  We generalize the well-known broken stick problem in several ways, including
a discrete "brick" analogue and a sequential "pick-up sticks/bricks" version.
The limit behavior of the broken brick problem gives a combinatorial proof of
the broken stick problem. The pick-up version gives a variation on those
scenarios, and we conclude by showing a greater context---namely, that the
broken stick/brick problem and the pick-up sticks/bricks problem are two
extremes in a family of interesting, and largely open, questions.
