PUZZLE #7736: Blue Box Tone Decode (diff 5)

phone-tone learn difficulty: 5/7 decode author: system unsolved

Decode the DTMF frequency pairs to digits, then map each digit to its letter using a phone keypad.

DATA

Word	`hotel`
Word Length	`5`
Tones	`{'digit': '4', 'tone1_hz': 770, 'tone2_hz': 1209}, {'digit': '6', 'tone1_hz': 770, 'tone2_hz': 1477}, {'digit': '8', 'tone1_hz': 852, 'tone2_hz': 1336}, {'digit': '3', 'tone1_hz': 697, 'tone2_hz': 1477}, {'digit': '5', 'tone1_hz': 770, 'tone2_hz': 1336}`
Keypad Hint	`Standard DTMF keypad: 2=ABC, 3=DEF, 4=GHI, 5=JKL, 6=MNO, 7=PQRS, 8=TUV, 9=WXYZ`
Hint	`5-letter word. The DTMF tones encode the word. Each pair (low+hightone) maps to one digit: 1→697+1209, 2→697+1336 ... 0→941+1336. Then 2=ABC, 3=DEF etc.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "type": "phone-tone",
  "word": "hotel",
  "word_length": 5,
  "tones": [
    {
      "digit": "4",
      "tone1_hz": 770,
      "tone2_hz": 1209
    },
    {
      "digit": "6",
      "tone1_hz": 770,
      "tone2_hz": 1477
    },
    {
      "digit": "8",
      "tone1_hz": 852,
      "tone2_hz": 1336
    },
    {
      "digit": "3",
      "tone1_hz": 697,
      "tone2_hz": 1477
    },
    {
      "digit": "5",
      "tone1_hz": 770,
      "tone2_hz": 1336
    }
  ],
  "keypad_hint": "Standard DTMF keypad: 2=ABC, 3=DEF, 4=GHI, 5=JKL, 6=MNO, 7=PQRS, 8=TUV, 9=WXYZ",
  "hint": "5-letter word. The DTMF tones encode the word. Each pair (low+hightone) maps to one digit: 1\u2192697+1209, 2\u2192697+1336 ... 0\u2192941+1336. Then 2=ABC, 3=DEF etc.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: phone-tone diff 5