How to play Magic grid puzzles
Place each number once so every row and column hits its target — by adding, subtracting, multiplying or dividing.
The rules
- Magic Sum: place every number from 1 to N exactly once. Each row and column must add up to the target shown at its edge.
- Magic Difference: start from the row's (or column's) anchor cell and subtract the others in turn — the result must match the target. Negative targets are optional.
- Magic Product: the numbers in each row and column multiply to the target.
- Magic Division: divide sequentially from the anchor cell; decimal targets are optional for a harder game.
- Magic Mixed: rows use one operation and columns another — ten combinations in all.
Playing Magic grid puzzles on Puzzle Solvers
- Choose a grid size and a difficulty, then press Generate Puzzle.
- Click a cell and type a digit, or use the on-screen keypad. Notes switches to pencil marks.
- Undo steps back; Force places one digit that has only one possible value; Check marks mistakes in red without giving away the answer.
- Stuck? Send to Solver opens the same puzzle in the step-by-step solver. Send to Slate opens it as a board on the Slate whiteboard, to solve in front of a class.
Using the Magic grid puzzles solver
- ① Build: choose the grid shape, enter row and column targets in the blue cells and any known values.
- ② Check, then ③ Solve — every step explained.
A worked example
A 3×3 Magic Sum uses 1–9 once. The top row's target is 6, which in three different numbers can only be 1+2+3. So the top row is 1, 2 and 3 in some order, and the columns decide which goes where.
In Magic Product, a row target of 30 in three cells must be 1×5×6, 2×3×5 or 1×3×10 — and 10 is too big on a 3×3, leaving two choices.
Strategies
- Biggest and smallest first. The largest numbers have the fewest places they can go without overshooting a target.
- Total check (Sum). All the row targets together add up to 1+2+…+N, and so do the column targets — a quick check on any guess.
- Think in factors (Product). Split each target into prime factors; a row target containing 7 needs the 7.
- Anchor first (Difference and Division). The anchor is the starting value, so it is usually the largest number in its line.
- Use hints wisely. The Hint button places one cell; it is better to use it once than to guess several.
Common mistakes
- Subtracting or dividing in the wrong order in Difference and Division — always start from the anchor.
- Reusing a number. Each number is placed once in the whole grid.
Where it comes from
These grid puzzles extend the ancient magic square, where every row, column and diagonal has the same sum, by giving each line its own target and operation.
Frequently asked questions
What is the anchor cell?
In Magic Difference and Magic Division, the first cell of a row or column. You start from it and subtract or divide the others in turn.
Is there a solver?
Yes, for Magic Sum: the Magic Sum Solver explains every step.
Which one should I start with?
Magic Sum is the gentlest. Product builds times-table fluency; Mixed is the hardest.
Keep going
- Play Magic grid puzzlesa fresh puzzle every time
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- BODMAS GameBuild equations that hit the target by applying the order of operations…
All guides: How to play every puzzle and game.