As a member of the campaign team for a mayoral candidate in Raleigh, your job is to

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Question:

As a member of the campaign team for a mayoral candidate in Raleigh, your job is to gather data on the public perception of your candidate for the purpose of making informed decisions related to the campaign. More specifically, you plan to send out a survey (collecting information on race, religion, gender identity, age bracket, income level, education level, party affiliation, intention to vote for your candidate, etc.) to 20,000 Raleigh citizens in hopes of receiving at least 5,000 responses.

In order to keep the responses anonymous, you plan to assign a 6-character code to each individual who receives a survey. In doing so, survey responses will be tied to codes rather than names, ensuring that the data collected is done akin to a blind study.

(a) Suppose that, for reasons tied to the software your team uses to process incoming data, you only have access to 8 unique digits: 2-9. Are you able to assign a unique code to each individual receiving the survey?

(b) The campaign wants to easily identify survey respondents with their party affiliation or their intention to vote for the candidate. To this end, you decide to restrict the first character in your coding system to the letters D, I, and R, while the last character can only be a Y or anN. The remaining characters must come from the digits 2-9. Is it possible to assign a unique code to each individual receiving the survey? You may assume that these letters are available to you for use in the software.

(c) Suppose now that the software either automatically assigns a 0 or a 1 to the first character or one of the letters X, Y , or Z to the last character. If the campaign no longer cares about easily linking codes to party affiliation or votes for their candidate, can enough codes be generated for the potential survey respondents?

(d) In your research, you come across a different software that permits the use of each letter of the alphabet (not case-sensitive) and all digits 0-9 when generating codes to assign to survey respondents. Design a simple coding system (i.e. with the fewest possible digits) that accommodates all 20,000 survey recipients satisfying the following requirements:

The system has at least one character that indicates education level. The options on the survey include some high school, high school diploma or equivalent, associate's degree, bachelor's degree, or graduate degree.
The system has at least one character that indicates an age bracket. The options on the survey are 18-24, 25-34, 35-44, 45-54, 55-64, and 65+.
Of the remaining characters, at least one must be a number.
Explain your coding system, how you know it has the fewest possible characters, and how it achieves the objectives above.