Balance strategy: pairs, counts and whole lines

Play Balance

Balance looks like a coin-flipping puzzle, but there's no luck in it. Every cell can be worked out, usually from just one row or column, and the techniques below are all you'll ever need here.

How the difficulty works

Each tier is set by the hardest step you'll need, not by how many symbols are given.

Easy (6×6) needs only pairs, gaps and counting.
Medium (8×8) needs at least one step where you read a whole line: only one arrangement of what's left works.
Hard (12×12) adds the rule that no two rows and no two columns may be identical, and needs it at least once.

Nothing needs guessing, and nothing needs following a "what if" across several lines.

Easy: the three basics

Pairs

Two of the same symbol side by side: the cells at both ends must be the other symbol, or you'd have three in a row. This is the move you'll make most often, in every tier.

The pair of rings in row 5 is hemmed in by dots on both sides. From Easy puzzle #2 — play it

Gaps

Two of a kind with a single empty cell between them: the middle cell must be the other symbol. Gaps are easy to miss because the two symbols don't touch, so look for them deliberately.

Two dots with one cell between them in row 1: the gap is a ring. From Easy puzzle #1 — play it

Counting

Every line holds exactly half of each symbol. As soon as a line has all of one, every empty cell left in it is the other.

Column 1 already has its three dots, so its two empty cells are rings. From Easy puzzle #1 — play it

Keep counting as you go, not just when a line looks nearly done. On bigger grids it's easy to place a fourth or a seventh of something without noticing; the game marks it in red the moment a line goes over.

Medium: read the whole line

When pairs, gaps and counts run dry, take a line that's mostly filled and ask how the rest of it could go. Usually a line needs just one or two more of one symbol. Try putting the scarce symbol in each empty cell in turn, fill the others with the opposite symbol, and see what happens. If one placement makes three in a row, it's ruled out. Any cell that comes out the same in every option that survives is settled.

Try a ring in the outlined cell, at row 4, column 1. Then there's no way to fill the rest of row 4 without three alike side by side or the counts going wrong. So it's a dot. From Medium puzzle #1 — play it

A few shapes come up again and again, and it's worth learning to see them at a glance:

One left goes in the long stretch. If a line needs only one more dot, and it has a stretch of three or more empty cells side by side, the dot must go somewhere in that stretch. Otherwise the whole stretch would fill with rings, three in a row.
Edges. Cells at the very end of a line have only one neighbour, so they're often the easiest to settle by trying both symbols.

The trial here never leaves the line, so you can do it in your head. If you want to be careful, place the symbol, look, and undo.

Hard: no two lines alike

On Hard, no row may copy another row, and no column another column. It only bites near the end of a line. When a line is nearly finished and every symbol it has so far matches a line that's already complete, the remaining cells must go the other way — otherwise the two would be identical.

Column 7 (tinted blue) could still be finished so that it matches column 4 (tinted red) exactly. That isn't allowed, which leaves only one way for the outlined cell to go. From Hard puzzle #1 — play it

The habit to build: whenever a line has two or three empties left, glance at the finished lines parallel to it. Most of the time nothing matches. When one does, you've found the move the puzzle was built around.

Good habits

After every move, look around it. A new symbol often makes a pair or a gap with its neighbours, in its row and its column.
Count the busiest lines first. Lines with few empties settle fastest.
Switch between rows and columns. Each cell you settle gives the crossing line something new.
Stuck? Hint names the technique and outlines the cells, without saying which symbol goes there. If things stop making sense, Check shows whether an earlier mistake is the real reason.