N-queens

The N-queens Problem is a wellknown puzzle in combinatorics. The goal is to put non-attacking queens on a checkerboard. A queen can attack another is they are on the same row, same column or the same diagonals.

Material

• Printer and paper
• Plastic Laminator and Plastic Sheet
• Whiteboard markers and eraser

DIY

1. Print the different checkerboards
2. Print the queens
3. Using the plastic sheets, laminate the checkerboards and the queens
4. Cut the queens

Activity description

1. Tell the rules to the participants
2. Let them play, and try to find one of the solutions
3. If they did not find any solution guide them towards one (cf. note)
4. When one solution is found, tell them that they found at most 8 solutions (considering symetries and rotations)
5. If they’re game, give them a bigger checkerboard and the corresponding number of queens

Sources

• different checkerboards (4x4, 5x5, 6x6, 8x8)
• the queens
• notes in english (4x4, 5x5, 6x6, 8x8) and in french (4x4, 5x5, 6x6, 8x8)

Other Activities

• Lights out
• TSP