PUZZLE #5045: Magnetic Flux Puzzle (diff 3)
A 5-letter word hidden as magnetic poles on a 5×19 grid. Strengths range 1–2. Invert the field to recover the poles.
DATA
| Difficulty |
3
|
| Char Count |
5
|
| Grid Width |
19
|
| Grid Height |
5
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Strengths |
1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 1.0, 1.0, 2.0, 2.0, 2.0, 1.0, 2.0, 2.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 1.0
|
| Flux Readings |
3.79443633, 1.83596283, -1.72369759, 1.52934053, -2.9170778, -0.02210753, -3.01971492, -0.62476681, -2.18551885, -1.47580085, -3.33762496, 1.07404486, -3.20380763, -1.46997347, -4.40823047, -1.13257727, -0.39207173, -0.33987887, 3.46922754, 3.03751002, 5.09098653, -0.96968937, -5.17389235, -1.09659987, -2.66798733, -2.3433237, -3.29608377, -2.65032805, 1.63701122, -3.65214702, -2.17318322, -2.89817535, -3.00602809, -5.0826066, -3.49393327, -1.25396816, 4.64624561, -0.31143648, 3.74369628, -2.01919253, -3.8941885, -7.17616638, -3.99560444, -6.19276911, -3.91004713, -4.60114229, -1.91620837, -4.27016351, -2.81950969, -2.924986, -1.44785236, -2.92510945, -7.01376328, -4.4015024, -2.48395333, 1.70029418, 0.67569059, 0.53953285, 0.66410649, -5.41578552, -7.76244568, -2.0960134, -3.63437962, -2.36095007, -2.33178212, -1.17244991, 1.75031835, -1.62709136, -1.41441725, -1.20020654, 0.27656047, -3.40467553, -3.37563443, -2.67844719, 2.20993106, 0.20465758, -0.1579309, -2.10452844, -5.69312264, -2.56813434, -4.73686129, -0.07060967, -3.05982617, -0.63602551, -0.02318088, -0.60548109, -1.66823787, 1.61530507, 0.79752815, 0.01442236, -3.22067704, -0.50501239, -1.70439968, -0.8073302, 1.83840337
|
| 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 3
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