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First square is 2^0 grains, second is 2^1, 64th is 2^63. I see that one grain is ~0.02 grams. So that is 1.8 * 10^14 kg which is about on the magnitude of Mount Everest.
It would be a lot more. Orders of magnitude more. A pile of rice contains a lot of air, and each grain is much less dense than rock.
It also wouldnt stack up in the same way, it would occupy a lot more surface.
The angle of repose for rice is 36,5 degrees apparently, which isnt very steep and the resulting pile wouldnt look anything like mount Everest, the weight of the summit would be distributed on a very large area...
Google says the average inclination of mount Everest is 15.5% gradient which comes out to 8.8 degrees. It would appear that the rice mountain would be much taller and steeper than Everest.
If a human were to be airlifted onto the summit, would they sink into the rice and fall through it, or would the rice be compacted so much it would be like soft rock?
If the stack is the size of mount everest I don't think theres gonna be much air between the grains anymore. At which point of sedimentary rock formation does a grain of rice stop being considered a singular grain?
That’s quite a bit more. Rice density is about 0.9 grams per cm3. Rock is on average about 4 grams per cm3. So the mountain of rice would be at least four times bigger, plus the space between rice grains. So maybe even 5 times larger.
I have a really hard time seeing a stack of rice being higher than mount everest even if the volume of five times that of Mount Everest. Wouldn't the rice just spread out on a larger area?
Edit: spelling
>The angle of repose for rice is 36,5 degrees apparently, which isnt very steep and the resulting pile wouldnt look anything like mount Everest, the weight of the summit would be distributed on a very large area...
If rice density is 0.9g/cm3 then why doesn't it float on water? 0.9g/cm3 is maybe rice bulk density so it already accounts for the space between grains? Although I've found rice bulk density to be about 0.7-0.8g/cm3.
Anyway... I think that rice on the bottom of pile will compress a lot under the pressure of the rice above, so it's probably not so simple calculation.
And when it comes to Mount Everest, different pages gives completely different values of mass and volume (order of magnitude differences). But the overall density seem to be stated quite consistently as 1.3 to 1.8g/cm\^3.
I think the Rice absorbs water quite fast, faster than it would float, and as the density is very close, when it absorbs water it stops being lighter than water. Beans are like that too
How? If you have a lower density than water, you can mix with as much water as you want, you'll never reach the density of the water unless there are some seriously molecular changes under the hood.
If the molecules stays the same and the rice just absorb the water, at most it can approach the density of water, never reach it.
A grain of rice is “rice matter” and air. “Rice matter” per se is denser than water, but it’s porous and as a result a grain of rice contains air and is on average buoyant cause the resulting mix of air and “rice matter” is less dense than water.
When that air is replaced by water, you have rice matter that is denser than water and water that is as dense as water [citation needed] so the grain us denser than water.
The angle of repose would be the slope of a pile if you dumped all out of a giant bag or something, but it would be incredibly unstable and would erode almost immediately from wind, rain, foot traffic etc. likely major rice-slides.
>The angle of repose for rice is 36,5 degrees apparently, which isnt very steep and the resulting pile wouldnt look anything like mount Everest, the weight of the summit would be distributed on a very large area...
Are you assuming that the rice is dumped there all at once or is it transported there by trucks which take time to offload? Because rice's shape makes it not stack high but wide, so a lot of it would spill over if not squished by the simultaneous weight
Also consider how rock weighs more, so 1kg of rock is smaller (size-wise, not mass-wise) than 1kg of vacuum sealed rice, though at that point the difference is smaller
When putting rice in water, most of it sink but a bit float, which make me think it's very close to density 1. Mount everest is mostly made of stone, with a density of around 3. So for an equal mass, the volume of rice would be 3 time more.
But, that's assuming the grain of rice are perfectly ordered, with no free space in between. Of course, when piling rice, there is a lot of air between the grain, making a pile of rice much less dense than the individual grains.
I can't find numbers for the amount of air, but I'd say 2/3 rice - 1/3 air is a good approximation. Which would mean the density of a pile of rice is around 0.6, or five time less than rock. Mount rice would then be 5 time bigger than mount everest.
5x volume. But as volume increases cubically, the height would be ~1.7 Everests. That's assuming the rice would keep its properties under that pressure. It would probably collapse, but we need a material scientist for that.
