instances/langford_n8__v5_h.json

{
  "name": "langford_n8__v5_h",
  "problem_type": "langford",
  "params": {
    "n": 8
  },
  "prompt": "Construct a Langford sequence L(2,8): a sequence of length 16 containing exactly 2 copies of each integer from 1 to 8, 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 16 integers in 1..8, or state \"UNSATISFIABLE\" if no such sequence exists.\n\nPartial assignment (fixed values that must be respected):\n- seq[4]=7, seq[8]=5, seq[10]=4\nReturn a complete solution consistent with these fixed assignments.",
  "satisfiable": true,
  "solution": {
    "seq": [
      2,
      3,
      8,
      2,
      7,
      3,
      6,
      1,
      5,
      1,
      4,
      8,
      7,
      6,
      5,
      4
    ]
  },
  "difficulty": {
    "solve_time_ms": 1339.8,
    "search_space": 20922789888000,
    "num_variables": 16,
    "num_constraints": 141,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 82.89,
    "solve_pct_type": 6.25
  },
  "partial_assignment": {
    "seq": {
      "4": 7,
      "8": 5,
      "10": 4
    }
  }
}