How to play Balance

Play Balance

Balance is the quickest puzzle on the site, and one of the most satisfying: two symbols, two rules, and a grid that falls into place a few cells at a time.

The rules

Fill every empty cell with a dot or a ring so that:

No three in a row. No row or column has three of the same symbol next to each other.
Every line is balanced. Each row and each column holds exactly as many dots as rings — three of each on a 6×6 grid.
On Hard only: no two rows are identical, and no two columns are identical.

The shaded symbols are given and can't be changed. Every puzzle has exactly one solution, and you can always reach it by reasoning — you never need to guess. The puzzle is also known as binary Sudoku, or simply the binary puzzle, because it works just as well with 0s and 1s.

An easy 6×6 puzzle with 12 symbols given. From Easy puzzle #1 — play it

Solved. Every row and column has three dots and three rings, and nowhere are three alike side by side.

Your first moves

The three-in-a-row rule does most of the early work. Whenever two of the same symbol sit side by side, the cells at either end of them must be the other symbol.

In row 5, two rings sit next to each other. A third on either side would make three in a row, so both neighbours, outlined in red, are dots. From Easy puzzle #2 — play it

The same goes for two of a kind with one empty cell between them: the gap can't match them.

The empty cell between the two dots in row 1 has to be a ring, or there would be three dots in a row. From Easy puzzle #1 — play it

Add counting — once a line has all its dots, the rest must be rings — and you can solve every Easy puzzle. The strategy guide covers the reasoning Medium and Hard need.

Playing on this site

Tap an empty cell for a dot, tap again for a ring, and once more to clear it.
Long-press (or right-click) goes the other way round: ring first, then dot.
Anything that breaks a rule — three in a row, too many of one symbol in a line, or on Hard two identical lines — is marked in red straight away. A symbol can be wrong without breaking a rule yet, though, and that's what Check is for: it shows any cell that doesn't match the solution, but only when you ask.
Hint names the next deduction and outlines the cells it settles, without saying which symbol goes there. One hint per puzzle is free; after that there's a one-minute wait between hints.
Undo and Redo go back as far as you like, and the game saves after every move.

Keyboard

Arrow keys move; 1 places a dot, 2 a ring, 0 clears; Space cycles.
Z undoes, Y redoes, H asks for a hint.

Sizes and the daily puzzle

Easy: 6×6.
Medium: 8×8.
Hard: 12×12, with the rule that no two rows or columns may match.

Each day's first puzzle is the same for everyone. They follow the week, from Monday's gentlest to Saturday's toughest, with Sunday the next toughest. After the day's puzzle, Next puzzle gives you as many more as you like, each numbered so you can share it.