How to Solve Cross Math: Rules, Tips and Strategies for Beginners
Cross math looks like a crossword but speaks arithmetic: every row and every column of the grid is a complete equation — digit, operator, digit, equals sign, result. Some digits are already filled in, and your job is to work out the missing ones so that every line is true. It's a gentle introduction to equation logic, and once you learn the three golden rules, the blanks fill themselves. Here's how it works and how to get good at it fast.
The rules in one minute
Fill every blank cell with a digit from 1 to 9. Every row is an equation read from left to right — the first two digits combined with the operator must equal the result on the right. Every column is an equation read from top to bottom the same way. Work strictly left to right (and top to bottom): there is no multiplication-before-addition precedence, so 2 + 3 × 4 means (2 + 3) × 4 = 20, not 14. Division is always exact — no remainders or fractions — and every result is a positive whole number. Every cross math puzzle has exactly one solution.
How to read the grid
Each line of the grid is a small equation with a single result digit, so all the arithmetic stays small: results are always one digit, and products and quotients are limited to the small times tables. A row like 4 + 2 = 6 or 8 ÷ 2 = 4 fills three cells, and the digit in the crossing column has to work for its own equation too. On our cross math generator the grid is drawn exactly this way — digits in the squares, operators between them, equals signs in the middle — so you can practice on a printed puzzle. If you just want the plain rules without the strategies, our rules page has them all in one place.
1. Start with the lines that are almost finished
A row or column with one blank left is a direct subtraction: take the two digits you can see and work out what the missing one must be. If a row reads 9 − ? = 4, the blank is 5; if a column reads 3 × ? = 12 — wait, results are always one digit, so 3 × ? = 9 means the blank is 3. Sweep the whole grid for near-complete lines first; each one you finish tightens the crossing lines that share its cells.
2. Use the crossing lines like sudoku
Every blank belongs to two equations at once — its row and its column. If a blank could be 2 or 6 to satisfy its row, but its column needs a digit that divides evenly (say 8 ÷ ? = 2, which needs a 4), the 4 wins. List what each line allows, and the digit that appears in both lists is the answer. This intersection logic is the heart of cross math, and it's what makes the puzzle feel like a crossword instead of a stack of equations.
3. Learn the small facts by heart
Because every result is a single digit, the equations come from a small pool of arithmetic facts. Addition and subtraction are straightforward (6 + 2 = 8, 9 − 5 = 4). Multiplication is limited to products of 9 or less: 2 × 4 = 8, 3 × 3 = 9, 2 × 3 = 6. Division must be exact: 8 ÷ 2 = 4, 9 ÷ 3 = 3, 6 ÷ 2 = 3, 8 ÷ 4 = 2. Knowing these cold means you recognize a line's options instantly instead of redoing the arithmetic.
4. Work left to right — never apply school precedence
This is the number-one mistake in cross math. Your brain is trained to do multiplication before addition, but this puzzle explicitly reads every line left to right with no precedence. 2 + 3 × 4 is (2 + 3) × 4 = 20, and 8 ÷ 2 + 1 is (8 ÷ 2) + 1 = 5. If a line seems impossible under normal math rules, check whether you accidentally applied precedence — almost always, reading it strictly left to right makes it work.
5. Division must come out even
On the harder levels, division appears in the equations, and it only works when it divides exactly: 8 ÷ 2 = 4, but 9 ÷ 2 has no whole-number result, so it can never appear. Use the reverse multiplication facts — 8 ÷ 2 works because 2 × 4 = 8. When a column or row contains a division sign, the blank digits are almost always a pair from the small times tables, which narrows the options dramatically.
6. Anchor on the given digits
The pre-filled digits are your footholds. A given result pins down its whole line once the other digits are known, and a given operand limits the possible operators' partners. Work outward from the cells the puzzle already gives you — they're placed exactly so that the grid unlocks from those starting points.
7. Jot down candidate digits
In the corner of each blank, pencil in the digits its row allows, then cross off any that its column rules out. Cross math grids are small, so tidy candidate marks turn a wall of equations into a simple elimination chart. On screen, our cross math maker lets you type digits directly and check your work as you go — wrong entries get flagged instantly.
8. Avoid the classic mistakes
Three errors trip up beginners. First, applying operator precedence instead of reading left to right. Second, accepting a division that doesn't come out even — if a line has a remainder, it's wrong. Third, forgetting that every blank must satisfy its column as well as its row; a line that works in isolation can still break the crossing equation. Check each finished line in both directions, and if you're stuck, revealing the answer key is a great way to see the pattern you missed.
Practice with a printable cross math
Cross math improves with practice, and the fastest way to practice is a fresh puzzle. Generate one in seconds on the cross math generator — pick a difficulty, then print the blank grid or solve on screen with instant checking. Start on easy, where only + and − appear, then move to medium, which adds multiplication, and finally hard, where division joins in and more digits are blanked out. If you enjoy the number logic, kakuro is a natural companion puzzle — and if you want a different take on equations in a grid, our sudoku guide has you covered.