PUZZLE #4581: Elliptical Gravitational Lensing (diff 7)

elliptical learn difficulty: 7/7 compute author: system unsolved

11 gravitational masses warp the grid. Each cell takes the letter of the mass whose gravitational influence is strongest. Read the letter sequence along the scan line (row 16) to reveal the answer.

DATA

Grid Size	`32, 32`
Masses	{'x': 4, 'y': 16, 'strength': 9.99, 'letter': 'T'}, {'x': 8, 'y': 16, 'strength': 8.12, 'letter': 'E'}, {'x': 12, 'y': 16, 'strength': 8.34, 'letter': 'N'}, {'x': 16, 'y': 16, 'strength': 10.34, 'letter': 'S'}, {'x': 20, 'y': 16, 'strength': 11.53, 'letter': 'O'}, {'x': 24, 'y': 16, 'strength': 9.99, 'letter': 'R'}, {'x': 24, 'y': 5, 'strength': 6.99, 'letter': 'I', 'distractor': True}, {'x': 22, 'y': 7, 'strength': 7.4, 'letter': 'X', 'distractor': True}, {'x': 11, 'y': 23, 'strength': 5.74, 'letter': 'J', 'distractor': True}, {'x': 26, 'y': 11, 'strength': 5.37, 'letter': 'C', 'distractor': True}, {'x': 20, 'y': 2, 'strength': 7.86, 'letter': 'D', 'distractor': True}
Scan Line	{ "row": 16, "start": 0, "end": 31 }
Hint	`Elliptical gravitational lensing — difficulty 7. Grid: 32x32. 11 masses. Scan row: 16. Formula: deflection = S_i / r_i for each mass. The strongest deflection determines the cell's letter. Read the scan line left to right. 5 distractor masses with random letters are placed off the scan line.`
Answer Format	`lowercase decoded message`

{
  "type": "elliptical",
  "grid_size": [
    32,
    32
  ],
  "masses": [
    {
      "x": 4,
      "y": 16,
      "strength": 9.99,
      "letter": "T"
    },
    {
      "x": 8,
      "y": 16,
      "strength": 8.12,
      "letter": "E"
    },
    {
      "x": 12,
      "y": 16,
      "strength": 8.34,
      "letter": "N"
    },
    {
      "x": 16,
      "y": 16,
      "strength": 10.34,
      "letter": "S"
    },
    {
      "x": 20,
      "y": 16,
      "strength": 11.53,
      "letter": "O"
    },
    {
      "x": 24,
      "y": 16,
      "strength": 9.99,
      "letter": "R"
    },
    {
      "x": 24,
      "y": 5,
      "strength": 6.99,
      "letter": "I",
      "distractor": true
    },
    {
      "x": 22,
      "y": 7,
      "strength": 7.4,
      "letter": "X",
      "distractor": true
    },
    {
      "x": 11,
      "y": 23,
      "strength": 5.74,
      "letter": "J",
      "distractor": true
    },
    {
      "x": 26,
      "y": 11,
      "strength": 5.37,
      "letter": "C",
      "distractor": true
    },
    {
      "x": 20,
      "y": 2,
      "strength": 7.86,
      "letter": "D",
      "distractor": true
    }
  ],
  "scan_line": {
    "row": 16,
    "start": 0,
    "end": 31
  },
  "note": "For each cell (x, y) in a 32x32 grid, compute the gravitational deflection for each mass: deflection = S_i / r_i where r_i is the Euclidean distance to mass i. The cell's letter is the letter of the mass with the STRONGEST deflection. Read the letters along the scan line (row 16, columns 0-31) and concatenate to get the answer. Ignore distractors (they have random letters).",
  "hint": "Elliptical gravitational lensing \u2014 difficulty 7. Grid: 32x32. 11 masses. Scan row: 16. Formula: deflection = S_i / r_i for each mass. The strongest deflection determines the cell's letter. Read the scan line left to right. 5 distractor masses with random letters are placed off the scan line.",
  "answer_format": "lowercase decoded message"
}

author's note: Pool fill: elliptical diff 7