Binary fills a grid with circles and diamonds. It has three simple rules, and most moves come from two of them meeting.
The three rules
Every row and every column holds as many circles as diamonds. No row or column may have three of the same symbol in a row. And between some neighbours you’ll find a clue: a double bar means the two cells match, a cross means they differ. Symbols with a small dot under them are fixed clues and can’t be changed.
Counting
On a four-cell row you need two of each symbol, so once two circles are in, the other two cells are diamonds. Columns work the same way. On bigger boards, keep a running tally of what each line still needs instead of filling by eye.
Counting and the no-three rule feed each other. Two circles side by side? The cells at either end of the pair can’t be circles. Circle, gap, circle? The gap has to be a diamond. Check the columns as well: a symbol forced by a column often finishes a row.
Worked example
Two circles force a diamond
- Row 1 begins with two fixed circles.
- A third circle beside them would make three in a row, so row 1, column 3 must be a diamond.
A teaching board, not one of today’s puzzles.
Bars and crosses
If one side of a double bar is a diamond, so is the other. If one side of a cross is a diamond, the other is a circle. Even with both cells empty, a cross tells you the pair holds one of each, which counts towards the line’s balance. Put that together with a count or a no-three pattern and you’ll often find a placement.
Check as you go
A row can balance while its column doesn’t, and a bar can be broken even when the counts look fine. After a few moves, run through all three rules. Mistakes are easy to undo, and a hint can point out a conflict or explain the next move.
Practice board
Finish a small Binary board
Fill the empty cells. Each row and column needs two circles and two diamonds, with no three of the same symbol in a row. This board is just for practice, so nothing here is saved or counted.
| Fixed circle | Fixed circle | Empty | Empty |
| Fixed circle | Empty | Fixed circle | Empty |
| Empty | Fixed circle | Empty | Fixed circle |
| Empty | Empty | Fixed circle | Fixed circle |
Enable JavaScript to fill this sample board. The worked example and rules above remain available.
Want to see every step first? Follow the complete Binary walkthrough.