PUZZLE #5023: Magnetic Flux Puzzle (diff 6)
A 7-letter word hidden as magnetic poles on a 5×27 grid. Strengths range 1–3. Invert the field to recover the poles.
DATA
| Difficulty |
6
|
| Char Count |
7
|
| Grid Width |
27
|
| Grid Height |
5
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Strengths |
3.0, 2.0, 3.0, 1.0, 1.0, 3.0, 3.0, 1.0, 3.0, 2.0, 1.0, 1.0, 1.0, 2.0, 3.0, 3.0, 3.0, 1.0, 3.0, 1.0, 2.0, 2.0, 1.0, 1.0, 3.0, 3.0, 3.0, 3.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 1.0, 3.0, 3.0, 3.0, 3.0, 1.0, 3.0, 1.0, 3.0, 3.0, 3.0, 1.0, 1.0, 1.0, 1.0, 2.0, 3.0, 2.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 2.0, 3.0, 1.0, 3.0, 3.0, 2.0, 3.0, 3.0, 2.0, 1.0, 1.0, 3.0, 1.0, 1.0, 3.0, 1.0, 3.0, 1.0, 3.0, 3.0, 1.0, 3.0, 3.0, 2.0, 2.0, 1.0, 3.0, 1.0, 2.0, 1.0, 3.0, 3.0, 2.0, 3.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.0, 3.0, 2.0, 1.0, 3.0, 1.0, 2.0, 2.0, 1.0, 3.0, 2.0, 1.0, 1.0, 3.0, 3.0, 2.0, 2.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 1.0, 3.0, 2.0, 3.0
|
| Flux Readings |
4.51996714, -1.40583502, -2.92414311, 0.96180864, -3.01957922, 2.83268571, -1.99340818, 4.71995483, 1.0063406, 0.78406302, 2.75210275, 0.35691974, 2.43471848, -0.6390809, 2.96123157, 2.41269046, -0.5314821, 1.97132948, -3.85888565, 2.30484082, -1.78914158, 4.09605788, -1.97872986, 0.72070277, -1.93623861, 3.70456224, 1.25017273, -2.77813961, 1.04723235, -1.33839026, -1.83209107, -4.95934776, 2.81088698, -1.30560697, 6.70216392, 2.6005539, 8.87418527, -6.00215711, 3.187845, 0.00310746, 8.08737139, -3.7037705, 2.94080023, 0.38037168, 3.85232518, -1.33502674, -3.46079624, 0.89747028, 2.53586506, -1.1321087, -4.38599048, -0.6785079, -2.16593986, 1.61738667, 2.14699929, -1.94342712, -6.54315898, -2.71595788, -1.91701116, 2.97416156, -0.10216295, 5.23219287, 2.87437059, -1.62067008, 2.13473068, -0.10702544, 0.05579411, 1.93389148, 4.04846944, 2.3936682, 0.90244065, -3.15094971, -7.42089495, -1.99944542, 0.59050968, 0.23913734, -0.94076824, -5.9851337, -7.2302037, -7.42638079, -2.76083759, -3.07069783, 0.90235751, -1.67178255, -2.05772923, -4.19457764, 4.03054151, -0.43305893, 3.64145056, 0.46642835, 7.02440583, -6.03438293, -0.12529566, 0.18072506, 3.74958989, -1.22256098, 2.43416876, -0.70900064, 1.65090214, -1.76247748, -3.45657982, -1.90658001, 4.50599531, -4.51024268, -6.12180677, -8.42209723, -8.40673312, -5.03334607, 3.1317414, -1.23173325, -3.86969458, 0.04366097, 2.86135464, -2.42974671, 1.18305139, 2.8322452, -1.4869455, 1.56346721, -3.07464062, 1.84119073, -4.38242536, 4.0718037, -2.87827982, 2.29592976, -0.13111729, -0.20292224, -3.91038716, 1.27565555, -2.45173858, 1.60136375, -3.62382441, -5.31076314, -3.46332794, -8.82653474, -2.57923756
|
| 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 135×135 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 6
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