Math Mania 2023

What is the smallest positive integer that cannot be written as the difference of two (positive) prime numbers?
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.
What is the next most likely term in the following sequence: 1, 1, 5, 13, 41, 121, …?
If a fair six-sided die is tossed four times, what is the probability that exactly two 6’s occur?
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?
If the polynomial x4 + k x3 + 5x2 + k has x−1 as a factor, what must k be?

1. The smallest such integer is 7.
3. The next most likely term is 365.
4. The probability is 25/216.
5. The ball's velocity is 160 m/s.
6. We must have k = −3.