The two messages contain the same number of characters. The amount of information in the first text is 1.5 times more

| November 19, 2020 | education

The two messages contain the same number of characters. The amount of information in the first text is 1.5 times more than in the second. How many characters do the alphabets used to write messages contain, if it is known that the number of characters in each alphabet does not exceed 10 and each character has an integer number of bits?

If the number of characters in each alphabet does not exceed 10 (that is, from 1 to 9), then this number of characters can be encoded using no more than 3 bits (2 ^ 3 = 8 characters). A 4 character code can already encode 16 characters.
There are 3 options for encoding:
1 bit: 2 characters in the alphabet;
2 bits: 4 characters in the alphabet;
3 bits: 8 characters in the alphabet.
In order for the first text to contain information 1.5 times larger than the second, it is necessary that in the first text each character is encoded with 3 bits, and in the second – with 2 bits.
Proof: Let x be the number of characters in the text. Then the first message contains 3x information, and the second – 2x. 3x / 2x = 1.5.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.