Suppose you have a set of $k$ bricks, each of varying sizes. we want to fit all these brings one by one on a straight pavement of length $N$. we know the sizes of each brick but we do not know
a) the order in which they are placed, and
b) the positions on the $N$-length pavement in which they will be placed. What is the minimum length of $N$ such that we can play any of the $k$ bricks in any order and in any position?