1. What is the smallest positive integer that cannot be written as the difference of two (positive) prime numbers?
2. A 4×4 sudoku is an array such that the digits 1,2,3,4 appear exactly once in each row, in each column, and in each of the outlined squares. An example of a completed 4×4 sudoku is shown on the left. Complete the partial 4×4 sudoku shown at the right.
3. What is the next most likely term in the following sequence: 1, 1, 5, 13, 41, 121, …?
4. If a fair six-sided die is tossed four times, what is the probability that exactly two 6’s occur?
5. On the planet Tralfamadore, a ball is tossed upward. It’s height after t seconds is given by h(t) = −8t² + 320t meters. What is the ball’s velocity when it first reaches a height of 2400 meters?
6. If the polynomial x⁴ + k x³ + 5x² + k has x−1 as a factor, what must k be?

Here are the answers.