TITLE: Help me to understand the potato paradox
QUESTION [11 upvotes]: From wiki - Fred brings home $100$ kg of potatoes, which (being purely mathematical potatoes) consist of $99\%$ water. He then leaves them outside overnight so that they consist of $98\%$ water. What is their new weight? The surprising answer is $50$ kg.
When I look at the problem, I assume that $99\%$ water is equal to $99$ kg and the rest is $1$ kg.
When the percentage of the water is now $98\%$ the weight is now $98$ kg and the rest is $2$ kg.
I don't understand how the total weight can be $50$ kg at the end, maybe the water turns into a solid?

REPLY [5 votes]: This is a picture of the potatoes before dehydrating.

About 99% water (not to scale). This is a picture of the potatoes after dehydrating:

About twice the amount of potato. Oh, and I should mention that I zoomed in on the second diagram so that it's the same width as the first. The second bar is actually half as wide as the first one, since it represents 50kg instead of 100kg. In fact, all that changed between the two bars is that the blue bar got cut roughly in half (50kg of water were removed from 99kg of water). Since the bar overall gets cut in half and the amount of potato doesn't change, the potato looks twice as big once you zoom in. In other words, its size relative to the total amount of mass is twice as much, or it constitutes double the percentage that it originally did.