PUZZLE #4623: Magnetic Flux Puzzle (diff 4)
A 7-letter word hidden as magnetic poles on a 5×27 grid. Strengths range 1–2. Invert the field to recover the poles.
DATA
| Difficulty |
4
|
| Char Count |
7
|
| Grid Width |
27
|
| Grid Height |
5
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Strengths |
1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.0, 1.0, 2.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 2.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 2.0, 1.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 2.0, 2.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 2.0, 2.0, 2.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 1.0, 2.0, 2.0, 1.0, 1.0, 2.0, 2.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 1.0, 2.0, 1.0, 2.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 1.0, 2.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 1.0, 2.0, 2.0, 2.0, 1.0, 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, 1.0, 2.0
|
| Flux Readings |
1.8571755, -0.19286726, -2.57432765, -2.16375931, 0.35896583, -5.3944051, 0.03279882, 0.05467998, -1.07511763, -1.52121487, 0.07460774, -3.37592568, -0.7587178, -4.77246419, -1.74296057, -0.79461581, -2.93783972, -2.69894972, -0.56691724, -3.85783857, 0.32295714, -5.27522258, 0.41757428, -1.81019218, -4.53225176, 1.86141517, -2.80915289, 0.31414966, 3.10315405, -3.43407969, -2.92100518, -3.33988944, 3.10377017, -3.36930369, -0.24323312, -0.5759149, 3.60206113, -4.81426276, -2.60882273, -4.46099939, 2.65534017, -3.7101594, -1.20543687, -3.26840288, 0.90132178, -4.70420081, -0.9330607, -2.36977891, 4.27149435, -3.01977345, -3.5012077, -0.12346152, -4.39667712, 0.24832632, 2.33602091, -4.57566235, -3.65890133, -3.74046717, -1.6920877, 0.43545671, 0.60805351, 0.99025833, 0.19699391, -2.68208538, -1.42934762, -1.82792589, -1.5825443, -1.5122517, -1.38441208, -0.28170668, -3.89625323, -1.5769046, -2.69853978, 1.37099417, 1.16468669, 1.30917961, -0.38231418, -1.57324373, -4.14447059, -4.42963872, -1.15811766, -0.16464274, -2.16166792, -5.80381443, -2.97824986, -0.84503736, 3.87961751, -0.46680328, 3.63716134, -1.86275253, 2.25340163, -3.92847455, -0.2256039, -2.31941797, 3.10926903, -2.9891485, -0.13443589, -3.68744426, 1.0717603, -3.72748833, 0.84169433, 0.67124627, 5.49956857, -0.89359565, -3.1212127, -3.44438085, -4.20539596, -3.09211136, -1.89484945, -1.6383944, -5.50589172, -2.23251606, -2.48640748, 3.27197734, -0.6286621, 2.83676686, -1.92039218, 2.42592779, -3.33891373, 1.22024484, -3.35304835, 1.41250911, -3.15014164, 0.33578085, -2.18445785, -2.45171993, -0.86792666, 0.99383218, -1.61444529, 2.77861134, -1.19919497, -2.40676842, -2.58533513, -5.08930028, -0.93796644
|
| 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 4
— website sponsored —
[ ad space ]