Question

In your research, you come across a different software that permits the use of letters Y-Z (case - sensitive) and digits 2-5 when generating codes to assign to survey respondents.

Design a simple coding system (i. e. with the fewest possible characters) that accommodates all 3, 000 survey recipients satisfying the following requirements:
• The system has one character that indicates income level. The options on the survey include yearly salaries of $0 - $11,000, $11, 001-$44, 725, $44, 726-$95, 375, $95, 376-$182, 100, $182, 101-$ 231,250, $231,251 - $578, 125, and $578, 126 or more.
• The system has one character that indicates whether or not the recipient intends to vote for the candidate (yes, no, or undecided).
• Of the remaining characters, at least one must be a letter.
• The system will generate unique codes for all 3, 000 survey recipients.

Explain your coding system, how you know it has the fewest possible characters, and how it achieves the objectives above.

Answer 1

A two-character code system can be created for 3,000 survey recipients; one character for income bracket with 7 possibilities (A, 2-5, Y, Z) and one for voting intention (y, N, U), resulting in a total combination of 378 unique codes, which satisfies the requirement.

Step-by-step explanation:

To design a simple coding system that accommodates all 3,000 survey recipients with the criteria specified, we can create a system using a two-character code.

The first character indicates the income level with 7 different options. We can use digits 2-5 and letters Y and Z (6 possibilities), and choose one additional letter from A to X, let's say A to signify the income level, fulfilling the requirement of at least one letter and indicating the income bracket. Therefore, we have A, 2, 3, 4, 5, Y, Z depicting the income levels.

The second character indicates the intention to vote, where Y stands for yes, N stands for no, and U stands for undecided. Since the alphabet from Y to Z is case-sensitive, we can use lowercase 'y' to denote 'yes' and uppercase 'Y' to differentiate the income level.

Thus, we use a combination of an income level character (A, 2, 3, 4, 5, Y, Z) and a voting intention character (y, N, U) to produce a unique code. This provides us with 6*3=18 unique codes for the voting intention and 21*6*3=378 unique codes for the income levels. Since we only need 3000 codes, and we have 378 unique codes available, a two-character code suffices, making it the system with the fewest possible characters.