{
  "name": "costas_array_n12__v4_h",
  "problem_type": "costas_array",
  "params": {
    "n": 12
  },
  "prompt": "Find a Costas array of order 12: place 12 marks on an 12x12 grid, one per row and one per column, such that all 12*(11)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.\n\nReturn x as a list of 12 integers in 0..11, where x[c] is the row of the mark in column c (permutation), or state \"UNSATISFIABLE\" if no such array exists.\n\nPartial assignment (fixed values that must be respected):\n- x[3]=8, x[8]=2\nReturn a complete solution consistent with these fixed assignments.",
  "satisfiable": true,
  "solution": {
    "x": [
      6,
      1,
      10,
      8,
      9,
      5,
      11,
      3,
      2,
      4,
      7,
      0
    ]
  },
  "difficulty": {
    "solve_time_ms": 1129.3,
    "search_space": 479001600,
    "num_variables": 12,
    "num_constraints": 13,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 77.63,
    "solve_pct_type": 83.33
  },
  "partial_assignment": {
    "x": {
      "3": 8,
      "8": 2
    }
  }
}