Two Tone

Two Tone is a balance puzzle. You fill a grid with suns and moons so that each row and each column holds the same number of each, and no symbol is allowed to run on too long.

How to play

Some squares already show a sun or a moon. You fill in all the others. Three rules decide every puzzle:

• Balance: every row and every column must hold as many suns as moons. On a 6 by 6 grid, that is three of each in every line.
• No long runs: you may not put more than two of the same symbol side by side, in a row or in a column. Three suns in a row is never allowed.
• Signs: a small = sign between two squares means they hold the same symbol. A small × sign means they hold different symbols. Signs appear from Medium on.

On Expert there is a fourth rule: no two rows may be exactly the same, and no two columns may be exactly the same.

Tap a square once for a sun, twice for a moon and a third time to clear it. The starting symbols cannot be changed. A square that breaks a rule is highlighted so that you can spot a mistake early. On a computer, use the arrow keys to move, press 1 or S for a sun, 2 or M for a moon, and Backspace, Delete or 0 to clear a square. Undo takes back a step, and Clear removes your entries.

The Hint button shows a square you can fill and tells you why. Every puzzle can be solved by thinking, and no puzzle needs a guess.

The levels

The levels change the size of the grid, the signs and the thinking required. Each puzzle was graded by the hardest step a solving program needed.

• Easy: a 6 by 6 grid and only the simple rules, with no signs.
• Medium: a 6 by 6 grid with = and × signs. It needs counting a whole row, to see which symbol is used up.
• Hard: an 8 by 8 grid with signs and fewer starting clues. It also needs whole-row counting, and it asks for more patience.
• Expert: a 10 by 10 grid. No two rows or two columns may be alike, and the solver needed the step that compares one line with another. You get 3 hints.

On the other levels Hint is unlimited.

Today's game

The daily game is a Medium puzzle. Everyone who plays on the same calendar day gets the same grid and the same signs.

Tips

1. Two suns side by side? The squares on both sides of them must be moons. That rule is the easiest one to use, so look for it first.
2. A sun, then a gap, then a sun: the square in the middle must be a moon, or else three would be in a row.
3. When a line has used up all its suns, fill every other empty square in that line with moons. The same is true for moons.
4. Follow the signs. An = sign copies a symbol and an × sign flips it, so one known square can tell you its neighbor.
5. Work from the lines with the most squares already filled. They have the fewest choices left.
6. On Expert, compare a nearly finished line with the others. If finishing it one way would copy another line, the last squares must go the other way.
7. If you are stuck, count each row and column. The balance rule often settles a square that the run rule leaves open.

A bit of history

Puzzles that fill a grid with two symbols under balance rules are often called binary puzzles. Their rules are short, and the logic behind them is easy to share.

Questions

Why can't I put three suns in a row? The no-long-runs rule allows at most two of one symbol in a row, whether sideways or up and down.

What do the = and × signs mean? An = sign means the two squares are the same. An × sign means they are different.

Does every puzzle have one answer? Yes. Each one was checked so that exactly one solution exists.

Why is a square marked? It breaks one of the rules. Look at its neighbors, and at the sun and moon counts in its row and column.