instances/langford_n16__v1_h.json

{
  "name": "langford_n16__v1_h",
  "problem_type": "langford",
  "params": {
    "n": 16
  },
  "prompt": "Construct a Langford sequence L(2,16): a sequence of length 32 containing exactly 2 copies of each integer from 1 to 16, 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 32 integers in 1..16, or state \"UNSATISFIABLE\" if no such sequence exists.\n\nPartial assignment (fixed values that must be respected):\n- seq[5]=14, seq[9]=4, seq[11]=15, seq[21]=9, seq[26]=13, seq[29]=10\nReturn a complete solution consistent with these fixed assignments.",
  "satisfiable": true,
  "solution": {
    "seq": [
      2,
      6,
      3,
      2,
      4,
      14,
      3,
      11,
      6,
      4,
      5,
      15,
      13,
      16,
      8,
      12,
      5,
      7,
      10,
      11,
      14,
      9,
      1,
      8,
      1,
      7,
      13,
      15,
      12,
      10,
      16,
      9
    ]
  },
  "difficulty": {
    "solve_time_ms": 2795.9,
    "search_space": 263130836933693530167218012160000000,
    "num_variables": 32,
    "num_constraints": 533,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 94.92,
    "solve_pct_type": 81.25
  },
  "partial_assignment": {
    "seq": {
      "5": 14,
      "9": 4,
      "11": 15,
      "21": 9,
      "26": 13,
      "29": 10
    }
  }
}