PUZZLE #5206: Galton Board Cipher (diff 4)
A 4-letter word in Galton board pin densities with 3 decoys.
DATA
| Difficulty |
4
|
| Char Count |
4
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Chars |
[[5.37, 0.69, 1.86], [1.85, 6.49, 7.72], [0.69, 5.64, 1.96], [0.75, 8.52, 1.65], [7.37, 1.82, 1.45]], [[1.67, 0.7, 0.67], [2.0, 1.46, 6.35], [1.07, 0.67, 6.82], [0.7, 1.75, 8.26], [0.6, 1.88, 0.85]], [[6.34, 1.66, 8.62], [1.15, 6.85, 0.63], [1.36, 1.5, 1.34], [1.18, 8.96, 0.87], [1.15, 8.23, 1.82]], [[1.24, 1.34, 7.9], [1.1, 6.73, 1.91], [1.97, 1.65, 6.14], [0.94, 5.23, 1.13], [1.3, 8.36, 0.56]]
|
| 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 |
3
|
| 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 15×5 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 4
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