Sum Circles is a small, quick addition puzzle. The nine squares hold the numbers 1 to 9, each once. Four circles sit where squares meet, and each shows the total of the four squares touching it.
Start with the biggest and smallest circles — a total of 10 can only be 1+2+3+4, and 30 only 6+7+8+9. The middle square touches every circle, so it’s often the key.
The colour version adds a total for each coloured group, and the 4×4 version uses 1 to 16 with nine circles — a real workout for mental addition.
Place 1 to 9 once each so every circle equals the total of the four squares around it.
The full guide, with a worked example and common mistakes: How to play Sum Circles.
Adding four numbers quickly, and partitioning: finding all the ways a total can be made from different numbers.
Yes — every puzzle here is checked to have exactly one solution.
Sixteen squares holding 1 to 16 with nine circles — the same rules on a bigger grid.
Open the Sum Circles Solver, type the circle totals and press Solve.