How to solve tango, step by step

Tango has three rules. Every row and column holds as many suns as moons. No more than two of the same symbol sit side by side. And cells joined by = hold the same symbol, while cells joined by × hold different ones. Each technique below is one of those rules used on a single row or column.

Pairs: close both ends

Two suns side by side can’t have a third next to them. So the cells on both sides of the pair are moons. The same goes for a pair of moons.

Gaps: fill the middle

A sun, an empty cell, then another sun: if the middle were a sun too, that would make three in a row. So the middle is a moon.

Count each line

A row of six holds three suns and three moons. Once a row has all three of one symbol, every empty cell left in it is the other one.

Follow the signs

An = between two cells copies whatever one of them holds into the other. A × gives the other cell the opposite symbol. Signs chain: if A = B and B × C, then A and C are different.

Think a line ahead

When none of the simple steps work, take a line with only a few empty cells and try each symbol in one of them. If one choice breaks a rule in that line, such as three alike or too many of one symbol, the cell holds the other symbol. You don’t need to guess further than that one line.

Putting it together

1. Close the ends of every pair.
2. Fill every gap between two of the same.
3. Count each row and column, and finish the ones with all of one symbol.
4. Follow every sign next to a cell you know.

Repeat until the board is full. Easy tangos need only the first three steps. Bigger boards lean on the signs and on counting.