A gumball machine has a random mixture of gumballs of C different colors.
A woman has K children.
What is the minimum number of gumballs she must buy from the machine
to guarantee that she has at least one set of K gumballs all of the same
color? (So she can give the same color gumball to each child.)
The most gumballs she can have without having K of the same color is
(K-1)C, so one more gumball will have to give her K children of the same color,
i.e., (K-1)C + 1.