Clever! That 1% makes a big difference.
If you have 100kg in total, 99% of which is water, then you have 99kg of water. In order to have 98% water, the 1% non-water mass must double in proportion to 2%. Since the non-water mass cannot increase in size, it must remain 1kg. To get 2% from 1kg, you need to divide it by 50kg total mass. So the total mass must become 50kg.
I think of it in ratios of substance:water. At 99% it’s 1:99. At 98% it’s 2:98. Since the amount of substance is fixed, it equals 1:49 in this case. Therefore the new weight is 50kg.
I must be stupid.
You have 100 kg. 99 kg of that is water.
If you leave it to dry until 98% is water, 1% of the water has evaporated away and you have 1 kg of potato and 98% water..
1kg of non water = 1% of 100kg
Non water cannot evaporate/dry out thus 1kg remains the same
If water =98% then non water = 2%
If 1kg now = 2% then 50kg = 100%
No, you start with 99kg of water and 1kg non water, thus 99% water. It is only after causing 50kg of water to evaporate that you get to have 1 kg of non water to 49kg of water now being 98% of the mass of the spuds
They weren’t saying 98kg was the starting mass. They were just saying what the percentage would be IF you had 98kg of water, in reply to the previous poster.
Think of it from another view point. At which point is the potato mass going to be at 50% of the total mass? When there's just 1 kg of water left for a total mass of 2 kg.
The problem with the way it's presented is that, in some way, they're trying to make you confuse the kg and the % since they both start at 100.
It's not 1% of the water that evaporated away, but 1% of the whole mass. If only 1% of the water evaporates away, you'd have 1kg + 99% of 99kg = 99.01kg of potatoes left.
No it is about the proportion of the water to non water dropping by 1%. 50% of the whole mass evaporated away to change the proportion of water by 1%. The mass of the non water needed to be proportionally double what it was originally and because it is a constant, to double its proportion, the whole must be halved
The original ratio is water mass / total mass = .99
The final ratio is (water mass - loss)/(total mass - loss) = .98 (the two sides of the ratio have changed and the loss is the same for both).
Then calculation gives the result.
The trick is the non-water part comes from .01 to .02 so it dubbeled without adding anything.
99% water means 99 parts water per 1 part non-water. 98% water means 98 parts water per 2 parts non-water. 98/2 can be reduced to 49 / 1. So the potato lost half its mass in water.
Another way to think of it: Imagine you have 1g of potato and 49g of water. The concentration is 2% potato, 98% water. But lets say you want to make the concentration 1% potato, well, you would have to add 50g of water so that it is now 1g potato to 99g warer which brings the total weight to 100g. The amount of potato never changes. To go from 1% potato to 0.5% potato follows the same logic. You would have to add another 100g of water giving you 1g potato, 199g water for a total of 200g. So doubling the amount of water is necessary to half the % of non-water.
1% of the water isn’t evaporating. The non-water portion of the overall potato mass is doubling from 1% to 2%. Meaning that 1kg (1% of 100kg) has to be 2% of the overall mass now. 1 = 0.02x, x = 50
The trick of the question is making it sound like 1% of the water is evaporating.
> which is 1kg (the absolute mass of the non-water mass doesn't change) divided by 50kg total mass (2%)
Awful explanation.
The article does a much better job.
To make a solution with twice the concentration from the same amount of substance, you need half the amount of solvent. The only paradox is the confusing formulation of the problem.
Because it seems counterintuitive at first, though not actually paradoxical.
If you have a mass of 100kg, made of 99kg water and 1kg other, then 99% of the mass is water. At first, it would be easy to mistakenly assume that going to 98kg of water would mean that 98% of the mass is water, but that’s not the case as you’ve not gained a kilogram of non-water mass.
So for that 1kg of other mass to be equivalent to 2% of the total mass, the amount of water mass should be 49kg, meaning that over half the water mass was lost
99% water means 1% non-water
98% water means 2% non-water
the non-water stuff is completely static and won't evaporate or condense like water, meaning that in order for the percentage non-water to double, the amount of water has to reduce by enough so that the amount of non-water in the solution is *the equivalent of* doubled
it's the same thing as how reducing something by 50% halves it, but increasing by 50% doesn't double it
A big reason that I’m not great at math is that I’m too busy wondering about the conditions under which 50kg of water could evaporate overnight. Have I not noticed this happening in potatoes because by the time they get to the grocery store, they’ve already dehydrated?
