How to Solve Bits: Binary Grid Logic Without Guessing

Bits uses a 6 by 6 grid, so every row and column must contain exactly three 0s and three 1s. No line may contain three identical digits in a row, and no two completed rows or columns may be identical. Locked cells provide starting digits. Some puzzles also include equals signs between neighbors that must match and multiplication signs between neighbors that must differ.

Most Bits deductions come from a small pattern library. The faster you recognize the patterns, the less the puzzle feels like testing 0 and 1 at random.

Pattern card 1: two together force the opposite

In a sequence such as 0, 0, blank, the blank must be 1. The mirror case blank, 1, 1 forces 0. This works horizontally and vertically, so every new digit deserves a scan in both directions.

Pattern card 2: matching ends force the middle

A pattern such as 1, blank, 1 forces the middle cell to 0. Otherwise you would create three 1s in a row. The equivalent 0, blank, 0 pattern forces 1.

These sandwich patterns are easy to miss because the equal digits are not adjacent. They are often the first move on a sparse board.

Pattern card 3: a full quota finishes the line

Once a row already contains three 0s, every remaining blank in that row is 1. Once it contains three 1s, the rest are 0. Apply the same count to columns.

Quota deductions can create a chain. Filling the final two cells of a row may produce a pair in a column, which forces an opposite digit, which completes another row.

Pattern card 4: equals and different signs are equations

An equals sign means its two neighboring cells carry the same digit. A multiplication sign means they carry different digits. If one side is known, the other is immediate. If neither side is known, preserve the relationship and combine it with the balance and no-three rules.

For example, an equals pair cannot occupy the last two blanks of a line that already contains two 0s and two 1s, because the line needs one of each. That relationship can rule out a candidate before either digit is individually known.

Pattern card 5: uniqueness breaks late ties

Suppose a nearly complete row could finish in two ways, but one completion would duplicate an existing row. Choose the other. The same argument works for columns.

Use uniqueness late, when enough of the comparison line is fixed. Two partially matching rows are not a contradiction; they become a problem only if every position would match.

How to recover when you are stuck

• Count 0s and 1s in every row, then every column.
• Scan for adjacent pairs and sandwich patterns.
• Propagate every equals or different relationship from known digits.
• Compare nearly complete rows and columns for duplicates.
• After placing one digit, rescan both crossing lines before moving on.

A worked cascade in miniature

Suppose a row reads 1, 1, blank, 0, blank, blank. The third cell must be 0 because three 1s are forbidden. The row now has two 1s and two 0s, so the final two blanks must contain one of each. If an equals sign joins those final cells, that candidate is impossible because they cannot be the same. If a different sign joins them, the relationship is consistent but their order still depends on the columns.

Now inspect those two columns. If one already contains three 0s, its blank must be 1, and the other cell in the row becomes 0. One no-three deduction, one balance count, and one neighbor relationship have combined to finish the line without testing either value.

Bits rewards rhythm. Place one forced digit, inspect its row, inspect its column, and let the consequences travel. A good solve is a cascade of local certainties, not a sequence of coin flips.

A new Bits puzzle is available every day. For more repetitions with the same rules, open Practice and choose Bits.