How to play Binary Puzzle

What you need

A Binary Puzzle is played on a square grid with an even number of squares along each side, such as 6 by 6, 8 by 8 or 10 by 10. Some squares already contain a 0 or a 1. These clues cannot be changed.

The three rules

Fill every empty square with a 0 or a 1, so that:

1. No three in a row. No more than two of the same number may sit next to each other, across or down. So 0 0 is allowed, but 0 0 0 is not.
2. Equal numbers. Every row and every column has the same number of 0s as 1s. On a 6 by 6 grid, that means three of each in every line.
3. No twins. No two rows are exactly the same, and no two columns are exactly the same.

A well-made puzzle has only one solution, and you never need to guess.

Getting started

Two simple patterns will fill a lot of squares.

Pairs

If you see two of the same number side by side, the squares at each end must be the other number. For example, in a row reading _ 1 1 _, both gaps must be 0, otherwise there would be three 1s in a row.

Gaps

If two of the same number have one empty square between them, that square must be the other number. In 0 _ 0, the gap must be 1.

Look for both patterns across every row and down every column. Each number you place may create a new pair or gap somewhere else.

Counting

Once a row or column has its full share of one number, the remaining squares must all be the other number. On an 8 by 8 grid, if a row already has four 1s, every empty square in it is 0.

Counting also helps earlier. If a row needs only one more 0, think about where that 0 could go without breaking the no-three-in-a-row rule.

The no-twins rule

This rule is mostly useful near the end. If a row has only two empty squares left, and filling them one way would copy another completed row, then they must be filled the other way.

Winning

The puzzle is solved when every square is filled and all three rules are met.

Common variants

Some versions use two colours, or Xs and Os, instead of 0s and 1s. Some newspapers print very large grids of 14 by 14 or more. Some puzzles leave out the no-twins rule, though most include it.

Tips for beginners

• Hunt for pairs and gaps first. They solve most of an easy puzzle.
• Count each line. As soon as a line has half of one number, fill the rest with the other.
• Work across and down. Every square you place belongs to a row and a column, so check both.
• Start small. A 6 by 6 grid is perfect for learning the patterns.
• Save the no-twins rule for the end. When you get stuck late on, compare nearly full lines with finished ones.