PUZZLE #4315: Galton Board Cipher (diff 2)
A 4-letter word in Galton board pin densities with 0 decoys.
DATA
| Difficulty |
2
|
| Char Count |
4
|
| Char Width |
3
|
| Char Height |
5
|
| Char Gap |
1
|
| Chars |
[[0.73, 6.5, 0.72], [0.73, 0.97, 0.63], [0.95, 6.98, 1.05], [0.66, 8.16, 1.43], [0.87, 6.21, 1.25]], [[5.39, 0.81, 7.63], [0.65, 5.5, 0.81], [1.54, 1.86, 1.14], [1.18, 8.8, 1.68], [0.89, 5.01, 0.56]], [[8.26, 1.1, 1.04], [1.51, 8.61, 7.51], [6.26, 0.83, 8.73], [5.4, 7.47, 1.59], [1.98, 0.83, 7.49]], [[7.7, 0.64, 1.91], [1.24, 5.51, 5.75], [6.47, 0.9, 7.09], [8.62, 5.79, 1.81], [1.99, 0.68, 6.98]]
|
| 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 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 2
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