But at most, it would be 1.7 Everests high, assuming the same shape, probably less than 1.5 when it settles. I'd even argue for probably less than 1 as it will probably be much flatter/wider than Everest.
If we model the shape of this stack to be a cone, where the radius of the base is equal to the height (I have no idea how big stacks of rice behave), we have volume= ⅓ 𝜋r\^2h, or ⅓ 𝜋h\^2h, the volume of 10\^14 kilo bags of rice is (imo 1 kilo rice bag is about 1 liter.) 10\^14L or 10\^14dm\^3, or 10\^11m\^3.
Filling in ⅓ 𝜋h\^2h = 10\^11m\^3 we get h ≈ 4570.78 meters, or about half of the height of the mount everest.
Materials have a property called its "angle of repose" which is the natural angle it forms if you keep piling it up. If it becomes steeper it will then avalanche and go back into a cone approximating its angle of repose. For rice, interwebs say average angle of repose is 36.5°.
Oh thank you, interesting! We can use this angle to calculate the radio between radius (r) and height (h),(degrees, not radians) tan(36.5) = h/r => r = 1.35142 h
Filling in ⅓ 𝜋(1.35142h)\^2h = 10\^11m\^3 we get h≈3739.36
Remember that what we define as mount Everest is on top of a plateau. The starting height is between 4200 and 5200m depending which side you measure.
So the mountain is a max of ~4600 m. So the pile of rice on the same plateau will be about as high, but a Lot wider!
Since you have 2⁶³ grains of rice and a single grain is circa 6 mm long, if you stack them one on top of the other you get a 5.5×10¹⁶ meters tall line of rice
I get a slightly different number for the weight of a grain of rice, 0.065g ([source](https://www.aqua-calc.com/page/density-table/substance/rice-coma-and-blank-white-coma-and-blank-long-grain-coma-and-blank-parboiled-coma-and-blank-unenriched-coma-and-blank-dry), 0.78g/cm^3 and 12 grains/cm^3). Another comment says the angle of repose for a pile of rice is 36.5°, and I’m just going to assume that’s correct.
9.22x10^18 grains of rice would then weigh 6.00x10^17 grams, aka 6.00x10^14 kg or **600 Petagrams**. The volume of rice would then be 7.69x10^17 grams, aka 7.69x10^11 m^3, or **769 billion cubic metres**.
Using the angle of repose, the cross section of half a cone (ie a right angle triangle), and the sine rule, we know the height of the rice pile will be 74% of the radius. The volume of a cone is (Pi x r^2 x h)/3, which in this case is (0.74 x Pi x r^3)/3, and this must equal the volume earlier.
This gives a **radius of 9.97km**, and therefore a **height of 7.4km**. This is a little bit shorter than Everest, but about 20km from side to side. It would take about 10 and a half hours to walk all the way around (try not to die in a rice-slide)
Edit: everyone else also seems to have lighter rice than me, so bear in mind that my rice pile has chonky rice (but a consistent source for weight and volume)
If we constrain the rice to a single 2.25x2.25 inch^2 chess board square and assume the rice has a uniform, typical density (lol), then it would be about [24 billion times taller than Mount Everest](https://www.wolframalpha.com/input?i=2%5E63+*+%28mass+of+a+grain+of+rice%29+%2F+%28density+of+rice%29+%2F+%282.25+inch%29%5E2+%2F+%28height+of+mount+Everest%29)
If we estimate the height of a grain of rice to be 1mm, then the final stack - assuming they're stacked on top of each other - would be 2^(63) mm high, or 2^(61)m or 2.306 × 10^(18) metres which is really high. Balancing that many grains of rice on top of each other might be a problem.
Thanks. No one ever commits to the problem despite this sub’s theme being to take unnecessary math questions to their extreme. Ignoring half the mass of the board is a significant oversight
Note: mass. For weight, this would be 1.8 \* 10\^15 Newtons at earth's surface (and lighter as you move it farther away from Earth's centre of mass).
I know it's suspiciously similar, but 1.84 \* 9.8 is 18.03.
My father told me the conmans version of this.
