PUZZLE #4984: Magnetic Flux Puzzle (diff 7)
A 5-letter word hidden as magnetic poles on a 5×19 grid. Strengths range 1–3. Invert the field to recover the poles.
DATA
| Difficulty |
7
|
| Char Count |
5
|
| Grid Width |
19
|
| Grid Height |
5
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Strengths |
2.0, 1.0, 1.0, 1.0, 3.0, 2.0, 2.0, 2.0, 2.0, 3.0, 1.0, 1.0, 3.0, 3.0, 1.0, 1.0, 1.0, 3.0, 1.0, 2.0, 2.0, 1.0, 1.0, 3.0, 2.0, 1.0, 1.0, 3.0, 3.0, 1.0, 3.0, 3.0, 3.0, 3.0, 1.0, 2.0, 1.0, 2.0, 1.0, 3.0, 2.0, 2.0, 1.0, 3.0, 2.0, 1.0, 3.0, 3.0, 2.0, 3.0, 1.0, 1.0, 1.0, 2.0, 3.0, 1.0, 3.0, 2.0, 3.0, 3.0, 1.0, 2.0, 3.0, 1.0, 3.0, 2.0, 3.0, 2.0, 1.0, 3.0, 1.0, 3.0, 3.0, 1.0, 2.0, 1.0, 3.0, 3.0, 1.0, 2.0, 2.0, 3.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 1.0, 3.0, 3.0, 2.0, 1.0, 2.0, 1.0
|
| Flux Readings |
1.68155242, 0.50055201, -2.88379462, -3.13382611, 1.05163065, -6.67775596, -0.46405102, 0.66331833, 1.306394, -1.75747544, -0.04570824, -5.44107018, 0.93542831, -6.76477223, -3.70429486, 0.05740654, 1.93376649, -0.20918275, 0.06401838, 1.32515304, 3.67426594, -4.11032581, -3.87747558, -8.07845916, -0.17449749, -4.57986358, 1.48548836, 0.43335555, 7.81529469, -7.05236605, -2.35696791, -9.72596206, -1.10252516, -4.3554806, -3.4324329, -0.20597716, 3.00162205, -0.91387852, 3.29816617, -6.85876463, -5.73998518, -5.06364794, -5.35585956, -1.46147881, -5.7011834, 1.46403026, 1.54470434, -3.31613918, -0.42989615, -2.73670111, -3.61934436, -5.2703967, -9.84675699, -3.70833421, -2.85708096, -3.16179643, -1.5688141, -0.72178434, -1.74670397, -8.0737009, -8.17755532, -8.52119025, -0.10236566, -6.90080009, 1.01170329, -1.79923186, 4.34374571, -5.09777405, -1.90900251, -5.09645297, -0.3371089, -2.91250437, -3.6980253, -2.6818321, 2.11899042, -2.5454989, -3.25313373, -2.05610263, -9.36749357, -6.04459502, -1.37094496, -7.97691194, -1.0763703, -1.43850198, -5.16218512, 3.09257902, -5.65361197, 1.58898466, 1.21391912, -1.77397125, -4.59862025, -0.0741045, -1.36999215, -1.27607084, -0.57779964
|
| 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 7
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