Problem 1: Let $S$ be a set with $n$ elements. How many subsets of $S$ are there?
Problem 2: Are there infinitely many prime numbers?
Problem 3: Let $k \le n$. Let $S$ be a set with $n$ elements. How many subsets of $S$ have $k$ elements?
Problem 4: Let $f(1,n) = n$. Let $f(m+1,n) = \sum\limits_{i = 1}^nf(m,i)$. What is $f(m,n)$?
Problem 5: How many graphs are there with 5 vertices up to isomorphism?
Problem 6: How many one-sided polyominos are there with 5 squares?
Problem 7: Let $S$ be a set with $n$ elements. How many permutations of $S$ are there?
Problem 8: Let $S$ be a set with $n$ elements. How many derangements of $S$ are there?
Problem 9: Notice 3, 5, and 7 are prime and of the form $(p,p+2,p+4)$. Are there any other 3 numbers like this?