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?