A town's rubbish tip took twenty years to fill one half of its pit. At the rate at which the town tips today, the remaining half will be filled in four years. Which of the following must be true?

Half the pit spread over twenty years is a fortieth of the pit in an average year; the same half spread over four is an eighth of the pit a year, which is five times as much. So today's tipping must exceed the average of the first twenty years, and that is all the figures compel. Population is one of many things that could lie behind the change and need not have moved fivefold; the town may have tipped a little every year, so no idle year is required; and an unvarying yearly amount over the first twenty is possible but nowhere forced.