Backtracking

Four Queens Solution

State the final non-attacking queen positions. This is a small deterministic example, not solver engineering.

combinatorics-search Every row is intentionally ordered and pinned to the lesson specification.

Example

State the final non-attacking queen positions. A solution places one queen in each row so that no two share a column or a diagonal, meaning none could capture another. Backtracking reached this arrangement by trying a column for each row in turn and undoing any placement that caused a conflict, until every row was filled safely.

highlighted = computed this step

Step 1 — Solution

Compute the highlighted combinatorics value.

queen cells((0, 1), (1, 3), (2, 0), (3, 2))\begin{array}{c|c}\text{queen cells}&\hlmath{\text{((0, 1), (1, 3), (2, 0), (3, 2))}}\end{array}

Step 2 — Verdict

Compute the highlighted combinatorics value.

verdictvalid solution\begin{array}{c|c}\text{verdict}&\hlmath{\text{valid solution}}\end{array}