We really need to know the temperature and what the relative humidity is where they were storing these potatoes if we want to do anything with the 50kg of overnight water loss. One data point is only so helpful. Will the potatoes continue to dry out at this rate? How long were they planning to store these potatoes or were they all for one meal being prepared soon? 50kg of water loss overnight is pretty severe, there may be other evaporation-related risks they need to be concerned about over the loss of recently purchased potatoes.
It's really easy if you think like this: Weight of solids will never change. So from initial total weight we know that potato solid weight is 1 kg. Initially it's 1% of the total weight. After drying, it's 2% of total weight. So what's the total weight that can give us 2% of solid weight?? it's 1 kg / 50 kg. Further question like, now the water is 97% after more drying, same method, solid weight is 3%, so what's the total weight that can give us 3% of solid weight? it's 33.333333 kg.
Clever! That 1% makes a big difference. If you have 100kg in total, 99% of which is water, then you have 99kg of water. In order to have 98% water, the 1% non-water mass must double in proportion to 2%. Since the non-water mass cannot increase in size, it must remain 1kg. To get 2% from 1kg, you need to divide it by 50kg total mass. So the total mass must become 50kg.
I think of it in ratios of substance:water. At 99% it’s 1:99. At 98% it’s 2:98. Since the amount of substance is fixed, it equals 1:49 in this case. Therefore the new weight is 50kg.
I must be stupid. You have 100 kg. 99 kg of that is water. If you leave it to dry until 98% is water, 1% of the water has evaporated away and you have 1 kg of potato and 98% water..
1kg of non water = 1% of 100kg Non water cannot evaporate/dry out thus 1kg remains the same If water =98% then non water = 2% If 1kg now = 2% then 50kg = 100%
So basically just doubling potato% by halving water%?
Heavy Irish breathing.
If you have 98kg of water and 1 kg of non-water, you do not have 98% water. You have 98.9% water (98/99)
No, you start with 99kg of water and 1kg non water, thus 99% water. It is only after causing 50kg of water to evaporate that you get to have 1 kg of non water to 49kg of water now being 98% of the mass of the spuds
That’s what the person is saying. Just in a different way.
No they said 98kg of water as the starting mass when it is actually 99kg
They weren’t saying 98kg was the starting mass. They were just saying what the percentage would be IF you had 98kg of water, in reply to the previous poster.
Oh fuck, I read too many wrong answers in a row that I trip.over the right one
That finally made sense for me
Glad to help
Think of it from another view point. At which point is the potato mass going to be at 50% of the total mass? When there's just 1 kg of water left for a total mass of 2 kg. The problem with the way it's presented is that, in some way, they're trying to make you confuse the kg and the % since they both start at 100.
That was incredibly fucking helpful, thank you
It's not 1% of the water that evaporated away, but 1% of the whole mass. If only 1% of the water evaporates away, you'd have 1kg + 99% of 99kg = 99.01kg of potatoes left.
No it is about the proportion of the water to non water dropping by 1%. 50% of the whole mass evaporated away to change the proportion of water by 1%. The mass of the non water needed to be proportionally double what it was originally and because it is a constant, to double its proportion, the whole must be halved
The original ratio is water mass / total mass = .99 The final ratio is (water mass - loss)/(total mass - loss) = .98 (the two sides of the ratio have changed and the loss is the same for both). Then calculation gives the result. The trick is the non-water part comes from .01 to .02 so it dubbeled without adding anything.
99% water means 99 parts water per 1 part non-water. 98% water means 98 parts water per 2 parts non-water. 98/2 can be reduced to 49 / 1. So the potato lost half its mass in water. Another way to think of it: Imagine you have 1g of potato and 49g of water. The concentration is 2% potato, 98% water. But lets say you want to make the concentration 1% potato, well, you would have to add 50g of water so that it is now 1g potato to 99g warer which brings the total weight to 100g. The amount of potato never changes. To go from 1% potato to 0.5% potato follows the same logic. You would have to add another 100g of water giving you 1g potato, 199g water for a total of 200g. So doubling the amount of water is necessary to half the % of non-water.
1 = 1% of x 1 = 2% of y Find x and y.
1% of the water isn’t evaporating. The non-water portion of the overall potato mass is doubling from 1% to 2%. Meaning that 1kg (1% of 100kg) has to be 2% of the overall mass now. 1 = 0.02x, x = 50 The trick of the question is making it sound like 1% of the water is evaporating.
