Let me first review the file you've uploaded and identify the discrete math problems. PyPDF2 import PdfReader

Load and read the uploaded PDF file

pdf_path = '/mnt/data/1739135510952nio2tun6.pdf' pdf_reader = PdfReader(pdf_path)

Extract text from all pages

pdf_text = '' for page in pdf_reader.pages: pdf_text += page.extract_text()

pdf_text[:1500] # Display the first 1500 characters of the extracted text to understand its contentsThe document contains several problems related to discrete mathematics. Here's a breakdown of the problems you've provided:

Problem 1:

Find a non-increasing subsequence of maximum length in the sequence:
4, 1, 16, 5, 2, 7, 2, 23, 10, 2, 15, 21, 3, 21, 17, 23

Problem 2:

Consider the business numbers on Stone Road, which have 4 digits and range from 2000 to 9999. How many of these house numbers:

1. (a) Have exactly 2 digits that are 7?
2. (b) Do not contain the same digit multiple times?
3. (c) Begin with an odd digit?

Problem 3:

DNA sequences are encoded with four symbols: A, C, G, T. Answer the following:

1. (a) How many DNA sequences of length 15 do not contain A?
2. (b) How many DNA sequences of length 15 contain AACCGGT as a substring?
3. (c) How many DNA sequences of length 15 contain exactly 3 of the 4 symbols?

Problem 4:

Prove that if a social platform (RedNote) has more than 300 million users, there must be at least two users who have the same number of friends.

Problem 5:

How many length-8 passwords made up of uppercase letters (A-Z) and digits (0-9) contain:

1. (a) The letter Q?
2. (b) The letter Q and the number 7?
3. (c) The letters Q and Z with Q appearing before Z?

---

I will now proceed to solve these problems one by one. Would you like me to start with the first problem or any other specific one?