Tango Unlimited: Play the Tango Game

Step 1: the gap technique

The starting row looks like this:

☀ · ☀ · · ·

Two suns with one gap between them. If we filled the middle cell with another sun, we would have three suns in a row, which is not allowed. So the middle cell must be a moon. This is the gap technique: any pattern of symbol, blank, symbol forces the blank to the opposite symbol.

☀ 🌙 ☀ · · ·

Step 2: the doubles rule

Suppose two cells later in the same row look like this after work in other rows:

☀ 🌙 ☀ · 🌙 🌙

We have a doubled moon in the last two positions. The doubles rule says: whenever two identical symbols sit next to each other, the cells immediately before and after must hold the opposite symbol. So the empty cell at position 4 must be a sun.

☀ 🌙 ☀ ☀ 🌙 🌙

Step 3: the counting method

Count what we have: three suns and three moons in the row. The row is now balanced and complete. The counting method works the other way too: if you ever reach the maximum (three) of one symbol in a row, every remaining empty cell in that row must be the opposite.

Step 4: = and × chains

A new row. Two suns are given, an = sign joins cells 4 and 5, and an × sign joins cells 5 and 6:

☀ · · ☀ = · × ·

Follow the chain from the known cell. Cell 4 is a sun, so the = makes cell 5 a sun too, and the × makes cell 6 the opposite: a moon. That puts three suns in the row, so the counting method turns cells 2 and 3 into moons.

☀ 🌙 🌙 ☀ ☀ 🌙

Three suns, three moons, never more than two of a kind side by side. The chain settled two cells and the count settled the other two. Even when neither side of an × pair is known yet, it always holds one sun and one moon, so it counts as one of each when you balance its row or column.

Step 5: progressive deduction

Every cell you place changes the picture for its row, its column, and any cell linked to it by a = or × marker. After each placement, scan all six rows and all six columns again. What was a dead end thirty seconds ago might now be a forced move. Most Tango boards take three or four passes before they fall.