Number of words

Содержание и основные понятия

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Alterna · Chapter 10 · page 10.2
Number of words
Formula A
n
, the work rule, Caesar's cipher, interactive visualizers and the OGE/EGE task bank.
How many different words can you draw from the alphabet? If the alphabet contains
A
the symbols, and the word is long.
n
that the number of words is equal to
A
n
This fundamental rule of combination is the basis of passwords, codes, ciphers and all digital information.
GEF
PIF
OGE No. 1-4
EEG No. 4
01
Rule of work, formula A
n
The basic principle of combinatorics for counting the number of words
Rule of work
If each of them
k
objects can be selected
n
1
,
n
2
, ...,
n
k
The total number of ways to select all k objects is equal to:
N = n
1
× n
2
× ... × n
k
Application to words
The word "n" from the power alphabet A is "n", each of which has any of the A characters.
Позиция 1: A вариантов
Позиция 2: A вариантов
...
Позиция n: A вариантов
Итого: A × A × ... × A = A
n
Rule of work for words
Item 1
A Options
×
Item 2
A Options
×
Item 3
A Options
...
×
Position n
A Options
Total: A × A x A x × ~ A = An
Number of different words of length n from power alphabet A
Basic formula
N = A
n
N
— number of different words
A
- Capability of alphabet (number of symbols)
n
- length of the word (number of symbols in the word)
Examples
Duplicate alphabet
A=2, n=3
N = 2³ =
8
000, 001, 010, 011, 100, 101, 110, 111
Alphabet {A, B, B}
A=3, n=2
N = 3² =
9
AA, AB, AV, BA, BB, BW, VA, VB, VV
Latin alphabet
A=26, n=2
N = 26² =
676
AA, AB, AC, ..., ZZ
Practical applications
Passwords:
4 digit password is 104 = 10,000 options
Number plates:
3 letters + 3 digits = 263 x 103 = 17 576 000
IP addresses:
4 octates at 256 values = 2,564 E 4.3 billion
PIN codes:
4 digits = 104 = 10,000 combinations
02
Visualizer A
n
Interactive calculator with word generation and progress bar
🔢
Visualizer of formula A
n
Ask the alphabet (A) power and the length of the word (n). For small values, all words will be shown, for large, the number and the first 20 examples.
A (alphabet):
2
n (length):
3
Word generation...
0%
03
Caesar's code: the capacity of the alphabet in action
Classic cipher for a setup — a visual application of formula A
n
GEF
OGE No. 1-4
Deepening
How Caesar's cipher works
Caesar's cipher replaces each text symbol with a symbol standing on
k
At the end of the alphabet, there is a "couple."
Открытый текст:
HELLO
Сдвиг (k=3): H→K, E→H, L→O, L→O, O→R
Шифротекст:
KHOOR
The number of possible keys(s) equals the power of the alphabet
A
The bigger the alphabet, the harder it is to crack the code with a cross-section!
🔐
Interactor: Caesar's Code
Alphabet:
Smooth (k):
0
Enter text:
The result of the encryption is:
Key space
04
OGE/EGB task bank
10 questions from the bank of tasks — mixed at each download
📝
Task bank (10 questions)
Do the task. Choose the answer or enter the number.
05
Mini test: number of words
40 cards - 5 randoms per round, a 1.8 s auto transition.
🎯
Quest test: 5 out of 40 cards
0 / 5