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Binary Puzzle

In Diem this puzzle is called Halves: discs ● and squares ■ instead of 0 and 1.

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Each row and column: half ●, half ■. Never three alike side by side.

 

Use the arrow keys to move between squares. Type 0 for a disc, 1 for a square, or press Space to switch; Backspace clears.

Binary puzzle rules

A solved 6 by 4 binary puzzle: each row has three discs and three squares, each column two and two, and never three alike side by side.
  1. Each row and each column holds half of each symbol.
  2. Never three alike side by side, across or down.

The classic binary puzzle, also called Takuzu, is written with 0 and 1. Diem draws the 0 as an orange disc and the 1 as a blue square, so the two never look alike, even at a glance or in a hurry. A row of six holds three of each; a column of four, two of each. Easy boards here are 6 wide and 4 tall; Medium and Hard are 6 × 6.

How to solve binary puzzles

These are the ideas Diem's Hint button names, easiest first. A hint rings the square you can work out next and names the idea; it never fills it for you.

1. Cross Out: next to two alike

Two squares side by side: the gap next to them must be a disc.
Two alike side by side: the squares at both ends take the other symbol. The two blue squares in the second row mean the gap to their left is a disc, and so is the gap to their right.

2. Only Fit: between two alike

A gap between two discs must be a square.
A gap between two alike takes the other symbol. In the last row a disc sits on each side of the gap, so a third disc would make three in a row: it is a square.

3. Last Spot: the half is full

The first column already has its two squares, so its other squares are discs.
Once a line has its half of one symbol, the rest of the line is the other. The first column (four squares tall) already has its two blue squares, so the top and bottom are discs.

4. No Room: what if?

A square in the ringed gap would leave three discs side by side, so it is a disc.
Try the other symbol and see if the line can still work. The last row has a square at each end. A third square in the ringed gap would fill the row's half, and the three gaps left would all be discs, side by side. So the ringed gap is a disc.

Easy boards fall to the first three ideas. Hard boards are built so that you need No Room. If you get stuck, Hint shows which idea the next square needs.

FAQ

What are the rules of a binary puzzle?

Fill every square with one of two symbols. Each row and each column holds as many of one as of the other, and three of the same never sit side by side in a line. Here the two symbols are an orange disc (●) and a blue square (■): tap once for ●, twice for ■, three times to empty the square.

Is a binary puzzle the same as Takuzu?

Yes. Takuzu is another name for the binary puzzle, and you will also find it under a few brand names. Classic versions write 0 and 1; Diem uses discs and squares, which are easier to tell apart at a glance.

Can two rows be the same?

In many classic Takuzu books a third rule says no two rows or columns may be identical. Diem uses only the two rules above, so two rows can match. Every board still has exactly one solution with those two rules alone.

What are good binary puzzle strategies?

Look for two alike side by side (the squares on either end take the other symbol), and for a gap between two alike (it takes the other one). Then count: once a line has its half of one symbol, the rest of it is the other. When that runs out, try one symbol in a square and see whether the line can still be finished.

Is there a daily binary puzzle?

Diem of the Day is one puzzle a day, the same for everyone, and every fourth day it is a Halves board: a binary puzzle, sometimes with Diem's own = and × links between two squares (the same, or different). On this page there is a new puzzle whenever you want one.

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