## Minimum 1-D finite pavement to fit in varying-length K bricks

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?