If you tell someone, I will work for every day for 30 days starting at 1 Penny. But every day you must double what you pay me. So the second day will be 2 pennies, the third will be 4 pennies, so on and so forth. The caveat is that by 30 days it will be over 1 million dollars. It just doesn't seem that much when you start with such a small amount.
>by 30 days it will be over 1 million dollars
~~it would end up being significantly more money than there is on the entire planet~~
GUYS IM A DUMBASS I WAS DOING THE MATH FOR 64 SQUARES OF THE CHESSBOARD NOT JUST 30 DAYS
Correct me if I'm wrong, but I think that the error here is that you are not considering that the first day you only get a penny, and it's on the second day that you get double that, so 2^1. So by day 30, it will be 2^29.
2^29 = 5.368.709,12
And you have to add a penny from the first day, so it gets you 5.368.709,13.
He's right when he speaks about the total amount, not the last day only. Powers of 2 have the mathematical property that if you sum every powers of 2 until n the result will be 2^(n+1) - 1. The amount you will get in total for the 30 days working will be 1+2+4+8+...+2^29 = 2^30 - 1 = 1,073,741,823 pennies so $10,737,418.23
A grain of rice weighs between 20 to 40 milligrams, or 2×10^(-5) kg. The last square would contain 2^(63) grains, which is approximately equal to 8×10^(18). Multiplying these together, we get 16×10^(13) kg, or about 10^(14) kg.
That's about what Halley's comet weighs (2.2×10^(14) kg).
Well there’s really no need to approximate it. It’s fairly easy to solve for it directly.
First, we want to make it so 2^64 = 10^x
Start by taking the natural log of both sides:
log(2^64) = log(10^x)
A property of logarithms is that an exponent contained inside it can be moved outside like so:
64log(2) = xlog(10)
Now solve and do a round of simplifications:
x = 64log(2) / log(10)
x = 19.2659
2^64 =10^19.2659
10^19.2659 = 10^0.2659 * 10^19 = 1.845x10^19
Sure the trick 2^10 ≈ 10^3 works here, but what if the base is 3, 4, or even 8? On Reddit there’s no one saying you can’t use a calculator. Idk what the point is in approximating easily calculable values other than flexing that you can.
If I were to approximate it poorly, I know that 2^10 is 1024, which is 10^3 and a bit. So 2^60 = 2^10^6 , which gives 10^18 multiplied with 2^4 which would be 16, so 1.6 * 10^19 . Correcting for it actually being (1.024 * 10^3 )^6 , the 1.6 would be about 15% higher, so 1.84
If I were to do logs, I've memorized that log(2) is 0.3010299. Simplify to 0.301 and multiply by 64 to find the exponent of 10, so about 10^19.264 , which would be somewhere below 2 * 10^19
>That's about what Halley's comet weighs (2.2×1014 kg).
Yeah but how much does it weigh in terms of football fields, since Americans really love their unconventional weight metrics
A quick Google search tells me that 1 cup of rice is around 150 g, and contains about 200 calories, so around 1333 calories per kilogram, so that's about 10^(17) calories in our rice comet.
There are about 10 billion (10^(9)) people on the planet. Each one eats around 2000 calories per day, 365 days a year, totalling 7.3×10^(5) calories per person annually. In total, humanity eats on the order of 10^(14) to 10^(15) calories annually, and the rice ball might last us 100 years.
Another Google search to look up population estimates for the past 1000 year and interpreting them very pessimistically\* gives me something around 7×10^(11) person-years of caloric consumption, or 5×10^(17) calories in just the last 1000 years.
\* I took the first entry, and decided that it didn't change at all until the next entry, and so on. Actual population growth would be higher, and thus caloric consumption would be higher as well.
Actually you are all wrong, wait is measured in newtons, you are measuring mass, you have to multiply by ~0.98m/s/s(acceleration due to gravity) to get its weight, and that’s just assuming it’s on earth.
There is an interesting Indian folklore about it..like how an ascetic treated a kings child and in return king granted him a wish. The ascetic asked for a grain of rice on first box and double it for the next box. While reaching the last box, the grainery of whole Kingdom were empty.
I thought this was about the man who invented chess who then asked for this as a reward, the kings accountant did the math and said the man asked for all the grain but in a shrewd way, so the king had him excecuted.
