How to play and solve cross math puzzles
A cross math puzzle is a crossword made of numbers. This is the step-by-step guide: the rules, one Easy puzzle solved from the first blank to the last, and what to do when no equation will give you a cell for free.
What is a cross math puzzle?
The clues are equations and the answers are numbers. Equations run across and down, and they share the cell where they cross, so a number you place has to make both directions true. The same idea is sometimes called a number crossword.
You are given a tile bank and a grid where some numbers are already printed. Fill every blank from the bank. There is one solution, and you can reach it by reasoning. Guessing is never required on a puzzle from this site.
Cross math rules
Each cell holds one whole number greater than zero. No zeros, no negatives.
Read across from left to right and down from top to bottom. A crossing is the same number in both equations.
On a longer line, multiplication and division come before addition and subtraction. 3 + 4 × 2 is 3 + 8, which is 11. Operators of the same rank still run left to right.
Division is always exact. 12 ÷ 4 = 3 can appear. 12 ÷ 5 cannot.
Every equation starts with at least one blank. Each bank tile is used once, and the blank answers are all different.
How to solve a cross math puzzle step by step
The board below is a real Easy puzzle, smaller than a daily so the whole solve fits on a screen. The bank is 5, 4, 3 and 10. Follow the numbers in order. Then try the same board yourself.
- 01Scan for an equation with one empty cell. Ignore the rest of the board until you find one. On this puzzle the top row is the one: 2 + □ = 7.
- 02Solve that cell from the bank. 7 − 2 is 5, and 5 is in the bank, so the top blank is 5. It is the only tile that makes the row true.
- 03Use the crossing. That 5 is also the top of the middle column, so the column now reads 5 − 1 = □. The blank at the bottom of the column is 4.
- 04Take the new single blank that just appeared. The left column is 2 + □ = 6, so its blank is 4. The other 4 on the board is printed, not a tile, so the bank still has a 4.
- 05The middle row is now 4 − 1 = □. Its last blank is 3. One tile is left.
- 06Check the last cell both ways before you place it. The right column is 7 + 3 = □ and the bottom row is 6 + 4 = □. Both describe the same cell, and both equal 10, which is the last tile. The puzzle is solved. Every tile was used once.
That chain is the whole Easy method. Every Easy puzzle on this site can be finished this way: one blank left, then the crossing, then the next single blank.
Try this puzzle yourself→When every equation has two blanks
Medium, Hard and Expert each have at least one moment where no equation has a single empty cell. Easy never does. This is the second technique, and it is still reasoning, not a guess.
Suppose a cell starts □ × 3 = □ across and □ + □ = 20 down, and the bank holds 4, 6, 12, 14 and 18. Across, the cell needs a tile whose triple is also in the bank: 4 (with 12) or 6 (with 18). Down, it needs a partner that makes 20: 6 (with 14) or 14 (with 6). Only 6 is on both lists, so the cell is 6.
Do the same thing from the tile's side. If 18 can sit in only one blank without breaking an equation, it goes there, even if that blank still looks open. Fill it, then go back to hunting single blanks. The two techniques take turns until the bank is empty.
On a longer Hard or Expert line, A operator B operator C = D, test a candidate from the left. A tile that survives the line still has to survive the equation that crosses it.
How to play cross math
Tap an empty cell, then tap a number in the bank. You can also tap the number first, or drag it onto the cell. With a cell selected, type the number if it is in the bank, Backspace clears it, and the arrow keys move to the next blank.
Tap a placed number to send it back to the bank. Undo reverses your last move.
When an equation is complete and true, its numbers get a dark outline. A wrong equation gives a short shake. There is no separate check button.
Stuck? Hint places one correct tile from the bank. You get three per puzzle, and a hinted cell keeps a small mark in its corner. Hint never creates a tile. Restart clears the board and does not count as a new puzzle.
Choose a level
Daily challenge and points
The daily gives everyone the same puzzle for each difficulty on a given day. A new one arrives at midnight, your local time. Past days stay in the daily archive, and yesterday's math crossword answers open from one fixed address the next day.
Signed-in players earn points for each win, from 10 on Easy to 80 on Expert, with a bonus for speed. Hints lower the score, and a daily win counts double, once per difficulty each day. The details are on the leaderboard.
Common questions
What is the order of operations in a cross math puzzle?
Multiplication and division come before addition and subtraction. 3 + 4 × 2 is 3 + 8, which is 11. Division is always exact, so 12 ÷ 4 can appear and 12 ÷ 5 cannot. A step that would be negative or not a whole number is left out.
Does a cross math puzzle have only one solution?
Yes. Every puzzle on Math Crosswords has one valid placement of the tiles. A number that fits the row still has to fit the column that crosses it, and a board that could be filled in two ways is never used.
Is each number tile used only once?
Yes. The bank starts with one tile for each blank, those answers are all different, and every tile is used exactly once. A printed number can match a tile, because printed numbers are not taken from the bank.
How do you solve a cross math puzzle when every equation has two blanks?
Compare candidates. List the bank tiles that could fill one cell in every equation that uses that cell. Only a tile on every list can go there. The reverse works too: if a tile fits only one blank on the board, that is where it goes. You do not have to guess.