The Greek mathematician Archimedes first noted that any object immersed or partly immersed in a fluid (i.e., a liquid or a gas) is buoyed upward by a force equal to the weight of the fluid displaced by the object. The crucial factor in determining an object's buoyancy is its density, the relationship between its weight, which is pulling it down, and its volume. If an object placed in water weighs more than an equal volume of water -- in other words, if the density of the object is greater than the density of water -- then the downward force of gravity will be greater than the upward buoyant force, and the object will sink. On the other hand, if the object weighs less than the fluid it would displace if submerged, it will sink only to the point where it displaces the amount of fluid equal to its weight. At that point, the upward force of the fluid equals the downward force of gravity, and the object floats.

In this featured brainteaser, when the 10-pound rock is in the boat, it is floating, so, in addition to what the boat would displace without the rock, it also displaces the amount of water with a weight equal to the rock. When the stone is hurled in the air -- so that it is out of the boat but not yet in the water -- the boat is relieved of the rock's weight and displaces less water. Consequently, the water level in the pool drops. When the rock enters the water, it displaces a volume of water equal to its size. Because the same volume of water weighs less (perhaps only 3 pounds) than the same volume of rock (10 pounds), the denser rock sinks to the bottom. The water level rises again, but not as high as it was when the rock was in the boat because it is now displacing less water. The net effect of throwing the rock in the pool, then, is a lowering of the water level.