How to play Square Sums
The rules
The grid is a 3×3 square. Place the digits 1 to 9 in it, each digit exactly once.
Four circled numbers sit on the points where four cells meet. Each circled number is the sum of the four cells around it: the 2×2 square it sits in the middle of.
Some cells start filled in: five on easy, four on medium, three on hard and one on expert. Every puzzle has exactly one solution, and logic alone is enough to reach it. You never have to guess.
How to play here
- Select a cell: click it, or use the arrow keys.
- Enter a digit: keys 1–9, or the number pad below the grid. A digit that is already on the board is shown in grey on the pad.
- Notes (small candidates): press N or the Notes button. In notes mode, a digit you type is recorded as a small candidate. Shift + digit also writes a note.
- Erase: Delete, Backspace or 0.
- Undo and redo: Ctrl+Z and Ctrl+Y (on a Mac: ⌘Z and ⌘⇧Z).
- Hint: each press of Hint tells you more: first where to look, then which technique works there, and finally the digit itself. If there is a mistake on the board, the hint shows you where.
A digit that appears in two cells is marked with stripes and a wavy underline. A circle turns green when its four cells are full and add up to it. It turns red with a wavy underline when its cells can no longer reach it: they add up to more than it, they are full and miss it, or the empty cells left are too few or too many to make the rest.
Difficulty levels
The level is set by the hardest technique the puzzle requires:
| Level | Techniques required |
|---|---|
| Easy | Singles and the last cell of a square |
| Medium | + Combinations |
| Hard | + Matching inside one square |
| Expert | + Two squares together |
Techniques
Singles
A cell with only one possible digit takes it. A missing digit that fits in only one cell goes there.
Last cell
When three cells of a square are known, the fourth is the circled number minus those three.
Combinations
Only some sets of four different digits reach a sum. A circle of 10 must be 1, 2, 3 and 4; a circle of 30 must be 6, 7, 8 and 9. Keep only the digits those sets allow, and only sets that contain the digits already in the square.
Matching
Try to fill one square with its possible digits. A digit that leaves no way to reach the sum can’t go in its cell.
Two squares together
Neighbouring squares share two cells, and the centre cell is in all four. Fill two squares at once: a digit that breaks one of the two sums can’t go there.
Tips
- Start with the centre cell: it is part of all four sums.
- Look at the smallest and largest circles first. They allow the fewest sets of digits.
- Write the possible digits of a cell as notes. When two squares share cells, compare their notes.
FAQ
- How does Square Sums work?
- The grid has 9 cells and you place each digit from 1 to 9 once. Four circled numbers sit where four cells meet. Each one is the sum of those four cells. Some cells start filled in.
- Is there a new puzzle every day?
- Yes. A new Square Sums puzzle is published every day at each of the four levels: easy, medium, hard and expert. Earlier puzzles are in the archive.
- Do I need an account to play?
- No. You play right in your browser, with no sign-up and no cookies. Your progress is saved in your browser.