# It's just a little weight

It's been a while since I've posed a riddle; so I'm back with a simple one! I hope you all enjoy, and as always, good luck!

Sally went to the farmer's market, with her daily $$100\,\text{lbs}$$ of potatoes. After sitting in the sun all day and no one showing interest, she decided to pack up and go home. But, she noticed something rather odd...

Sally only had $$50\,\text{lbs}$$ of potatoes left. But how? No one even glanced at her stand.

What happened? Make sure you explain the drastic difference.

This is sort–of a "footnote" to mocarsha2019's answer, but I've decided to post my own answer instead.

As mocarsha noted, the potatoes probably dried out and lost some of their weight in water.

This question reminded me of this video by Vsauce2. The question they pose sounds awfully similar to the situation encountered here... but posed the other way.

Imagine you have a sack of potatoes which is $$99$$% water and $$1$$% "potato". Overnight (or during the day, in this case), the potatoes dry out a bit and now they're $$98$$% water and $$2$$% potato. How much weight have the potatoes lost?

The counterintuitive solution is that the potatoes have lost half of their weight (kinda like the scenario described above!

To show this, we can imagine that we have $$100$$ potatoes, of which $$99$$ are water and $$1$$ is actually "potato". That'll yield a $$99$$% concentration of water and a $$1$$% concentration of potato. To reach the desired configuration of $$98$$% water and $$2$$% potato, $$50$$ of "water" the must evaporate. That sounds counterintuitive, but it makes sense: after $$50$$ "water" evaporate, we'll have $$49$$ "water" and $$1$$ "potato" bit. That's a total of $$50$$ bits (so half the weight as before), which are $$98$$% water and $$2$$% potato.

This explains the drastic weight loss — $$1$$% of the water evaporating is equal to a $$50$$% weight loss! (which is technically an incorrect conclusion to draw, but it's more to increase the "paradoxiness" of the puzzle)

• So after watching the video, you’re right! It does sound oddly familiar haha I was actually reading this and decided to pose the question here. Commented Feb 9, 2019 at 22:20
• @PerpetualJ Pretty much the same thing, I'd say. The "Potato Paradox" is such an interesting concept! Commented Feb 10, 2019 at 0:26
• It is indeed! I stumbled across it while researching a topic for a paper. Commented Feb 10, 2019 at 0:29
• This absolutely does not make sense, if you include water into the 100 lbs, 50 lbs of water MUST evaporate (which is unlikely). If you do not include water, you start with 100 lbs of potato end up with 100 lbs potato and lose nothing (the water was never included anyway) Commented Feb 10, 2019 at 18:50
• Well, it reads just like how the potato paradox is usually formulated but misses its most important points. And the it turns out the real formulation is the answer to this puzzle. Oh well... Commented Feb 10, 2019 at 21:24

The potatoes were boiled and got dried in the sun, losing weight.

The market is on a space ship. She flew up from a planet on which the potatoes weighed 100lbs. On the space ship there is a rotating whatzit that creates an artificial gravity equal to half that of the planet's surface. It's a dystopian world. They are still using pounds: had she been using the galactic standard units (GI) she'd be measuring in kg and her potatoes would be fine. Also no-one would have been able to take advantage of her. She got lucky this time not having any sales. "This would never happen in Europe. Or Japan. Or Australia. Or Kenya. Or really anywhere else in the free thinking world. Or even most of the various dictatorships." What kind of craziness have we gotten (using the archaic form) ourselves into? Her scientific literacy was not great, thanks to the recent tax cuts for the wealthy which had necessitated a cut in school funding. But the trillionaires will be fine which consoled her for some reason. One educational theme that still featured strongly was that this coddling of trillionaires was important for some reason. But never fear: when she gets back home her potatoes will be 100 pounds again. It's a sad day, though, when all her efforts getting to market on a rocket don't yield a single sale...

Here is an alternative solution

Sally only has half her potatoes left because

the other half is on her right.

This happened because water evaporated from the potatoes.

Let $$x$$ represent the raw potatoes' weight.

Then, the water initially present is $$100-x$$.

Now, we assume that some water evaporated and that the remaining water is $$50-x$$.
Let $$a$$ represent the percentage of water evaporated.
$$50-x=(100-a)/100×(100-x)$$

On solving,
$$x=(1-50/a)×100$$
This shows that more than 50% water must be evaporated.

The question would be more interesting as If the water percentage in 100 lbs potatoes is dehydrated from 99% to 98% , what is its final weight? And the answer would be 50 lbs.

• If the question was "If the water percentage in 100 lbs potatoes is dehydrated from 99% to 98%, what is its final weight?", it would probably get moved to Math.SE. I assume that PerpetualJ's intended "puzzle" was more determining the "how" aspect. Commented Feb 10, 2019 at 6:29
• Okay I am new in stack exchange so still a beginner. I shall take care from next time Commented Feb 10, 2019 at 7:23
• no problem, don't worry about it! Commented Feb 10, 2019 at 19:42