1. N-queens problem Original problem: How to place 8 queens on an 8x8 chessboard so that no two queens attack each other N-queen problem: Generalization for N queens on NxN chessboard

2. N-queens as a CSP N variables: Q1, …, QN Domain of each variable is {1,2,…, N 2 } (for each possible field) Q1 = 1, Q2 = 15, Q3 = 21, Q4 = 32 Q5 = 34, Q6 = 44, Q7 = 54, Q8 = 59 Representation has 64 8 (281 474 976 710 656) possible assignments Problem representation

3. N-queens as a CSP N variables: Q1, …, QN Domain of each variable is {1,2, …, N} (i-th queen is in i-th column, the domain specifies available rows) Q1 = 1, Q2 = 5, Q3 = 8, Q4 = 6 Q5 = 3, Q6 = 7, Q7 = 2, Q8 = 4 Representation has 8 8 (16 777 216) possible assignments More compact representation

4. N-queens as a CSP No queen can attack any other queen: Vertically (for the compact representation explicit) Horizontally: Qi ≠ Qj Diagonally: |i-j| ≠|Qi-Qj| Constraints