Why a Sudoku Column Can Rule Out a Number
A Sudoku grid is built from overlapping groups: each row, each column, and each outlined 3-by-3 box must use the same set of nine digits. A square belongs to all three groups, so placing a number there affects three parts of the puzzle at once.
That overlap is what makes the column rule useful. If a column already contains a 6, every other empty square in that column is barred from holding a 6—even when several of those squares still look possible by row or box alone. The solver can cross those options off without guessing.
How One Placement Starts a Chain
Suppose a row has only two empty squares, and one of them lies in a column that already contains an 8. That square cannot be 8, so the other empty square must be. The new 8 then rules out other possibilities in its row, column, and box. A constraint in one column can therefore unlock a deduction somewhere else on the board.
Solvers track the digits still missing from each group and compare them with the restrictions imposed by neighboring groups. A candidate is a digit that could still fit in a particular empty square. As placements narrow those candidate lists, a puzzle that looked open-ended can become a sequence of forced choices.
Why Duplicates Matter
A duplicate is more than a local mistake: it means the grid’s constraints have been violated, and it can make later deductions unreliable. That is why careful solvers check a placement against its whole column as well as its row and box. The column rule turns a simple-looking grid into an interconnected logic system—one wrong digit can quietly distort the options in several places at once.
