PUZZLE #4482: FHSS Frequency Hopping (diff 6)

fhss learn difficulty: 6/7 simulate author: system unsolved

6 characters transmitted over 30 channels (11 jammed). Each character sent 3 times. LCG seed 7172 governs the hop schedule.

DATA

Hop Frequencies	`25, 8, 27, 14, 15, 24, 15, 14, 29, 10, 5, 16, 3, 18, 11, 8, 21, 2`
Transmissions	{'hop': 0, 'freq': 25, 'char_idx': 0, 'char': 'L', 'jammed': False}, {'hop': 1, 'freq': 8, 'char_idx': 1, 'char': 'I', 'jammed': False}, {'hop': 2, 'freq': 27, 'char_idx': 2, 'char': 'Z', 'jammed': False}, {'hop': 3, 'freq': 14, 'char_idx': 3, 'char': 'Y', 'jammed': False}, {'hop': 4, 'freq': 15, 'char_idx': 4, 'char': 'T', 'jammed': False}, {'hop': 5, 'freq': 24, 'char_idx': 5, 'char': 'F', 'jammed': False}, {'hop': 6, 'freq': 15, 'char_idx': 0, 'char': 'L', 'jammed': False}, {'hop': 7, 'freq': 14, 'char_idx': 1, 'char': 'I', 'jammed': False}, {'hop': 8, 'freq': 29, 'char_idx': 2, 'char': 'Z', 'jammed': False}, {'hop': 9, 'freq': 10, 'char_idx': 3, 'char': 'Y', 'jammed': False}, {'hop': 10, 'freq': 5, 'char_idx': 4, 'char': 'T', 'jammed': False}, {'hop': 11, 'freq': 16, 'char_idx': 5, 'char': 'F', 'jammed': False}, {'hop': 12, 'freq': 3, 'char_idx': 0, 'char': None, 'jammed': True}, {'hop': 13, 'freq': 18, 'char_idx': 1, 'char': None, 'jammed': True}, {'hop': 14, 'freq': 11, 'char_idx': 2, 'char': 'Z', 'jammed': False}, {'hop': 15, 'freq': 8, 'char_idx': 3, 'char': 'Y', 'jammed': False}, {'hop': 16, 'freq': 21, 'char_idx': 4, 'char': 'T', 'jammed': False}, {'hop': 17, 'freq': 2, 'char_idx': 5, 'char': 'F', 'jammed': False}
Jammed Channels	`1, 3, 7, 9, 17, 18, 19, 20, 22, 26, 28`
N Channels	`30`
N Chars	`6`
Redundancy	`3`
Seed	`7172`
Lcg A	`1103515245`
Lcg C	`12345`
Lcg M	`2147483648`
Hint	`LCG: x_i+1 = (a·x_i + c) mod m. Compute hop sequence from seed, find which hops survived jamming. Group surviving letters by char_idx to reconstruct the word.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "type": "fhss",
  "hop_frequencies": [
    25,
    8,
    27,
    14,
    15,
    24,
    15,
    14,
    29,
    10,
    5,
    16,
    3,
    18,
    11,
    8,
    21,
    2
  ],
  "transmissions": [
    {
      "hop": 0,
      "freq": 25,
      "char_idx": 0,
      "char": "L",
      "jammed": false
    },
    {
      "hop": 1,
      "freq": 8,
      "char_idx": 1,
      "char": "I",
      "jammed": false
    },
    {
      "hop": 2,
      "freq": 27,
      "char_idx": 2,
      "char": "Z",
      "jammed": false
    },
    {
      "hop": 3,
      "freq": 14,
      "char_idx": 3,
      "char": "Y",
      "jammed": false
    },
    {
      "hop": 4,
      "freq": 15,
      "char_idx": 4,
      "char": "T",
      "jammed": false
    },
    {
      "hop": 5,
      "freq": 24,
      "char_idx": 5,
      "char": "F",
      "jammed": false
    },
    {
      "hop": 6,
      "freq": 15,
      "char_idx": 0,
      "char": "L",
      "jammed": false
    },
    {
      "hop": 7,
      "freq": 14,
      "char_idx": 1,
      "char": "I",
      "jammed": false
    },
    {
      "hop": 8,
      "freq": 29,
      "char_idx": 2,
      "char": "Z",
      "jammed": false
    },
    {
      "hop": 9,
      "freq": 10,
      "char_idx": 3,
      "char": "Y",
      "jammed": false
    },
    {
      "hop": 10,
      "freq": 5,
      "char_idx": 4,
      "char": "T",
      "jammed": false
    },
    {
      "hop": 11,
      "freq": 16,
      "char_idx": 5,
      "char": "F",
      "jammed": false
    },
    {
      "hop": 12,
      "freq": 3,
      "char_idx": 0,
      "char": null,
      "jammed": true
    },
    {
      "hop": 13,
      "freq": 18,
      "char_idx": 1,
      "char": null,
      "jammed": true
    },
    {
      "hop": 14,
      "freq": 11,
      "char_idx": 2,
      "char": "Z",
      "jammed": false
    },
    {
      "hop": 15,
      "freq": 8,
      "char_idx": 3,
      "char": "Y",
      "jammed": false
    },
    {
      "hop": 16,
      "freq": 21,
      "char_idx": 4,
      "char": "T",
      "jammed": false
    },
    {
      "hop": 17,
      "freq": 2,
      "char_idx": 5,
      "char": "F",
      "jammed": false
    }
  ],
  "jammed_channels": [
    1,
    3,
    7,
    9,
    17,
    18,
    19,
    20,
    22,
    26,
    28
  ],
  "n_channels": 30,
  "n_chars": 6,
  "redundancy": 3,
  "seed": 7172,
  "lcg_a": 1103515245,
  "lcg_c": 12345,
  "lcg_m": 2147483648,
  "hint": "LCG: x_i+1 = (a\u00b7x_i + c) mod m. Compute hop sequence from seed, find which hops survived jamming. Group surviving letters by char_idx to reconstruct the word.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: fhss diff 6