From the rulebook
How to Solve Crossmath
Crossmath is a math crossword. The grid holds interlocking across and down equations with the operators already fixed and the numbers missing, plus a bank of number tiles to place. Drag every tile into the grid exactly once so that all the equations are true at the same time. This guide takes you from the rules to the techniques that crack the hardest grids without guessing.
The rules of Crossmath
A Crossmath grid is laid out like a crossword, with runs of cells forming equations that read left to right and top to bottom. Each equation is a simple three-number statement: a first number, an operator, a second number, an equals sign and a result, for example 3 plus 2 equals 5. The operator and the equals sign are printed for you and never change.
Below the grid sits a bank of number tiles. Your job is to place every tile into an empty cell so that each tile is used exactly once and every across and down equation comes out true. Many cells sit where an across equation crosses a down equation, so a single tile often has to satisfy two equations at once. Entries give no live feedback as you play, so when you think every tile is placed, press Check to test the board. There is no mistake limit, so you can keep editing or clear the board and start over.
Start with the most constrained equation
The fastest opening move is to find the equation with the least freedom. That is usually the one with the fewest empty cells, a fixed result already showing, or an extreme target that only a few tiles can reach. An equation that already has two of its three numbers in place leaves only one tile that can possibly complete it.
Work outward from there. Each tile you lock in becomes a known value in any crossing equation, which tightens those equations in turn. Crossmath unravels the way a crossword does, one confident answer opening up its neighbours.
Treat crossings as the pivot points
The cells where an across and a down equation meet are where the real deductions happen. A tile placed there has to make both equations true at once, so test every candidate against both lines before committing. A tile that balances the across equation but breaks the down equation is simply in the wrong cell.
When you are unsure of a tile, check which crossing equations touch its cell and see whether any of them already pins the value. A crossing where one equation is nearly complete will often force the shared cell outright, and that single placement can cascade through the rest of the grid.
Use the operator to narrow candidates
Each fixed operator tells you what kind of tile can fit. For an addition equation the result must be larger than either input, so a small printed result rules out the big tiles. A subtraction result must be smaller than the first number, which often fixes the order. On the harder grids, multiplication results have to factor cleanly into available tiles, and division equations only work when one number divides the other exactly, with no remainder, so they pin down their tiles fast.
Read the bank alongside the operator. If an equation needs two numbers that multiply to 24 and the only tiles left that fit are 4 and 6, that pair is forced. Eliminating tiles you have already placed shrinks the bank and makes the next operator check sharper.
Combine tile counting with equation logic
Crossmath is a placement puzzle as much as an arithmetic one. Because every tile is used exactly once, the bank itself is a constraint: once a value is placed, it is gone, so an equation that could only be completed by a tile already used must be wrong somewhere. Keep an eye on which values remain in the bank as you go.
Apply the techniques in order: solve the most constrained equation first, lock the crossings, run the operator checks, then watch the dwindling bank to confirm each placement. On Puzzle Lair every Crossmath puzzle is generated and verified to have exactly one solution reachable by logic alone, so if you are stuck there is always a deduction waiting, never a guess. Bigger grids with multiplication and division are what make the hard set a genuine workout.
Frequently asked questions
- What is Crossmath?
- Crossmath is an arithmetic crossword. Instead of words, the grid holds interlocking across and down equations with the operators and equals signs printed in and the numbers missing. You place number tiles from a bank into the empty cells so that every equation, read left to right and top to bottom, is true.
- How do you start a Crossmath puzzle?
- Begin with the most constrained equation, the one with the fewest empty cells or an extreme result that only a few tiles can reach. Place its forced tile, then use that known number in any crossing equation to narrow the next placement. Crossmath opens up the way a crossword does, one confident answer at a time.
- What makes a cell important in Crossmath?
- Cells where an across equation crosses a down equation are the pivot points. A tile placed there must make both equations true at once, so always test a candidate against both lines. A tile that works horizontally but breaks the vertical equation is in the wrong cell.
- Does solving Crossmath ever require guessing?
- No. Every Puzzle Lair Crossmath puzzle is generated and verified to have exactly one solution reachable by pure logic. Being stuck means there is a deduction you have not spotted yet, often a crossing that one equation already pins down or an operator check you have not run. When you think every tile is placed, press Check to test the board. There is no mistake limit.
- What operators are used in Crossmath?
- Easy puzzles use only addition and subtraction with small values. Harder puzzles add multiplication and exact division, where one number must divide the other with no remainder, and use larger values up to 99. The operators are always fixed in the grid, so your job is to find the numbers that satisfy them.