Binary puzzles: four rules for finding balance
A grid of zeros and ones is solved through balance, limits and differences. No arithmetic operations are needed.
2 min · RafaGonMar · October 20, 2026
Three of each digit
On Pausa’s 6 × 6 board, every row and column contains three zeros and three ones. Once a row has all three zeros, its empty cells must be ones. The same deduction works in columns.
No triples allowed
Three consecutive zeros or ones are forbidden horizontally and vertically. Two equal adjacent digits force different digits immediately outside them, wherever those cells exist.
1 1 · → 1 1 00 · 0 → 0 1 0The first case avoids a consecutive triple. The second prevents the gap from creating a triple between matching digits.Lines must differ
No two complete rows may be identical, and no two complete columns may be identical. This rule can resolve a line when other conditions still leave two choices. Compare like with like: a row may match a column.
Combine the clues
A cell can be constrained by its row’s balance and a pair in its column. Make safe deductions and scan the grid again after each change. One new digit can unlock several lines.
Using Check
Check looks for rules broken by current entries. No contradictions does not mean every entry is final: an error can remain consistent with visible clues until later. Generated puzzles are verified to have exactly one solution.