Nine-number magic square: rules and printable materials

Place nine different numbers so every row, column and diagonal totals fifteen.

Suggested group

1–6

Plan for

12–20 minutes

Bring

Number tiles 1–9, grid and pencils

Prepare one shared puzzle

Cut out number tiles 1 to 9 and give each table a blank three-by-three grid. Every number must be used exactly once. State all eight checks: three horizontal rows, three vertical columns and two corner-to-corner diagonals must each total 15. Numbers cannot overlap in a cell, be turned into other digits, or be combined into a two-digit number. Keep the solution page with the host until checking.

Work as a team

Use groups of one to six; for more guests, print independent sets. Give two minutes for quiet examination, then ten minutes to arrange and revise. Move tiles instead of repeatedly erasing digits. A recorder can calculate one line while another player checks that no number has been duplicated. Take turns suggesting a move so one fast solver does not silently complete everything.

A useful worked check

If the top row contains 8, 1 and 6, its sum is 15. That does not prove the whole square works. Check the first column and both diagonals as well. For example, 8–5–2 makes one diagonal total 15, while the other diagonal must be checked separately. The printable checklist has eight boxes; tick a box only after adding its actual three values.

Use hints in stages

After four minutes, offer the first hint only if the table wants it: the centre can be 5. A second hint says opposite cells around the centre can form pairs totalling 10. A final hint gives one complete top row, 8–1–6. Do not make a hint cost a point or expose the complete answer to a team that still wants to explore. The goal is a valid arrangement, not remembering a famous picture.

Verify and finish

The host sheet shows 8–1–6, 3–5–7, 4–9–2. It is one solution, not the only accepted orientation: a rotated or reflected valid grid also counts. Check all eight sums and that the set of values is exactly 1 through 9. Stop after a verified solution or the announced fifteen-minute solving limit, then compare strategies. For a gentler round, start with the centre 5 already placed. Do not change the target to another number while keeping the same nine-tile set.

Printable materials

Preview before printing at 100% scale; turn off browser headers and footers. Keep host answers separate. This is a manual tabletop kit, not computer opposition or an automatic judge.