Takuzu

Goal of the game

Fill every cell with an amber or sapphire token, following three rules:

• never more than two identical tokens side by side, horizontally or vertically;
• every row and every column contains as many amber tokens as sapphire tokens;
• no two rows (or two columns) may be identical.

Controls

• Tap a cell to cycle through: amber, sapphire, empty.
• Drag your finger or the mouse to paint several cells the same colour.
• Keyboard: arrow keys to move, 1 or A for amber, 2 or S for sapphire, 0 or Backspace to clear, Space to cycle.
• The counters at the end of each line show how many tokens of each colour are still to be placed.

Techniques

• Pair: two identical neighbouring tokens must be flanked by the other colour.
• Sandwich: an empty cell between two identical tokens takes the other colour.
• Count: a line that already has half of one colour is completed with the other.
• Uniqueness: a nearly full line must not repeat a line that is already complete.

About the AI

The generator starts from a valid random solution, then removes tokens as long as the grid remains solvable with the techniques of the requested level; at Diabolical level, the grid is made minimal and its unique solution is checked by an exhaustive search. The hints and the Solve button use the same logical solver, which explains each of its deductions.