How to play Equation Square

Place 1 to 9 once each so every row and column, worked through with its signs, gives the answer at its end. Also known as Arithmetic square, Number square, Sum square.

▶ Play Equation Square ⊞ Open the solver

The rules

Each number from 1 to 9 is used exactly once.
Rows are worked from left to right and columns from top to bottom.
Classic working does one step at a time: 2 + 3 × 4 = 5 × 4 = 20. BODMAS working does × and ÷ first: 2 + 3 × 4 = 14.
Every division must come out exactly.

Playing Equation Square on Puzzle Solvers

Choose which signs to use, left-to-right or BODMAS working, and a difficulty, then press New Puzzle.
Tap a square, then a number on the pad (or type it). Each number 1–9 is used once.
Each answer box goes green when its row or column works out, red if it doesn’t.
Hint shows which numbers fit an equation and why.

Open the Equation Square game →

Using the Equation Square solver

Choose left-to-right or BODMAS working, set the twelve signs and six answers, and add any given numbers — or press Sample.
Press Solve and step through each equation: the ways it can be made, and which numbers that leaves.

Open the solver →

A worked example

Row 1 reads □ × □ − □ = 47 with the classic working. The product must be at least 48, so it’s 6×8 = 48, 7×7 (not allowed), or 8×9 = 72 or 9×6 = 54…

48 − 1 = 47 works with 6, 8 and 1. 54 − 7 and 56 − 9 also work, so check the columns: whichever leaves every column possible is the answer.

Strategies

Start with ÷. A line with division can only use pairs that divide exactly — often just a handful.
Big answers need ×. An answer like 72 needs a large product; small answers with × usually involve 1 or a subtraction.
Odd and even. With + and −, the answer’s odd or even tells you how many odd numbers the line holds.
Work backwards. In a left-to-right line a op b op c = R, undo the last step: (a op b) must equal R undone by c.
Use the unused. Once a number is placed it can’t appear anywhere else — keep a list of what’s left.

Common mistakes

Using BODMAS when the puzzle is left-to-right (or the other way round).
Allowing a division that leaves a remainder.
Using a number twice.

Where it comes from

Sum grids like this have been printed in puzzle magazines and newspapers for decades and are a favourite in maths classrooms for practising all four operations.

Frequently asked questions

What’s the difference between the two workings?

Left to right does each step in order. BODMAS does multiplication and division before addition and subtraction, like a calculator.

Can an answer be negative?

Not in the puzzles generated here, but the solver accepts negative answers.

Is there always one answer?

Yes — every puzzle here is checked to have exactly one solution.

How do I solve one from a book?

Open the Equation Square Solver, set the signs and answers and press Solve.

Keep going

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