{
  "name": "knight_tour_n8__v1_h",
  "problem_type": "knight_tour",
  "params": {
    "n": 8
  },
  "prompt": "Find an open knight's tour on an 8x8 chessboard that starts at cell 0 (row 0, column 0). A knight's tour visits every cell exactly once via knight moves; cells are numbered in row-major order so cell k is at row k//8, column k%8. A knight move between cells a and b changes the row by 1 and column by 2, or row by 2 and column by 1.\n\nReturn a list of 64 integers giving the cell visited at each step (a permutation of 0..63 starting with 0), or state \"UNSATISFIABLE\" if no such tour exists.\n\nPartial assignment (fixed values that must be respected):\n- x[2]=27, x[3]=21, x[10]=16, x[11]=1, x[19]=24, x[21]=3, x[27]=51, x[38]=38, x[50]=43, x[51]=60, x[59]=53, x[61]=42\nReturn a complete solution consistent with these fixed assignments.",
  "satisfiable": true,
  "solution": {
    "x": [
      0,
      17,
      27,
      21,
      6,
      12,
      2,
      19,
      4,
      10,
      16,
      1,
      18,
      8,
      25,
      35,
      50,
      56,
      41,
      24,
      9,
      3,
      20,
      5,
      15,
      30,
      36,
      51,
      34,
      49,
      32,
      26,
      11,
      28,
      22,
      7,
      13,
      23,
      38,
      44,
      29,
      14,
      31,
      37,
      47,
      62,
      52,
      58,
      48,
      33,
      43,
      60,
      54,
      39,
      45,
      55,
      61,
      46,
      63,
      53,
      59,
      42,
      57,
      40
    ]
  },
  "difficulty": {
    "solve_time_ms": 56542.2,
    "search_space": 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000,
    "num_variables": 64,
    "num_constraints": 67,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 99.81,
    "solve_pct_type": 87.5
  },
  "partial_assignment": {
    "x": {
      "2": 27,
      "3": 21,
      "10": 16,
      "11": 1,
      "19": 24,
      "21": 3,
      "27": 51,
      "38": 38,
      "50": 43,
      "51": 60,
      "59": 53,
      "61": 42
    }
  }
}