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Cryptology - Unofficial St. Mary's College of California Web Site

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10.6. LETTER CONNECTIONS 197<br />

F 2 G 2 I 2 Y 2 P 3 D 4 C 5 L 5 W 5 M 6 N 6 S 7 T 7 R 8 H 10 E 12 A N 19 T 14 L 10 R 10 S 10 C 5 D 4 I 3 M 3 B 2 G 2 P 2 V 2 Y 2<br />

L 3 I 4 N 4 R 4 U 4 Y 4 M 5 T 5 S 7 O 9 D 10 A 13 E 13 B E 30 L 12 O 11 U 11 A 8 Y 7 I 5 R 5 S 2<br />

D 2 Y 2 T 3 R 4 U 4 O 5 S 7 N 11 A 13 I 16 E 19 C O 19 E 15 H 14 A 13 T 9 I 6 K 4 L 3 R 3 U 3<br />

D 2 O 4 R 4 L 6 I 7 A 9 N 27 E 28 D E 15 I 13 T 10 A 9 O 7 S 6 B 4 H 3 R 3 U 3 W 3 C 2 D 2 F 2 L 2 M 2<br />

G 2 I 2 P 2 W 2 B 3 C 3 E 3 D 5 L 5 M 5 N 5 S 5 V 5 T 7 R 11 H 20 E R 14 S 10 D 9 N 9 A 7 T 6 C 4 L 4 E 3 I 3 M 3 W 3 F 2 O 2 P 2<br />

Y 2 L 3 R 3 T 3 D 4 N 4 A 5 F 5 S 5 I 6 E 13 O 36 F O 17 T 15 I 11 A 9 E 8 R 7 F 5 L 3 U 3 C 2 H 2 S 2<br />

D 2 S 2 O 4 R 4 U 6 A 9 E 9 I 11 N 42 G E 15 H 12 A 10 I 8 O 8 R 8 T 7 S 4 L 3 U 3 N 2<br />

D 2 N 2 E 4 G 4 W 6 S 7 C 8 T 54 H E 48 A 16 I 13 O 8 T 4<br />

C 2 G 2 V 2 A 3 F 3 M 3 W 4 E 5 N 5 D 7 L 7 R 8 S 8 H 9 T 15 I N 25 S 12 T 12 C 7 O 7 L 5 D 3 E 3 M 3 R 3 A 2 F 2 G 2 V 2<br />

G 2 Y 4 O 5 R 5 T 5 A 6 S 6 B 7 D 8 N 10 E 14 F 15 J U 28 O 25 E 19 A 13 I 3 T 2<br />

L 4 E 7 I 7 S 7 N 8 O 11 R 12 A 14 C 20 K E 34 I 15 N 7 S 7 A 6 O 4 T 4 H 2 L 2 W 2<br />

C 2 N 2 R 2 S 2 T 3 B 4 P 4 U 6 O 7 I 8 L 12 E 13 A 19 L E 16 I 12 L 12 A 11 Y 9 O 8 D 6 S 3 T 3 U 2<br />

Y 2 D 3 M 3 N 3 T 3 U 4 S 5 R 6 A 10 I 10 E 18 O 18 M E 25 A 19 I 11 O 11 P 6 U 4 B 3 M 3 S 3 T 3<br />

R 2 U 4 E 17 O 18 A 22 I 26 N T 17 D 15 G 11 E 9 O 7 A 6 S 6 C 5 I 5<br />

B 2 G 2 W 2 D 3 M 3 O 3 P 3 Y 3 E 4 L 4 F 5 H 5 N 6 C 7 I 7 S 7 R 8 T 13 O N 17 R 13 F 11 U 10 M 6 T 6 L 4 W 4 O 3 S 3 C 2 D 2 P 2 V 2<br />

L 2 X 2 Y 2 D 3 I 3 N 3 T 3 R 4 P 5 U 5 M 8 A 9 O 10 S 11 E 17 P E 18 R 16 O 13 A 12 L 10 I 5 P 5 T 4 H 3 U 3 S 2<br />

O 2 R 2 C 3 T 3 A 4 D 4 N 5 I 8 S 12 E 43 Q U 98<br />

D 2 G 2 F 3 I 4 P 5 T 5 U 6 A 14 O 16 E 28 R E 23 A 10 O 10 I 9 S 7 T 7 D 3 Y 3 C 2 M 2 N 2<br />

L 2 Y 2 D 3 O 4 T 5 U 5 R 6 N 7 S 7 A 12 I 13 E 20 S T 18 E 11 A 9 I 9 O 8 S 7 H 6 C 3 P 3 U 3 W 3 M 2<br />

H 2 Y 2 C 3 F 3 U 3 D 4 O 5 R 5 T 5 E 8 I 9 A 12 N 13 S 13 T H 32 I 11 O 11 E 10 A 6 T 5 S 4 R 3 U 2 W 2<br />

G 2 H 2 N 2 P 2 A 3 C 3 E 3 F 3 L 3 M 3 Q 3 D 4 R 4 B 6 T 7 S 9 O 28 U R 14 S 13 T 13 N 12 L 10 C 5 G 4 P 4 A 3 E 3 I 3 M 3 B 2 D 2<br />

D 2 L 2 N 4 R 5 O 15 A 17 I 20 E 24 V E 65 I 19 A 9 O 5<br />

L 2 A 4 R 4 Y 4 N 5 D 6 T 10 S 11 O 17 E 20 W A 22 H 17 I 17 E 16 O 11 N 4<br />

O 5 I 7 A 8 E 74 X P 26 T 17 I 12 A 11 C 10 E 7 O 2<br />

H 2 M 2 O 2 D 3 S 3 N 6 B 7 E 9 T 10 R 11 A 12 L 21 Y O 13 T 11 A 10 S 9 E 7 I 6 W 5 B 4 C 3 F 3 H 3 M 3 P 3 D 2 L 2 R 2<br />

N 2 U 2 T 3 O 4 E 5 Z 7 A 14 I 51 Z E 44 A 18 I 11 Z 7 O 5 L 2 Y 2<br />

Figure 10.2: Appearances before and after the given letter, in %.<br />

To use the charts correctly, we need to carefully note the meanings <strong>of</strong> three<br />

different possible numbers:<br />

1. If we ask “I have V. How <strong>of</strong>ten is V followed by E”, look for E in the V<br />

row <strong>of</strong> Figure 10.2. The answer is 65% <strong>of</strong> the time. V is (almost) always<br />

followed by a vowel, and E is the mostly likely one.<br />

2. If we ask “How <strong>of</strong>ten is E preceded by V” the answer is much smaller, only<br />

5%, as seen also in Figure 10.2. Why smaller That is the “conditional”<br />

part <strong>of</strong> the probability. Looking at a V one feels that a vowel is probably<br />

next. Looking at an E we are somewhat surprised if the preceding letter<br />

is V.<br />

3. If we ask “Here are two letters. Are the VE” we find 64 in Figure 10.3,<br />

meaning .64% = 0.0064 <strong>of</strong> all letter pairs are VE’s. So this pair is quite<br />

uncommon, as matches our intuition.

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