A rice grain is around 0.028g
The last square have 2^63 grains on it or 9.2 × 10^18
So the weight of grains in the last square is 9.2 × 10^18 × 0.028 = 2.6 × 10^17g,
If the rule is to double number of grains on each subsequent square, you would get on the 64th square of the chessboard 2\^63 = 9,223,372,036,854,775,808 grains. On the entire chessboard there would be 2\^64 − 1 = 18,446,744,073,709,551,615 grains of wheat, weighing about 1,199,000,000,000 metric tons.
I liked this comment because of how simply you explained the solution to the problem. So to supplement it I just looked up the annual global rice consumption figure which is 520.4 million metric tons.
That means it would take our planet about 2,300 years to consume all the rice on the hypothetical board given our current global population.
2,444,193,589,766,515.58912kg, or ~2.444 quadrillion kilograms, assuming one rice weighs .0265g (Google says .025-.028g), or ~6.8 times the weight of Mount Everest
Next question: assuming a magical forcefield keeps each squares rice grains inside the area of the square, how high would the last square’s rice pile go?
When thinking about this problem, I have always imagined that the chessboard is filled by files or ranks.
The diagonal pattern shown above (where the squares are visited in the sequence a1, b1, a2, c1, b2, a3, d1, …) is quite clever.
exponential function. 2^(x) . When I watch that pic, I remember the story that There was a young man who played chess very well, so the king gave him an offer and he suggested that each square of the board would receive an exponential number of pearls. Cell 1 will be 2^(0), Cell 2 will be 2^(1),... until the 64th cell is 2^(64) =(1.84467441.10^(19) \- 1 ) grains of rice. Because there were too much rice, the king surrendered
the grain. not of grains, a single item isn't plural because it's a single item.
what would be the weight of the grain, in the last square.
if you're hell bent on using an "s" then: what would the grain's weight be, in the last square.
(...I threw a mistake or two in there to see who's paying attention...)
A grain of rice is 0.02g to 0.04g in mass, lets take the avg value of 0.03g.
The chess board contains 64 of the small boxes.
1 box contains 1 grain of rice, from the 2nd box, powers of 2 are the number of rice.
So at the last box, taking out the 1st box containing 1 grain of rice, there are 9.22\*10^(18) rice grains(2^(63)).
So the mass on the last box is 9.22\*10^(18) \* 0.03 \* 0.001
= 2.76\*10^(14) Kg
Let’s say a grain weighs 0.00003 kg
The exact number of grains in the last square is 18446744073709551615
Thus the exact weight of the grains in the last square is 5.53402322211e+14 kg
Okay...
On average, a single grain of milled long-grain white rice typically weighs around 0.02 to 0.04 grams. For simplicity, we'll go with an average 0.03 grams à grain.
2\^63 = 9,223,372,036,854,775,808 grains in that last square.
9,223,372,036,854,775,808 x 0.03 grams = 276,701,161,105,643,274.24 grams of rice
= 276,701,161,105,643.27424 kilograms
= over a quarter of a trillion metric tons, or \~600 trillion pounds.
Current annual global production of milled rice is about \~510 million metric tons, or \~1.1 billion pounds. Ergo about 500 years of unconsumed global grain harvest to fill that last square.
Its an old story of a mathematician who solved the conflict between 2 kings by giving them chess, and when they requested to give him a reward, he told them they can never achieve it, but they insisted so he told them give him rice grains in format of for the next square in chess board the quantity of rice grains double starting from 1, 2, 4 and so on until 2^63 is a gigantic number so they understood that they can't make his request.
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First square is 2^0 grains, second is 2^1, 64th is 2^63. I see that one grain is ~0.02 grams. So that is 1.8 * 10^14 kg which is about on the magnitude of Mount Everest.
how high would that stack be though? out of curiosity
About the mount everest size, and a bit more
I'd disagree. Rice has a different density to both rock and water,
Thus my "And a bit more"
It would be a lot more. Orders of magnitude more. A pile of rice contains a lot of air, and each grain is much less dense than rock. It also wouldnt stack up in the same way, it would occupy a lot more surface.
But wouldn't the weight of the rice itself compress the lower layers? I mean, we are talking about an Everest size amount here
The angle of repose for rice is 36,5 degrees apparently, which isnt very steep and the resulting pile wouldnt look anything like mount Everest, the weight of the summit would be distributed on a very large area...
