How to play Number Order

Rearrange the same set of numbers in every row and column so each line, worked out with BODMAS, makes its total. Also known as Row and column totals puzzle.

▶ Play Number Order ⊞ Open the solver

The rules

Every row and every column contains the same numbers once each (and, on the top levels, the same signs).
Signs sit between the numbers; each line's total is shown at its end.
Work each line out with BODMAS: powers first, then × and ÷ from left to right, then + and − from left to right. Division must come out whole.
Swap tiles within a row or a column until every total is right. Locked tiles cannot move.

Playing Number Order on Puzzle Solvers

Choose a level — from 3×3 with + and − up to 5×5 with powers and moving signs — then press New Puzzle.
Tap a tile, then another tile in the same row or column, to swap them (or drag one onto the other). Locked tiles stay put.
Each line is worked out with BODMAS: powers, then × and ÷ left to right, then + and −. A total turns green when its line is right.
Hint sets the next line you can be sure of and explains why — the only order of its numbers that makes its total.

Open the Number Order game →

Using the Number Order solver

Choose the size and whether the signs may move, then type the grid and totals (or press Sample).
Press Solve: lines with only one possible order are set first, then squares that every remaining order agrees on.

Open the solver →

A worked example

Row: _ − _ × _ = 2, using 3, 5 and 1. Try 5 − 3 × 1 = 2 — yes. Check the others: 3 − 5 × 1 = −2, 5 − 1 × 3 = 2 as well.

Two orders work, so look at the columns: whichever puts the right number in the column that needs it wins.

Strategies

List the orders. With three numbers there are only six orders. Work out each one's total and see which match.
Multiplication first. In a line with ×, the two numbers either side of it matter most — try the big totals with the big numbers there.
Rows help columns. Once a row is fixed, each column has one of its numbers settled, which cuts that column's choices.
Watch the division. A ÷ only works if the left side divides exactly, which rules out many orders at once.

Common mistakes

Working left to right instead of BODMAS: 2 + 3 × 4 is 14, not 20.
Swapping between rows and columns that don't share the tile — numbers only move along their own row or column.

Where it comes from

The Number Order Challenge was made for this site to practise order of operations as a logic puzzle.

Frequently asked questions

Is there only one answer?

Yes — every puzzle is checked, and locked tiles are added where needed to make it unique.

When do the signs move?

From level 5 (Expert) the signs can be swapped within their row or column too.

What does ^ mean?

A power: 2 ^ 3 = 2 × 2 × 2 = 8. It is worked out before × and ÷. Powers appear on the Genius level.

Keep going

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