Four queens placement: rules and printable materials

Place four queens so that no two share a row, column or diagonal.

Players

1–4 (cooperative)

Plan for

10–15 minutes

Bring

4 counters, 4×4 grid and checking sheet

Read the coordinates

Columns A–D run left to right, rows 1–4 bottom to top. Put four counters on four different cells. Each represents a queen attacking every cell in its row, column and both diagonal directions, however far away. There are no blockers: even another piece between two queens would not make sharing a row acceptable. The goal is to find one valid placement, not beat a hidden opponent.

Build a candidate

A convenient search places one queen in each row. Choose a column in row 1, then try row 2 without reusing a column or a diagonal. If a row has no legal cell, move back and change an earlier choice. Removing an unsuccessful candidate is allowed; keep a separate trial log rather than erasing the final answer unclearly. Partners can alternate proposing and checking a move.

Check every pair

For two occupied cells, compare the difference in column numbers with the difference in row numbers. Equal absolute differences mean a diagonal conflict. A1 and C3 conflict because both gaps are two; A1 and C2 do not because the gaps are two and one. Same row or same column is also a conflict. Test all six pairs, not only neighbors.

Worked solution and finish

One valid bottom-to-top column sequence is B, D, A, C: B1, D2, A3, C4. Rows and columns are distinct; the six pairs also avoid equal diagonal gaps. A reflected arrangement gives another solution. The host key is deliberately separate from the player grid. Stop after one checked solution or agree to enumerate all placements; do not claim a unique answer for this four-queen task.

Make the search comfortable

There is no time penalty. A helper may read coordinates or record choices. Use four identical large counters, with no need for chess knowledge or special pieces. If solving together, give everyone a chance to check one pair before revealing the key. Print another grid for an independent attempt, keeping the host key face down. This is a finite paper puzzle with a manual verification method.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.