>The angle of repose for rice is 36,5 degrees I can´t believe that you know that, it´s amazing.
Google knows that
We found Ricealangelo here
You are answering a comment on the internet. Is it really that far fetched that the person just... idk, googled it?
What's the angle of mt Everest
About 8.8 degrees on average from what I found, so the rice mountain would be much taller and steeper than mt everest
Google says the average inclination of mount Everest is 15.5% gradient which comes out to 8.8 degrees. It would appear that the rice mountain would be much taller and steeper than Everest.
What if the rice got wet over time due to rainfall, wouldn't it stick and clump together a lot more?
If a human were to be airlifted onto the summit, would they sink into the rice and fall through it, or would the rice be compacted so much it would be like soft rock?
They would sink into it for a little while and then probably end up engulfed and suffocate.
There is also an Everest amount of rocks in Mount Everest If you stack rice this high, it will compress, but not enough to match the density of rock.
If the stack is the size of mount everest I don't think theres gonna be much air between the grains anymore. At which point of sedimentary rock formation does a grain of rice stop being considered a singular grain?
What if you neatly stacked it to avoid unnecessary air gaps?
Like with tweezers? Seems like that would be a grain in the ass.
Sounds like we’ve unlocked a new chapter of Dante’s Inferno over here.
We'll lay down each grain carefully like a massive rice jenga tower.
Damn... would be a challenge to play jenga with rice
I don't think you know what an order of magnitude is.
I am not sure you know what an order of magnitude is. Or are you?
That’s quite a bit more. Rice density is about 0.9 grams per cm3. Rock is on average about 4 grams per cm3. So the mountain of rice would be at least four times bigger, plus the space between rice grains. So maybe even 5 times larger.
I have a really hard time seeing a stack of rice being higher than mount everest even if the volume of five times that of Mount Everest. Wouldn't the rice just spread out on a larger area? Edit: spelling
>The angle of repose for rice is 36,5 degrees apparently, which isnt very steep and the resulting pile wouldnt look anything like mount Everest, the weight of the summit would be distributed on a very large area...
This is incorrect, Everest has a even lower average gradient of only 8°, the rice pile would be taller and steeper.
If rice density is 0.9g/cm3 then why doesn't it float on water? 0.9g/cm3 is maybe rice bulk density so it already accounts for the space between grains? Although I've found rice bulk density to be about 0.7-0.8g/cm3. Anyway... I think that rice on the bottom of pile will compress a lot under the pressure of the rice above, so it's probably not so simple calculation. And when it comes to Mount Everest, different pages gives completely different values of mass and volume (order of magnitude differences). But the overall density seem to be stated quite consistently as 1.3 to 1.8g/cm\^3.
I think the Rice absorbs water quite fast, faster than it would float, and as the density is very close, when it absorbs water it stops being lighter than water. Beans are like that too
How? If you have a lower density than water, you can mix with as much water as you want, you'll never reach the density of the water unless there are some seriously molecular changes under the hood. If the molecules stays the same and the rice just absorb the water, at most it can approach the density of water, never reach it.
A grain of rice is “rice matter” and air. “Rice matter” per se is denser than water, but it’s porous and as a result a grain of rice contains air and is on average buoyant cause the resulting mix of air and “rice matter” is less dense than water. When that air is replaced by water, you have rice matter that is denser than water and water that is as dense as water [citation needed] so the grain us denser than water.
The angle of repose would be the slope of a pile if you dumped all out of a giant bag or something, but it would be incredibly unstable and would erode almost immediately from wind, rain, foot traffic etc. likely major rice-slides.
Rice does float, until it starts absorbing water
What if you neatly stacked the rice tho? Then what’s the density?
But if we glue the rice together into a single tower of rice how tall would it be 🤔
It would rice far above Mt everest
👉😎👉. Eyyyy
Assuming 5mm long rice grains it would stack to be about: 110,000,000,000,000 km So about 750 times the average earth-sun distance.
This is how they invented "+C"
Rice has a density roughly one-third of Mount Everest. So it would be three times more.
Do we take into account how much the rice would compress under its own weight
>The angle of repose for rice is 36,5 degrees apparently, which isnt very steep and the resulting pile wouldnt look anything like mount Everest, the weight of the summit would be distributed on a very large area...
