Beacon Balance Glossary: Binary Puzzle Terms and Definitions

The grid

Grid: The whole puzzle: 36 cells in six rows and six columns. Beacon Balance calls it the signal grid.
Cell: One square of the grid. It holds a sun or a moon when solved. Also called a tile.
Line: Any row or column: six cells in a straight run. The rules apply to every line in the same way.
Beacon: LarkSpark’s name for a symbol placed in a cell. Every beacon is a sun or a moon.
Sun and moon: The two symbols of Beacon Balance. They stand in for the 0 and 1 of the classic binary puzzle, and nothing in the rules favors one over the other.
Fixed beacon: A sun or moon placed in the grid at the start, shown with a diamond mark. It can’t be changed. The wider puzzle world calls it a given or a clue.
Link: A small sign on the border between two neighboring cells that tells you how they relate. Links are clues, like fixed beacons. Some designers call them edge clues.
Equals link: A link marked =. The two cells it joins hold the same symbol.
Not-equals link: A link marked ≠. The two cells it joins hold different symbols, one sun and one moon. Some versions of the puzzle draw this link as a cross.

Balance: The rule that every row and every column holds exactly three suns and three moons. A line with four of either symbol can’t be completed.
Triple: Three matching symbols side by side in a row, or one above another in a column. Triples are never allowed, anywhere in a line.
Unique-line rule: No two finished rows may show the same pattern, and no two finished columns may either. Rows are compared with rows and columns with columns, so a row may match a column.
Conflict: A place where the tiles on the grid break a rule: a triple, a line with too many of one symbol, a broken link or a repeated line. Beacon Balance shows conflicts as you work.
Unique solution: A properly made puzzle has exactly one finished grid that fits its fixed beacons and links, and you can reach it by logic without guessing.
Hint: Help from the game that places one correct beacon for you. It adds fifteen seconds to your time and is counted in the daily result.

Pair: Two matching symbols side by side in a line. The cell at each end of the pair must take the opposite symbol, or there would be a triple.
Gap: Two matching symbols with one empty cell between them. The empty cell must take the opposite symbol. Also called a sandwich.
Count to three: Using balance to fill a line. Once a line has three suns, every empty cell in it is a moon, and the same holds with the symbols swapped.
Last-symbol placement: When a line needs one more of a symbol, any cell where that symbol would force a triple among the cells left over is ruled out. Often only one cell remains.
Link counting: Two cells joined by a not-equals link always hold one sun and one moon, so the other four cells of that line must hold two of each. You can count this before you know which cell is which.
Scanning: Looking along every row and column for pairs and gaps. It is the first thing to do on a new grid and worth repeating after each placement.
Line comparison: Applying the unique-line rule near the end. If one way of finishing a line with two empty cells would copy a completed line, the other way is the answer.

Binary puzzle: The general name for this type of puzzle: a grid filled with two symbols so that every line is balanced, has no triple and repeats no other line. Also called Binary Sudoku, though it shares little with Sudoku.
Binairo: The name under which the Belgian company PeterFrank has published the puzzle since 2009. The company marks the name as a registered trademark.
Takuzu: A name for the puzzle used mainly in French publications, and the one mathematicians often borrow.
Tohu wa Vohu: The name the Italian puzzle author Adolfo Zanellati gave his version of the puzzle. The phrase is Hebrew, from the Book of Genesis.
Tic-Tac-Logic: The name under which Conceptis publishes the puzzle with Xs and Os, presented as tic-tac-toe for one player in which three in a row is forbidden.
NP-complete: A class of problems for which no fast general method is known. Deciding whether a binary puzzle of any size has a solution is in this class. A 6×6 daily grid is far too small for that to matter.