PUZZLE #4464: FHSS Frequency Hopping (diff 3)

fhss learn difficulty: 3/7 simulate author: system unsolved

6 characters transmitted over 24 channels (4 jammed). Each character sent 2 times. LCG seed 6025 governs the hop schedule.

DATA

Hop Frequencies	`6, 7, 12, 13, 18, 19, 8, 17, 22, 7, 20, 13`
Transmissions	{'hop': 0, 'freq': 6, 'char_idx': 0, 'char': None, 'jammed': True}, {'hop': 1, 'freq': 7, 'char_idx': 1, 'char': 'V', 'jammed': False}, {'hop': 2, 'freq': 12, 'char_idx': 2, 'char': 'S', 'jammed': False}, {'hop': 3, 'freq': 13, 'char_idx': 3, 'char': 'Y', 'jammed': False}, {'hop': 4, 'freq': 18, 'char_idx': 4, 'char': 'Q', 'jammed': False}, {'hop': 5, 'freq': 19, 'char_idx': 5, 'char': None, 'jammed': True}, {'hop': 6, 'freq': 8, 'char_idx': 0, 'char': 'A', 'jammed': False}, {'hop': 7, 'freq': 17, 'char_idx': 1, 'char': 'V', 'jammed': False}, {'hop': 8, 'freq': 22, 'char_idx': 2, 'char': 'S', 'jammed': False}, {'hop': 9, 'freq': 7, 'char_idx': 3, 'char': 'Y', 'jammed': False}, {'hop': 10, 'freq': 20, 'char_idx': 4, 'char': 'Q', 'jammed': False}, {'hop': 11, 'freq': 13, 'char_idx': 5, 'char': 'E', 'jammed': False}
Jammed Channels	`0, 6, 19, 21`
N Channels	`24`
N Chars	`6`
Redundancy	`2`
Seed	`6025`
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": [
    6,
    7,
    12,
    13,
    18,
    19,
    8,
    17,
    22,
    7,
    20,
    13
  ],
  "transmissions": [
    {
      "hop": 0,
      "freq": 6,
      "char_idx": 0,
      "char": null,
      "jammed": true
    },
    {
      "hop": 1,
      "freq": 7,
      "char_idx": 1,
      "char": "V",
      "jammed": false
    },
    {
      "hop": 2,
      "freq": 12,
      "char_idx": 2,
      "char": "S",
      "jammed": false
    },
    {
      "hop": 3,
      "freq": 13,
      "char_idx": 3,
      "char": "Y",
      "jammed": false
    },
    {
      "hop": 4,
      "freq": 18,
      "char_idx": 4,
      "char": "Q",
      "jammed": false
    },
    {
      "hop": 5,
      "freq": 19,
      "char_idx": 5,
      "char": null,
      "jammed": true
    },
    {
      "hop": 6,
      "freq": 8,
      "char_idx": 0,
      "char": "A",
      "jammed": false
    },
    {
      "hop": 7,
      "freq": 17,
      "char_idx": 1,
      "char": "V",
      "jammed": false
    },
    {
      "hop": 8,
      "freq": 22,
      "char_idx": 2,
      "char": "S",
      "jammed": false
    },
    {
      "hop": 9,
      "freq": 7,
      "char_idx": 3,
      "char": "Y",
      "jammed": false
    },
    {
      "hop": 10,
      "freq": 20,
      "char_idx": 4,
      "char": "Q",
      "jammed": false
    },
    {
      "hop": 11,
      "freq": 13,
      "char_idx": 5,
      "char": "E",
      "jammed": false
    }
  ],
  "jammed_channels": [
    0,
    6,
    19,
    21
  ],
  "n_channels": 24,
  "n_chars": 6,
  "redundancy": 2,
  "seed": 6025,
  "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 3