The Melon Paradox

Abstract

This is a curious problem that comes up regularly in math competitions. You will see it in one form or another in published collections of problems from these competitions. It’s not that the math itself is difficult. The difficulty lies in believing the results. As an example, let’s start with a melon weighing 50 ounces. Only 1% of the mass of the melon is made up of solid matter, while the remaining 99% is water. The melon is left in the sun and dehydrates to such an extent that it now only contains 98% water. The question is: how much does the melon weigh now? The answer is easy, provided you do your sums properly. But let’s start by guessing the weight. Will it be about 49 ounces? Or even 49 and a half ounces? Or just 45 ounces?