that the boy is more energetic and agile than the old man, you might
think at first that the conflict would end with all of the apples
on the old man's side (Phases I and II).
It is true that with equal
numbers of crabapples on either side, the boy will throw apples
across the fence faster than the old man can return them. But this
only means that apples will become more plentiful on the old man's
side, and easier to reach.
They will become scarcer on the boy's side, and require more running
around to locate. Eventually a standoff, or equilibrium, will be
reached, in which the number of apples crossing the fence is the
same in both directions.
The old man will throw less quickly but will have less trouble finding
apples (Phase III); the boy will throw more rapidly but will waste
time scurrying around hunting for the relatively few crabapples
on his side (Phase IV). The ratio of apples on the two sides of
the fence ultimately will be determined by the relative agility
of the two combatants, but all of the apples will not end
up on one side (Phase V).