Why don't the cornflakes at the bottom of the box get crushed by the weight of the flakes on top? That's the question on this Moment of Science.
Friction And Arrangement
Research by mathematician Bruce Pitman of the State University of New York at Buffalo indicated there are two factors that protect the bottom flakes: their arrangement in the box, and friction.
Some of the flakes bear the weight of several, some lean against neighbors, are wedged in between other flakes, their rough edges catch on adjacent flakes, or they're pressed against the walls of the container.
Piles Vs Puddles
These interactions create friction between flakes, and between flakes and the wall. This friction allows each flake to partially support another. The interlocking of the flakes transfers the weight in several directions, with most of it ultimately ending up at the walls of the box rather than the bottom.
The friction between the flakes is the same force that causes sand to form a pile rather than spread out like a puddle. In fact, this same principle applies to all granular materials. If you cut the corner out of a bag of flour only a small amount will come out. If the bag contained water, which has low friction, all of it would run out.
Why So Much "Dust?"
Incidentally, there are broken flakes and cereal "dust" in boxes, but this is the result of shaking during shipping and handling, not simply the weight of the upper flakes on the lower ones.
The effect of friction is very important in the cereal manufacturing process, which involves huge vats of flakes. Even in those vats the friction-induced weight distribution keeps the bottom flakes from being turned to dust, and allows whole flakes to tumble into our breakfast bowls.