{
  "name": "langford_n15__v3_h",
  "problem_type": "langford",
  "params": {
    "n": 15
  },
  "prompt": "Construct a Langford sequence L(2,15): a sequence of length 30 containing exactly 2 copies of each integer from 1 to 15, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2, 1, 3].\n\nReturn seq as a list of 30 integers in 1..15, or state \"UNSATISFIABLE\" if no such sequence exists.\n\nPartial assignment (fixed values that must be respected):\n- seq[3]=2, seq[11]=14, seq[13]=11, seq[26]=14, seq[27]=7, seq[28]=10\nReturn a complete solution consistent with these fixed assignments.",
  "satisfiable": true,
  "solution": {
    "seq": [
      2,
      6,
      3,
      2,
      4,
      12,
      3,
      15,
      6,
      4,
      13,
      14,
      9,
      11,
      1,
      5,
      1,
      10,
      12,
      7,
      8,
      5,
      9,
      15,
      13,
      11,
      14,
      7,
      10,
      8
    ]
  },
  "difficulty": {
    "solve_time_ms": 2620.2,
    "search_space": 265252859812191058636308480000000,
    "num_variables": 30,
    "num_constraints": 470,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 94.17,
    "solve_pct_type": 68.75
  },
  "partial_assignment": {
    "seq": {
      "3": 2,
      "11": 14,
      "13": 11,
      "26": 14,
      "27": 7,
      "28": 10
    }
  }
}