February 26, 2024

Janessa Angela Alerre

10th Grade

George Washington High School

Introduction

The Potato Paradox, a brain teaser with the use of potatoes, is a mathematical calculation with counterintuitive results. To break it down, a paradox is a statement or situation that seems contradictory, though it expresses truth. The potatoes come into play as there is a contradiction of potatoes weighing more than it’s been cooked.  

The Universal Book of Mathematics describes the problem as, “Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water (being purely mathematical water). He then leaves them outside overnight so that they consist of 98% water.” Thus, the question that arises is, “What is their new weight?” 

Method One

Surprisingly, the potatoes' new weight was 50 kilograms. Though, how is this possible? There are two solutions to this problem. First, Since the potatoes are 99% water, they contain 0.99 (100) = 99 pounds of water. Thus, the dry mass would be the remaining 1%. If the water is somehow decreased to 98%, then the 1 pound of solid makes up 2% of the whole new weight. 1 is 2% of 50, thus resulting in the new weight being 50 kilograms.

Method Two

To delve deeper into this problem, we can use the variable x to represent the weight of the water lost. Thus, the potatoes would weigh 100 - X pounds. In the beginning, there are 99 pounds of water in the potatoes. This can be shown as 0.99(100) = 99 pounds of water. After Fred leaves the potatoes outside overnight, the potatoes consist of 98% water. This can be represented as 0.98(100 - x) = 98 - 0.98x. The difference would be the amount of water that was lost -- using x as our variable. 

The equation can be solved below:

Based on our results, the potatoes have lost 50 pounds of water.

To understand the Potato Paradox, it’s crucial to understand that when potatoes lose water, their solid mass stays constant whereas their water amount decreases. It’s based on the idea that the decrease in water of 98% is correlated to the calculation of the final weight, rather than the initial weight. The potatoes are dehydrated until only 2% of them remain as dry mass. So, this solid element makes up 2% of the reduced overall weight of the potatoes.