The potato paradox It is a mathematical enigma that puts our ability to interpret the percentages in crisis. The situation is this: there are 100 kg of potatoes composed at 99% of water that are left to dry until they drop the percentage of water to the 98%. How many kilos weigh the potatoes now? This apparently simple question brings behind an anything but banal riddle. We see the surprising solution of this dilemma, because it can be called a paradox, and we see a possible application to an economic context.
What is the paradox of the potato
The situation is this: we have 100 kg of potatoeswhich are composed to 99% of waterand let them dry. After some time the percentage of water is descended to 98% And the potatoes, which contain a little less water than before, weigh a little less than 100 kg, but how exactly they weigh?
This apparently easy dilemma has a surprising solution. If you thought that in the end the Pesino 99 kg potatoes, of which 98 kg of water … you were wrong! But don’t worry, it’s a common, albeit erroneous response.
The key to solving the problem is focus on the dry part instead of the water. At the beginning, when the water constitutes 99% of the potatoes, the dry part corresponds to the remaining 1% of the total 100 kg of potatoes, then it weighs exactly 1 kg: we have 99 kg of water and 1 kg of dry part. During the drying process, potatoes lose only water, so the dry part does not decrease and continues to weigh 1 kg. Once the drying process is finished, if the water constitutes 98% of the potatoes, then the dry part corresponds to the remaining 2% of the total, but continue to weigh 1 kg. So what is the solution?
The solution to the mathematical paradox
At this point we can get to the solution through a proportion. Considered that 1 kg potatoes correspond al 2% total We can write the proportion
2%: 100% = 1 kg: Total kg
that is to say
The percentage part (2%) is to the total percentage (100%) as the part in kg (1 kg) is to the total in kg.
You can write different equivalent proportions, but all will give the calculation as a solution
Total kg = (1 kg × 100%) ÷ 2% = 100 kg ÷ 2 = 50 kg
Therefore, The total weight of the potatoes has halvedas we can also see intuitively from the image below.
Because we call it a paradox and how we can apply it to other situations
Actually This is not a real paradoxbut of a apparently trivial problem that has a surprising solutionvery different from what we would expect at first sight. Problems like this put us about the difficulties and unexpected results in which we can come across when we deal with with proportions and percentagestwo mathematical concepts with which many feel at ease but which sometimes reserve unwelcome surprises.
But how can we apply this paradox to other contexts? We can do it in all those situations in which there are a total composed of parts divided into different percentages and in which, following some event, the percentages of composition of the total change. For example, Suppose we have 1000 € of which 99% in cryptocurrency (like bitcoins), and suppose that following a drop in the value of the cryptocurrency the percentage of bitcoins in my capital drops from 99% to 98%: how much money do we have in the end? By applying the reasoning seen above, we know that a drop from 99% to 98% corresponds to a halving of the total, therefore ours capital will have gone from € 1000 to € 500a difference that is not a little.