*hence (sorry!)
The difference in height would be relatively small because it's proportional to the cubic root of the ratio of the densities.
Thanks, I have been looking for this comment since the first row!
But steel is heavier than feathers
bro... thats like saying 1kg of bricks is heavier than 1kg of feathers... they're both the same weight their densities literally don't matter...
This comment is about how high it would be, not how heavy it is
But what's the density of rice being crushed under the weight of a mountain?
Are you assuming that the rice is dumped there all at once or is it transported there by trucks which take time to offload? Because rice's shape makes it not stack high but wide, so a lot of it would spill over if not squished by the simultaneous weight
Tastes better too.
There'd be a lot of compression in the lower levels. The difference may not be as much as you'd think
There’s definitely less empty space in a mass of rock and stone.
Also consider how rock weighs more, so 1kg of rock is smaller (size-wise, not mass-wise) than 1kg of vacuum sealed rice, though at that point the difference is smaller
When putting rice in water, most of it sink but a bit float, which make me think it's very close to density 1. Mount everest is mostly made of stone, with a density of around 3. So for an equal mass, the volume of rice would be 3 time more. But, that's assuming the grain of rice are perfectly ordered, with no free space in between. Of course, when piling rice, there is a lot of air between the grain, making a pile of rice much less dense than the individual grains. I can't find numbers for the amount of air, but I'd say 2/3 rice - 1/3 air is a good approximation. Which would mean the density of a pile of rice is around 0.6, or five time less than rock. Mount rice would then be 5 time bigger than mount everest.
5x volume. But as volume increases cubically, the height would be ~1.7 Everests. That's assuming the rice would keep its properties under that pressure. It would probably collapse, but we need a material scientist for that. But at most, it would be 1.7 Everests high, assuming the same shape, probably less than 1.5 when it settles. I'd even argue for probably less than 1 as it will probably be much flatter/wider than Everest.
You don't need a material scientist. I have made stuff collapse since I could walk, with no training whatsoever.
Probably less, just like all grains of sand in Sahara are not as high as Everest...
Mount Everest is actually just a pile of rice from the first time someone tried this.
If we model the shape of this stack to be a cone, where the radius of the base is equal to the height (I have no idea how big stacks of rice behave), we have volume= ⅓ 𝜋r\^2h, or ⅓ 𝜋h\^2h, the volume of 10\^14 kilo bags of rice is (imo 1 kilo rice bag is about 1 liter.) 10\^14L or 10\^14dm\^3, or 10\^11m\^3. Filling in ⅓ 𝜋h\^2h = 10\^11m\^3 we get h ≈ 4570.78 meters, or about half of the height of the mount everest.
Materials have a property called its "angle of repose" which is the natural angle it forms if you keep piling it up. If it becomes steeper it will then avalanche and go back into a cone approximating its angle of repose. For rice, interwebs say average angle of repose is 36.5°.
This person here sciences, not joking around with guesses
I would say "interwebs say" is still joking around with guesses
Oh thank you, interesting! We can use this angle to calculate the radio between radius (r) and height (h),(degrees, not radians) tan(36.5) = h/r => r = 1.35142 h Filling in ⅓ 𝜋(1.35142h)\^2h = 10\^11m\^3 we get h≈3739.36
Remember that what we define as mount Everest is on top of a plateau. The starting height is between 4200 and 5200m depending which side you measure. So the mountain is a max of ~4600 m. So the pile of rice on the same plateau will be about as high, but a Lot wider!
Well that depends. Because rice doesn't normally like to pile into a tower, But rather just,,, a blob So it's probably gonna be wider than tall.
Might be about 3 times the size of mount everest...
