How to Solve Binary Puzzle: Beginner Strategies Step by Step

To solve a binary puzzle, scan the grid with the same four questions again and again: is a cell next to a pair, is it in a gap between two identical digits, has a line reached its count of 0s or 1s, and would a line become a copy of another? Every answer fills a cell, and every filled cell feeds the next scan. This page shows the scan on a real 8 x 8 puzzle, in the order a solver would follow it.

A four-question scan

1. Pair. Two identical digits side by side? The cells on both sides must be the other digit.
2. Gap. Two identical digits with one empty cell between them? That cell must be the other digit.
3. Count. Has a line already got half of its cells as 0 (or as 1)? Then every empty cell of the line is the other digit.
4. Duplicate. Does a line have two empty cells left, and would filling them one way make it identical to a finished line? Then fill them the other way.

Always check rows and columns. A cell has a row and a column, and either of them can give the answer.

An 8 x 8 puzzle, start to finish

This is a medium puzzle from the LogikLand generator. It has 16 digits given, so 48 cells are left to find.

We solved it with a separate solver that applies the four questions in this order: pairs and gaps first, then counts, then duplicates. All 48 cells were found without a single guess. In the order we followed, 32 cells came from a pair or a gap, 12 from a count and 4 from the duplicate check. A different order gives different numbers, but never a different grid.

The first moves

1. A pair in a column. Column 1 has a 1 in row 3 and a 1 in row 4. Rows 2 and 5 of column 1 must be 0.
2. A gap in a row. Row 2 now reads 0 _ 0 in columns 1 to 3. The empty cell cannot be a 0, so row 2, column 2 is a 1.
3. That 1 starts a pair. Column 2 has a 1 in row 1 and, now, a 1 in row 2. Row 3 of column 2 must be a 0.
4. The chain goes on. Row 3 now reads 1 0 0 _ in its first columns, which makes a pair of 0s. Column 4 of row 3 is a 1. Each new cell creates new pairs and gaps for the next questions.

When counting takes over

After about fifteen cells, pairs and gaps run out for a moment. Look at the counts. In this grid, column 2 holds four 1s (rows 1, 2, 5 and 7) once the pairs and gaps have been used. That is half of 8, so every other cell of column 2 is a 0. This filled row 8, column 2, which no pair or gap could reach.

The last cells: no identical lines

Late in the puzzle, a line may have exactly two empty cells. Compare it with each finished line. In our puzzle, row 5 reads 0 1 _ _ 1 0 0 1 and row 2 is the finished line 0 1 0 1 1 0 0 1. Putting 0 and 1 in the empty cells would copy row 2. The only other way to fill them is 1 and 0, so row 5 is 0 1 1 0 1 0 0 1. The same check settled two cells of column 5, using column 2 as the model.

Habits that prevent mistakes

• Work in pencil. One wrong digit makes a count fail much later, and you will look for the mistake in the wrong place.
• Finish a line before you leave it: when a line is complete, recheck its three rules once.
• Say the count aloud on large grids: "that is five 1s, so the rest are 0".
• Do not mark two cells at once from one clue unless both are forced. A pair forces its two neighbours, and a count forces all the rest.

Making a book

LogikLand has no free single-puzzle tool for binary puzzles. To make a book, create a free account and open the Binary Puzzle assistant: four levels from 6 x 6 to 12 x 12, 1, 2 or 4 puzzles per page, and a "How to play" page that includes a worked 6 x 6 example. Our suggestion, not a rule: a book that moves from 6 x 6 up to 10 x 10 lets readers learn the four questions before they meet the long counts.

Questions