PUZZLE #4305: Magnetic Flux Puzzle (diff 2)
A 10-letter word hidden as magnetic poles on a 5×39 grid. Strengths range 1–1. Invert the field to recover the poles.
DATA
| Difficulty |
2
|
| Char Count |
10
|
| Grid Width |
39
|
| Grid Height |
5
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Strengths |
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0
|
| Flux Readings |
1.40689051, -0.44650832, 0.19921171, -1.89423751, 0.05297608, -2.3230001, 0.52324732, 0.15938865, -0.05434426, -0.71802602, 0.24433329, -1.75655199, 0.19282613, -2.2044239, 0.61976578, 0.20843591, -0.70259073, 3.16301216, -0.69858924, 0.21743412, 0.63651062, -2.1735801, 0.24866536, -1.6868473, 0.14198455, -1.47420578, -1.52043296, 1.30493175, -0.24997459, 3.74891935, 0.02961049, 2.23815541, 0.50457121, 0.34047541, -1.84422004, -0.00768942, -1.44419378, 1.1150315, -0.0654833, 1.4259095, 3.04391994, -3.62970983, -0.90592851, -2.138222, 2.83002978, -1.52745054, 0.9717141, -0.09827762, 2.97516683, -3.24153604, -0.50042095, -1.85544245, 3.01979097, -1.38792175, 1.11247758, 0.7127518, 0.96057376, 0.71642864, 1.12114439, -1.36971097, 3.06337354, -1.72465499, -0.03000498, -2.55775513, 0.32941614, -0.03800763, 0.23382809, 1.5235951, 2.95907371, 1.89521482, 2.184381, 0.1327, 1.77757317, -1.98970005, -3.67623519, -0.8111133, -1.01959979, 1.11782834, 1.71899119, -1.58444677, -1.34336554, -1.55898437, -0.30024565, 0.44769993, 0.48736698, 1.52861917, 0.50982099, -0.8476704, 0.82157338, -0.3548004, 0.22729731, 0.72396296, 0.65562177, 1.61327973, -0.11976361, 3.04309167, -0.1170944, 1.619481, 0.66900517, 0.76125512, 0.38684529, 0.92781914, -1.48687729, 0.54451708, -2.36265108, 1.18397529, 1.62539068, 2.9743897, 1.90217058, 2.16573636, 0.55474622, -2.13410689, -3.12083093, -5.0211936, -2.74543417, -2.35024759, -0.6459613, 0.40491923, -0.26493354, -3.73581902, -2.11177649, -1.25910135, 2.53085835, -0.39060983, 1.4502005, -0.43971146, 2.12859041, -2.04561085, 0.70373003, -0.47690906, 2.87568848, -0.20349537, 1.52895171, -0.65809646, 1.60241463, -0.65695106, 1.53080072, -0.20210188, 2.87399972, -0.487552, 0.67106886, -2.12678013, 1.97129226, -0.57990488, 1.59437639, 0.17607324, 3.52398545, 0.30983794, 1.92349311, 0.02377356, 1.64947506, -2.28211, -4.56908103, -2.83702435, -2.62065219, -0.90668766, -0.67346169, -1.01123543, -3.14230082, -1.47357925, -1.95211142, 1.39165108, -1.2197942, 1.51452929, -1.18875658, 1.49762045, -1.40511621, 1.36327293, -1.15995079, 1.74080217, -1.02851496, 1.62744387, -1.12506065, 1.61277075, -1.12534188, 1.62517582, -1.03865794, 1.70084637, -1.34045511, 0.00937685, 0.68510725, -0.60548975, 0.2117854, 1.87643885, -0.7998247, 2.05361199, -0.75124659, 1.97202633, 0.34788828, 0.13645778, -2.3203138, -2.0388588, -1.72261115, -2.65153531, -0.34153381
|
| 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 195×195 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 2
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