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Puzzle

Binary

Every cell takes one of two symbols, an open ring or a filled dot. Three rules decide them all, and the grid always has exactly one solution.

Your game is saved in this browser as you play.This game also turns up as the Puzzle lamp

The three rules

  1. No more than two equal symbols next to each other, across or down.
  2. Each row and each column holds as many rings as dots.
  3. No two rows are the same, and no two columns are the same.

Tap a cell to cycle it from empty to ring to dot and back. On a keyboard use 0, 1 and Space. Undo, redo and a hint are always there, and the hint names the reason a cell is forced.

Solving technique

Pairs. Two equal symbols side by side must be closed off with the other symbol at both ends. Sandwiches. A gap between two equal symbols must take the other one. These two patterns alone carry the easy grids a long way.

Counting. When a row of eight already has four dots, every empty cell in it is a ring. Look for lines that are nearly balanced after each move.

Last cells. Late in the puzzle, a line with three empty cells often has only one way to finish without making three in a row. The hard grids need this step, and also the rule about identical lines: if two rows would end the same, the open cells must be swapped.

Always fill the forced cells first and look along the rows and columns that just changed. One new symbol often sets off three more.

A worked opening

Take a fresh 6×6 grid. Sweep each row for two equal symbols side by side and put the opposite symbol at both ends. Sweep again for a gap between two equal symbols and fill it with the opposite. Then count: any row or column with three of one symbol is finished with the other. After these three sweeps an easy grid is usually half full, and the rest follows in the same way.

If a sweep along the rows finds nothing, turn to the columns. One direction is often stuck while the other is wide open.

Questions

What sizes are there?

Easy grids are 6×6, medium 8×8 and hard 10×10. Every size has one solution only.

Can I make a mistake and continue?

Yes. The game lets you place anything, and the hint first points at a cell that breaks a rule. Undo takes you back step by step.

Where are the numbered Binary grids?

There are 42 numbered Binary grids, fourteen per difficulty, each on its own page with a count of its givens, pairs and sandwiches.

Is this the same as other two-symbol puzzles?

The rules are the classic ones for this type of grid, played here with rings and dots.

42 numbered Binary puzzles