PUZZLE #5284: Galton Board Cipher (diff 1)
A 7-letter word in Galton board pin densities with 0 decoys.
DATA
| Difficulty |
1
|
| Char Count |
7
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Chars |
[[7.26, 1.22, 0.66], [1.86, 5.26, 8.84], [0.5, 8.75, 8.77], [1.97, 5.56, 6.56], [7.37, 0.94, 1.11]], [[8.05, 1.06, 5.39], [1.03, 7.4, 0.59], [1.71, 5.97, 1.15], [1.73, 5.9, 0.86], [7.71, 1.72, 6.29]], [[1.97, 7.48, 7.42], [1.61, 6.46, 8.87], [1.15, 7.96, 5.0], [1.83, 7.45, 7.77], [1.7, 0.91, 0.81]], [[0.62, 5.91, 6.21], [1.82, 7.12, 7.29], [1.11, 7.24, 7.78], [0.57, 6.52, 5.66], [1.75, 0.88, 1.9]], [[1.87, 1.31, 1.16], [7.14, 1.73, 5.84], [7.52, 1.35, 8.47], [5.66, 0.6, 5.3], [1.07, 0.7, 1.1]], [[0.93, 0.88, 7.04], [1.7, 7.61, 1.47], [1.49, 5.72, 1.54], [1.93, 5.93, 0.75], [1.96, 1.94, 5.87]], [[1.19, 0.82, 1.41], [0.91, 6.09, 5.21], [1.76, 0.74, 6.35], [0.71, 9.0, 6.89], [1.85, 1.81, 0.85]]
|
| 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",
"101"
],
"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"
]
}
|
| Decoy Count |
0
|
| Instructions |
1. Each character is a 3x5 grid of Galton-board pin densities.
2. Low pin density (<3.5) = balls pass through = pixel ON.
3. High pin density (>3.5) = balls blocked = pixel OFF.
4. DECOYS: some empty cells also have low density.
5. Run 2-means clustering (k=2) on all values to find LOW cluster.
6. Set threshold at (low_mean + high_mean)/2.
7. For each character, try ALL font patterns, pick the closest match.
|
| Hint |
2-means cluster 27×5 pin densities. Low cluster ≈ ON, high cluster ≈ OFF. Match each 3×5 bitmap to the 26-letter font.
|
| Answer Format |
comma-separated bin counts
|
author's note: Pool fill: galton diff 1
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