three digits in a row fills three cells in a row, which is why the digit pad is faster than it looks on a phone.

7. Hints, restart and pinning a puzzle

Hints are unlimited here, and they are counted. The counter in the top bar rises with every hint, and the win message reads it back to you ("Solved in 74s with 2 hints"). So the pressure is not a limit; it is the number you have to look at afterwards.

Position matters, because a hint targets the selected cell first. If you have a cell selected and it is empty, the hint writes the solution digit there. If the selected cell is a given or already filled, the hint falls back to the first empty cell in reading order. That means you can aim a hint: select the cell whose two candidates you cannot separate, and the hint settles that cell rather than some unrelated one at the top of the board.

Restart reloads the same puzzle and clears every digit you placed — the givens come back, the timer resets to zero, and the hint counter resets with them. Next puzzle advances within the current tier and wraps around at the end. Two URL parameters are worth knowing: ?tier=easy, ?tier=medium or ?tier=hard opens a tier at its first puzzle, and ?level= followed by an id from 1 to 28 pins that exact puzzle, which is how you go back to one you did not finish. Progress — your tier, your index and which puzzles you have solved — is kept in the browser's local storage, so closing the tab does not cost you the board.

The timer starts on your first digit or your first hint, whichever comes first. There is no time limit and no score beyond that clock and the hint count.

8. Common mistakes

• Applying operator precedence. Each line has one operator. a op b = c is the entire grammar; nothing binds tighter than anything else.
• Reading a red line as "wrong operator". The operators are fixed by the puzzle. Red means a digit is wrong.
• Treating a hint as free. It is unlimited, which makes it feel free, but it is counted in the win message and it always writes the true digit — so spending one on a cell you were about to solve is a straight loss on the number you will see at the end.
• Guessing with 9. Nine does not appear anywhere in the 28 solutions. Small digits are where the answers live.
• Hunting for sudoku logic. There are no boxes and no all-different rule. Two cells in the same row can hold the same digit as long as the equations hold.
• Filling the bottom row first. Those three cells are results of both their row and their column, so a wrong digit there breaks two lines at once. Derive them last.

FAQ

How do you solve a math crossword puzzle?

Read it as six separate equations, not one expression. Find a line that already holds two numbers, invert its operator to get the third, and repeat. When no line has two numbers left, list the candidate digits per cell, delete what no valid triple allows, and only branch when a cell still holds two. On this build that chain finishes all 8 easy puzzles outright, and per-line elimination finishes 22 of the 28 without any guessing.

Is cross math the same thing as Math Grid?

Cross math is the genre name for this shape: a grid where rows and columns each form an arithmetic equation with the operator printed in place. Math Grid is this site's own implementation of it — a 3x3 grid, digits 1-9 with repeats allowed, 28 puzzles across three tiers, an independent engine and puzzle book, no third-party app or site involved. If you have played a "math crossword" or "cross math" worksheet on paper, the rules will feel familiar; the difference here is that the board checks the six lines for you as you fill them.

Why is my row red when the numbers look right?

The line is checked as a whole: a op b = c with the operator printed on that line. A row can look plausible and still be false — 6 − 4 = 2 is true, 6 − 2 = 4 is a different equation. Red also appears the moment the third cell of the line is filled, so it is worth checking the operator before you change any digits.

Can the same digit appear more than once?

Yes, freely. There is no all-different rule anywhere in this game: the same digit can repeat inside a row, inside a column, and across the whole grid. One of the 28 puzzles is solved with a single digit repeated in all nine cells. Any "sudoku" instinct you bring will cost you time.

Do I get a limited number of hints?

No. Hints are unlimited and each one is counted in the top bar and in the win message. A hint writes the correct digit into the selected cell (or the first empty cell in reading order if your selection is a given or already filled), so the useful move is to select the cell you are stuck on before pressing it.

Is there a time limit or a score?

There is a timer and a hint counter, and nothing else. No lives, no score, no loss condition, no leaderboard. Win by making all six equations true with all nine cells filled; the win panel then reports your time and hint count.

Where can I play it?

On this site's Math Grid page. The build is Playnesta-original under MIT: the 3x3 equation grid, the 28-puzzle book with its exhaustive uniqueness check, the renderer, the digit pad, the line validation, the persistence and the analytics bridge are all Playnesta work, and no upstream code, artwork, audio or font is redistributed. Cross math and math crossword are descriptive names for the genre; this game is not affiliated with any app or site of a similar name. Playnesta Games is the developer and publisher of this web implementation.