PUZZLE #4481: Magnetic Flux Puzzle (diff 5)
A 9-letter word hidden as magnetic poles on a 5×35 grid. Strengths range 1–3. Invert the field to recover the poles.
DATA
| Difficulty |
5
|
| Char Count |
9
|
| Grid Width |
35
|
| Grid Height |
5
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Strengths |
2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 1.0, 3.0, 3.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 3.0, 3.0, 2.0, 1.0, 1.0, 3.0, 1.0, 2.0, 1.0, 2.0, 1.0, 3.0, 1.0, 1.0, 3.0, 3.0, 3.0, 1.0, 3.0, 2.0, 3.0, 3.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.0, 2.0, 1.0, 2.0, 3.0, 3.0, 1.0, 2.0, 1.0, 2.0, 2.0, 3.0, 1.0, 1.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 2.0, 1.0, 3.0, 2.0, 1.0, 3.0, 3.0, 3.0, 3.0, 2.0, 2.0, 3.0, 2.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 3.0, 3.0, 3.0, 3.0, 1.0, 1.0, 1.0, 1.0, 2.0, 3.0, 2.0, 1.0, 3.0, 2.0, 3.0, 3.0, 1.0, 2.0, 2.0, 3.0, 3.0, 1.0, 3.0, 2.0, 3.0, 1.0, 2.0, 2.0, 1.0, 1.0, 2.0, 2.0, 3.0, 1.0, 2.0, 2.0, 3.0, 3.0, 3.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0, 1.0, 3.0, 2.0, 2.0, 3.0, 2.0, 3.0, 1.0, 1.0, 1.0, 3.0, 1.0, 3.0, 3.0, 3.0, 2.0, 2.0, 2.0, 1.0, 2.0, 3.0, 1.0, 2.0, 3.0, 3.0, 1.0, 2.0, 3.0, 3.0
|
| Flux Readings |
2.40429568, 0.76872288, -0.22160819, -2.16233596, -1.45416972, -0.46284848, -3.06414625, 0.36228854, -0.21657492, -2.55186971, 0.02166717, 1.11690896, 1.38882451, 6.93566389, 2.38933544, 4.38680556, 1.46231172, 0.55795105, -7.31706976, -3.62772507, -1.17517059, -7.48589152, 0.44853584, -1.64207118, -3.17505437, 6.13485361, -2.84910617, -0.52082439, -0.84717098, -5.38867192, -6.69598851, -1.97566388, -0.21971826, 0.88155952, 0.63894645, 3.23381854, 4.51204002, -6.34222386, -0.74677919, -3.33335053, 1.8867038, -4.50595115, -2.57567157, -1.37438069, 5.37299526, -5.70179823, -0.26167389, 2.32171027, 5.37169744, 4.60371901, 5.24590984, -0.52955189, 3.05868733, -4.73147021, -6.93062659, -5.69689508, 4.77043574, -4.61938497, -0.34097609, 0.38126427, 2.93435773, 2.653112, 1.05809989, -6.02447815, -4.623109, -6.64219542, -5.05506311, -1.67783399, 5.60525046, 0.61277094, 3.04958071, -2.56223665, -0.90942563, -4.74586307, -0.64432697, -7.59298753, -4.22532888, -2.21646956, -0.95425045, -3.12388593, 2.0839353, -0.29789765, 0.14933929, 8.42231524, 2.44859338, 5.46124426, 4.27825932, -4.91125077, -6.00233692, -4.82401187, -1.96752131, 2.13629714, 0.32659299, 3.03464151, 1.05311919, 4.36072424, 3.21262906, 0.57940656, -2.6246748, -3.9839917, -10.30794069, -3.08101435, -1.34417497, -4.18615758, -0.12224624, 1.11673696, -1.03601273, -6.35616348, -2.58416008, -2.30002157, 3.06201463, -4.98942756, -3.89043048, -1.33936481, 6.29382842, -4.92516958, 1.71119772, -0.46924113, 4.96072624, -0.02669157, 6.23569065, 0.72990304, 3.82426726, -2.03994326, -3.24044319, -0.55171407, 6.31372653, -0.09150415, 1.42808095, -0.2018366, 5.06071028, 0.85903299, 3.77606717, -4.35357662, 0.47160382, -1.73624995, -0.56174125, -0.61441115, 6.69119789, 0.84636622, -1.56090122, -1.77971592, -3.9908137, -1.55526262, -0.36285569, -1.59885892, -4.19968358, 1.59314118, -2.66996287, 4.24664912, -2.36498103, 3.79197373, -2.51674893, 3.36340491, 0.33332694, 3.72874513, 1.81766168, 3.7525513, -4.88054592, 3.44819699, -2.52834373, 5.19330793, -1.8490205, 2.20527221, -2.21730797, 4.1749505, -1.56666529, 1.35916042, 4.00425084, -1.05041876, -1.67348254, 3.28942185, 2.94793518, 1.54989739, -0.84098316
|
| Font |
{
"A": [
"010",
"101",
"111",
"101",
"101"
],
"B": [
"110",
"101",
"110",
"101",
"110"
],
"C": [
"011",
"100",
"100",
"100",
"011"
],
"D": [
"110",
"101",
"101",
"101",
"110"
],
"E": [
"111",
"100",
"110",
"100",
"111"
],
"F": [
"111",
"100",
"110",
"100",
"100"
],
"G": [
"011",
"100",
"101",
"101",
"011"
],
"H": [
"101",
"101",
"111",
"101",
"101"
],
"I": [
"111",
"010",
"010",
"010",
"111"
],
"J": [
"111",
"010",
"010",
"010",
"110"
],
"K": [
"101",
"101",
"110",
"101",
"101"
],
"L": [
"100",
"100",
"100",
"100",
"111"
],
"M": [
"101",
"111",
"101",
"101",
"101"
],
"N": [
"101",
"111",
"111",
"101",
"101"
],
"O": [
"010",
"101",
"101",
"101",
"010"
],
"P": [
"110",
"101",
"110",
"100",
"100"
],
"Q": [
"010",
"101",
"101",
"110",
"011"
],
"R": [
"110",
"101",
"110",
"101",
"101"
],
"S": [
"011",
"100",
"010",
"001",
"110"
],
"T": [
"111",
"010",
"010",
"010",
"010"
],
"U": [
"101",
"101",
"101",
"101",
"010"
],
"V": [
"101",
"101",
"101",
"010",
"010"
],
"W": [
"101",
"101",
"101",
"111",
"101"
],
"X": [
"101",
"010",
"010",
"010",
"101"
],
"Y": [
"101",
"010",
"010",
"010",
"010"
],
"Z": [
"111",
"001",
"010",
"100",
"111"
]
}
|
| Instructions |
1. This grid has h×w cells, each containing a magnet with pole N(+1) or S(-1)
2. N/S spells a word in 3x5 pixel font (row-major, gap between chars)
3. You receive flux readings: cumulative field from all OTHER magnets
4. Flux_i = Σ_{j≠i} strength_j × pole_j / distance(i,j)²
5. Build n×n matrix A where A[i][j] = strength_j / distance(i,j)², A[i][i]=0
6. Solve A·x = flux_readings — x gives pole vector (±1)
7. x[j] > 0 → N pole → pixel ON; x[j] < 0 → S pole → pixel OFF
8. Decode the 3×5 pattern against the font reference
9. Use numpy.linalg.lstsq for a stable solve
|
| Hint |
Build 175×175 matrix A, solve A·x = flux. Each char occupies 3 cols × 5 rows.
|
| Answer Format |
single digit or integer
|
author's note: Pool fill: flux diff 5
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