PUZZLE #3872: Magnetic Flux Puzzle (diff 1)
A 5-letter word hidden as magnetic poles on a 5×19 grid. Strengths range 1–1. Invert the field to recover the poles.
DATA
| Difficulty |
1
|
| Char Count |
5
|
| Grid Width |
19
|
| 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
|
| Flux Readings |
1.40261922, 0.41958289, -1.91700095, -0.11933014, -1.59871962, 0.79349517, -1.24417277, 0.89249165, -0.18971538, -0.0344935, -2.02248677, -0.01573619, -2.89325067, -2.21771236, -3.90675763, -1.78913778, -0.90551187, -0.83993913, 1.6058724, 1.18003953, 1.7974609, -2.14805649, -3.81389762, -0.93100452, -1.32334909, -0.25765521, -1.02372198, -0.86581261, 1.40592138, -1.88344868, -2.0308606, -3.07875488, -3.27228987, -5.35518979, -2.85841639, -1.68568483, 1.9359912, -0.83419178, 1.39514994, -2.50818843, -3.62926562, -5.21121774, -2.63949104, -2.34481261, -1.73891098, -1.59368474, -0.53523449, -2.44177099, -2.7496024, -2.50020292, -3.00633572, -3.03695707, -5.16576898, -2.81760787, -1.97165848, 1.1598569, 0.06948735, 0.13481062, -0.77906691, -4.72410423, -4.85758929, -1.26242588, -1.44434505, -0.3045126, -1.03630429, -0.8532303, 1.45277877, -1.76245273, -1.69943924, -2.03506322, -0.69624213, -2.77866197, -1.81318748, -1.35134083, 2.06198967, -0.77886525, -0.87794009, -1.33535766, -3.67103461, -2.39699408, -2.13411042, 0.59909575, -1.32159518, 0.87131923, -0.16854297, 0.04292892, -1.82808735, 0.51965461, -0.61558674, -0.4636787, -2.15181708, 0.49142154, -0.3646499, -0.6362666, 1.69876932
|
| 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 95×95 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 1
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