Play 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 — illegal. 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 — the uniqueness rule

Imagine row 1 reads ☀ 🌙 ☀ ☀ 🌙 🌙 and row 4 currently reads ☀ 🌙 ☀ ☀ · ·. The two empty cells in row 4 could be either 🌙 🌙 or 🌙… but 🌙 🌙 would make row 4 identical to row 1, which is forbidden. So the answer is 🌙 ☀ by elimination.

The uniqueness rule — no two rows or columns may be identical — is the technique that cracks most “hard” boards once doubles and gaps run out.

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.