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.

A steel toy submarine floats because its hollow interior is filled with air, causing its overall density to be less than that of water. As a result, the buoyant forces pushing up on the toy sub are greater than the weight pulling it down (gravity). Objects that float are positively buoyant. In its present state, the toy sub -- the subject of this brainteaser -- is less dense than water. Thus, the weight of the sub is less than the weight of the water that is displaced when the sub is submerged in the water. If the empty space inside the sub were filled with a pound of sand, the force pulling down on the toy sub would be exactly the same as the force pushing up on it. Since objects in a suspended state have neutral buoyancy and will remain suspended at the same depth until another force acts on them, the toy sub would be suspended in the water, neither sinking to the bottom nor rising to the top. When a bit more than a pound of sand is added to the sub, however, the downward force -- a weight now greater than two pounds -- exceeds the upward force, and the boat sinks. Objects that sink are negatively buoyant.