Potato paradox

Potato Paradox is a mathematical puzzle that involves the counterintuitive aspects of percentages and mass in relation to the water content of potatoes. Despite its name, the Potato Paradox is not a true paradox but rather a mathematical problem that leads to surprising and unexpected results. The problem typically presents a scenario in which the water content of a potato or a batch of potatoes changes, leading to seemingly paradoxical outcomes regarding the total weight or mass of the potatoes.

Problem Statement

The classic form of the Potato Paradox is stated as follows: "A farmer has 100 kg of potatoes, which are 99% water by weight. He leaves them outside overnight, and they dehydrate until they are 98% water. What is the new total weight of the potatoes?"

Solution

The solution to the Potato Paradox involves basic principles of percentage and mass conservation. Initially, the water content is 99% of 100 kg, which is 99 kg of water and 1 kg of dry matter. When the water content changes to 98%, the 1 kg of dry matter now represents 2% of the total weight (since 100% - 98% = 2%). To find the new total weight (W) of the potatoes, we can set up the equation: 1 kg / W = 2% or 1 kg = 0.02W. Solving for W gives us 50 kg. Thus, the new total weight of the potatoes is 50 kg, which is counterintuitively half of the original weight, despite a seemingly small change in the percentage of water content.

Mathematical Explanation

The paradox arises from a misunderstanding of how percentages work. A small percentage change in the water content leads to a significant change in the total weight because the base of the percentage (the total weight) is also changing. This problem is a good illustration of the importance of understanding the relationship between parts and wholes in percentages, and it highlights how intuitive assumptions can lead to incorrect conclusions in mathematics.

Applications and Educational Use

The Potato Paradox is often used in educational settings to teach concepts related to percentages, ratios, and proportional reasoning. It serves as an engaging example to challenge students' preconceived notions and to encourage deeper understanding of mathematical principles. Additionally, it can be used to introduce topics in logic and critical thinking, as it requires the solver to carefully consider the information given and to apply mathematical reasoning to arrive at the correct conclusion.

See Also

• Mathematical puzzle
• Paradox
• Percentage
• Water content