Three points, $P_1$, $P_2$ and $P_3$, are randomly selected within a unit square. Consider the three rectangles with sides parallel to the sides of the unit square...
A positive integer $n$ is considered cube-full, if for every prime $p$ that divides $n$, so does $p^3$. Note that $1$ is considered cube-full. Let $s(n)$ be...
We stack $n$ plates into $k$ non-empty piles where each pile is a different size. Define $f(n,k)$ to be the maximum number of plates possible in the...
A standard deck of $52$ playing cards, which consists of thirteen ranks (Ace, Two, …, Ten, King, Queen and Jack) each in four suits (Clubs, Diamonds, Hearts...