Sum Circles Solver

Sum Circles Solver — Step by Step

Click a circle and type its total; click a square to type a given number. In the colour version, click a total under the grid to type it, and use 🎨 to set a square’s colour. Then press Solve. Or play a generated puzzle and send it here with one click.

Sum Circles Solver: rules, how to use it, tips

Place 1 to 9 once each so every circle equals the total of the four squares around it.

The rules

Each number from 1 to 9 is used exactly once (1 to 16 in the 4×4 version).
A circle sits where four squares meet and shows their total.
In the colour version, the squares of each colour add up to that colour’s total.
Given numbers can’t be changed.

Using the solver

Choose the version, type each circle total (and colour total) and any given numbers — or press Sample.
Press Solve and step through: the ways each circle can be made, the only digit or only place left, and what-ifs.

Tips

Extreme totals. The smallest possible circle is 10 (1+2+3+4) and the largest 30 (6+7+8+9). Totals near these have very few ways to be made.
The middle square. In the 3×3 grid the centre touches all four circles, the edge squares touch two, and the corners just one.
Add all four circles. The four circles together count the centre four times, each edge square twice and each corner once — a quick check on what the centre can be.
Shared squares. Two neighbouring circles share two squares, so the difference between their totals is the difference between their other two squares.

The full guide, with a worked example and common mistakes: How to play Sum Circles.

Questions

What maths does it practise?

Adding four numbers quickly, and partitioning: finding all the ways a total can be made from different numbers.

Is there always one answer?

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

What is the 4×4 version?

Sixteen squares holding 1 to 16 with nine circles — the same rules on a bigger grid.

How do I solve one from a newspaper?

Open the Sum Circles Solver, type the circle totals and press Solve.