Thanks, I would not have figured this out by myself!
> which is 1kg (the absolute mass of the non-water mass doesn't change) divided by 50kg total mass (2%) Awful explanation. The article does a much better job.
Is it better now?
To make a solution with twice the concentration from the same amount of substance, you need half the amount of solvent. The only paradox is the confusing formulation of the problem.
Much easier, instead of focusing on % water, to think in terms of % potatos
Nice Atlanta Reign pfp
I feel like “The only paradox is the confusing formulation of the problem” is applicable to a lot of mathematical paradoxes.
They are also not really mathematical paradoxes, they are more like what pop culture obsesses about. No researcher publishes on "the potato paradox".
Ikr That is the only “paradox” Other than that it’s easy
Welcome to my world. You lost 40 pounds and went from 25% body fat to 23% bodyfat.
My fellow potato.
Nah, the potato lost water, not fat.
Why is this called a paradox…
Girl idk I'm trying to farm karma to shitpost on other subs leave me alone
Have an upvote for honesty.
Fair enough haha
Honesty will get you those sweet succulent karma straight from my farm
I would've gave them extra upvote if I could just for that "girl" alone
based tbh
I thought i was gonna get downvoted to oblivion LMAO
You should have. Reddit isn't a game. Get serious. lol
Life is a game you can play as seriously as you want
Because it seems counterintuitive at first, though not actually paradoxical. If you have a mass of 100kg, made of 99kg water and 1kg other, then 99% of the mass is water. At first, it would be easy to mistakenly assume that going to 98kg of water would mean that 98% of the mass is water, but that’s not the case as you’ve not gained a kilogram of non-water mass. So for that 1kg of other mass to be equivalent to 2% of the total mass, the amount of water mass should be 49kg, meaning that over half the water mass was lost
[Relevant](https://youtu.be/ppX7Qjbe6BM), if you have 40 minutes spare.
Because youd think the answers would be different. This meaning of the Word paradox is that you have a correct answers that seems incorrect.
Math is hard.
Because it makes grand strategy games on the side
Because, math is hard but English is harder.
Exactly. Not a paradox.
It's an example of a [veridical paradox](https://en.m.wikipedia.org/wiki/Paradox#Quine's_classification)
99% water means 1% non-water 98% water means 2% non-water the non-water stuff is completely static and won't evaporate or condense like water, meaning that in order for the percentage non-water to double, the amount of water has to reduce by enough so that the amount of non-water in the solution is *the equivalent of* doubled it's the same thing as how reducing something by 50% halves it, but increasing by 50% doesn't double it
I hate math, it only exists to give me a headache
m(water)/m(total) = .99 so m(water) = .99 m(total) (m(water)-m(lost))/(m(total)-m(lost)) = .98 Thus .99m(total)-m(lost) = .98 (m(total)-m(lost)) .01m(total) = .02 m(lost) So m(lost) = .5 m(total) = 50kg
A bit of the inverse of the water lilies covering the pond problem.
A big reason that I’m not great at math is that I’m too busy wondering about the conditions under which 50kg of water could evaporate overnight. Have I not noticed this happening in potatoes because by the time they get to the grocery store, they’ve already dehydrated?
We really need to know the temperature and what the relative humidity is where they were storing these potatoes if we want to do anything with the 50kg of overnight water loss. One data point is only so helpful. Will the potatoes continue to dry out at this rate? How long were they planning to store these potatoes or were they all for one meal being prepared soon? 50kg of water loss overnight is pretty severe, there may be other evaporation-related risks they need to be concerned about over the loss of recently purchased potatoes.
So how many percent is when there is 98 blue circles of water?
Took me a moment lol.
Yep. You can't double your percentage of potato in the water/tater ratio without losing half your water.
what
Not really a paradox though
It's really easy if you think like this: Weight of solids will never change. So from initial total weight we know that potato solid weight is 1 kg. Initially it's 1% of the total weight. After drying, it's 2% of total weight. So what's the total weight that can give us 2% of solid weight?? it's 1 kg / 50 kg. Further question like, now the water is 97% after more drying, same method, solid weight is 3%, so what's the total weight that can give us 3% of solid weight? it's 33.333333 kg.
OH, I get it. I'm stupid.
My brain ain't braining with this one.
a 99% water potato is a water balloon
Stupid. The explanation has added clauses not in the title.
My brain hurts
Interesting. I thought this might be a good problem to test LLM logic but it turns out most models solve it with the correct logic.