How to play Equation Grid
The rules
The grid is a 3×3 square. Place the digits 1 to 9 in it, each digit exactly once.
Between the cells of each row and each column is a sign: plus (+), minus (−) or times (×). Each row ends with = and a result on the right, and each column ends with = and a result below. Every row, read from left to right, and every column, read from top to bottom, must be a true equation.
Multiply first, then add and subtract from left to right. For example, 2 + 5 × 3 = 17, and 1 − 9 × 8 = −71. There is no division.
Some cells start filled in: five on easy, three on medium, and none on hard and expert. Every puzzle has exactly one solution, and logic alone is enough to reach it. You never have to guess.
How to play here
- Select a cell: click it, or use the arrow keys.
- Enter a digit: keys 1–9, or the number pad below the grid. A digit that is already on the board is shown in grey on the pad.
- Notes (small candidates): press N or the Notes button. In notes mode, a digit you type is recorded as a small candidate. Shift + digit also writes a note.
- Erase: Delete, Backspace or 0.
- Undo and redo: Ctrl+Z and Ctrl+Y (on a Mac: ⌘Z and ⌘⇧Z).
- Hint: each press of Hint tells you more: first where to look, then which technique works there, and finally the digit itself. If there is a mistake on the board, the hint shows you where.
A digit that appears in two cells is marked with stripes and a wavy underline. A result turns green when its three cells are full and the equation is true. It turns red with a wavy underline when the equation is false, or when its empty cells can no longer make it true.
Difficulty levels
The level is set by the hardest technique the puzzle requires:
| Level | Techniques required |
|---|---|
| Easy | Singles and equations with one empty cell |
| Medium | + Equations with two empty cells |
| Hard | + Equations with three empty cells |
| Expert | + A row and a column together |
Techniques
Singles
A cell with only one possible digit takes it. A missing digit that fits in only one cell goes there.
One missing
When an equation has one empty cell, only one digit makes it true.
Two missing
Try the pairs of different digits that make an equation with two empty cells true. A digit that is in no such pair can’t go in that cell.
Three missing
The same for an equation with all three cells empty: try the triples of digits that make it true.
Crossing
A row and a column share one cell. Solve them together: a digit that breaks one of the two equations can’t go there.
Tips
- Start with the equations that have a times sign and a large result. Few digits can make them.
- Look at the cell where a row and a column cross: it has to work in both equations.
- Write the possible digits of a cell as notes, and remove a digit when it is placed somewhere else.
FAQ
- How does Equation Grid work?
- The grid has 9 cells and you place each digit from 1 to 9 once. Between the cells are plus, minus and times signs. Each row and each column is an equation with its result at the end, and all six must be true. Some cells start filled in.
- Do I multiply first?
- Yes. Multiply first, then add and subtract from left to right (top to bottom in columns), as in normal arithmetic. So 2 + 5 × 3 is 17. Results can be negative.
- Is there a new puzzle every day?
- Yes. A new Equation Grid puzzle is published every day at each of the four levels: easy, medium, hard and expert. Earlier puzzles are in the archive.
- Do I need an account to play?
- No. You play right in your browser, with no sign-up and no cookies. Your progress is saved in your browser.