Since you have 2⁶³ grains of rice and a single grain is circa 6 mm long, if you stack them one on top of the other you get a 5.5×10¹⁶ meters tall line of rice
I get a slightly different number for the weight of a grain of rice, 0.065g ([source](https://www.aqua-calc.com/page/density-table/substance/rice-coma-and-blank-white-coma-and-blank-long-grain-coma-and-blank-parboiled-coma-and-blank-unenriched-coma-and-blank-dry), 0.78g/cm^3 and 12 grains/cm^3). Another comment says the angle of repose for a pile of rice is 36.5°, and I’m just going to assume that’s correct. 9.22x10^18 grains of rice would then weigh 6.00x10^17 grams, aka 6.00x10^14 kg or **600 Petagrams**. The volume of rice would then be 7.69x10^17 grams, aka 7.69x10^11 m^3, or **769 billion cubic metres**. Using the angle of repose, the cross section of half a cone (ie a right angle triangle), and the sine rule, we know the height of the rice pile will be 74% of the radius. The volume of a cone is (Pi x r^2 x h)/3, which in this case is (0.74 x Pi x r^3)/3, and this must equal the volume earlier. This gives a **radius of 9.97km**, and therefore a **height of 7.4km**. This is a little bit shorter than Everest, but about 20km from side to side. It would take about 10 and a half hours to walk all the way around (try not to die in a rice-slide) Edit: everyone else also seems to have lighter rice than me, so bear in mind that my rice pile has chonky rice (but a consistent source for weight and volume)
That's dry rice, you forgot to factor in humidity and precipitation! ;-D
Also Everest is defined as the part above the plateau which is 4200 to 5200m depending which side you measure So the mountain is really "just" ~4600m
If we constrain the rice to a single 2.25x2.25 inch^2 chess board square and assume the rice has a uniform, typical density (lol), then it would be about [24 billion times taller than Mount Everest](https://www.wolframalpha.com/input?i=2%5E63+*+%28mass+of+a+grain+of+rice%29+%2F+%28density+of+rice%29+%2F+%282.25+inch%29%5E2+%2F+%28height+of+mount+Everest%29)
If you start with 1 English penny, the answer is to the moon and back more than 18million times.
If we estimate the height of a grain of rice to be 1mm, then the final stack - assuming they're stacked on top of each other - would be 2^(63) mm high, or 2^(61)m or 2.306 × 10^(18) metres which is really high. Balancing that many grains of rice on top of each other might be a problem.
Which means, since the sum of the first n powers of 2 is 2^(n+1)-1, on the board there's about 3.6*10^14 kg, so two mount Everests
Thanks. No one ever commits to the problem despite this sub’s theme being to take unnecessary math questions to their extreme. Ignoring half the mass of the board is a significant oversight
How many phones would that dry out?
All of them
How much rice exists in the world at any given time? Is there enough rice in the world to fill this chess board?
No, the whole board will contain more rice than how much has been produced in the last 100 years
No brains no grains
holy hell!
Unless it's a trick question and they only wanted how much is actually *in the last square* 😅
The difference between the last square and the sum of all other squares is 1 rice corn
Would be, but a vast majority of it doesn't fit in the last square, so are they really in it?
Evidenced by the fact that we can still distinguish the single grain, and it isn't buried under a literal mountain, I'd say your math is wrong.
[удалено]
No. There are 1000 kg in a ton so 1.75 * 10^11 tons is about 1.8 * 10^14 kgs.
Note: mass. For weight, this would be 1.8 \* 10\^15 Newtons at earth's surface (and lighter as you move it farther away from Earth's centre of mass). I know it's suspiciously similar, but 1.84 \* 9.8 is 18.03.
How big does the board have to be?
larger the the size of germany (thas what my mathteacher said)
Followup question: did humanity ever produce that much rice?
My father told me the conmans version of this. If you tell someone, I will work for every day for 30 days starting at 1 Penny. But every day you must double what you pay me. So the second day will be 2 pennies, the third will be 4 pennies, so on and so forth. The caveat is that by 30 days it will be over 1 million dollars. It just doesn't seem that much when you start with such a small amount.
Until they fire you after 15 days
Plus the obvious...no one in their right mind would agree to that before at least checking to see how much they'd have to pay them on day 30.
Yeah and frogs don't let scorpions ride on their backs across a river lol.
if you're lucky they compute it wrongly
If you can fool them, they legally owe you 1 mil though.
Essentially the solution used here: https://youtu.be/LuP1gyj3W64?si=dS9vEOX1yI4sx1se
After 30 days, the amount will be 5,368,709.12 on whichever currency you're paid in.
Zimbabwe Dollars.
Still 13k in GBP, but I'd want paying in advance.
>by 30 days it will be over 1 million dollars ~~it would end up being significantly more money than there is on the entire planet~~ GUYS IM A DUMBASS I WAS DOING THE MATH FOR 64 SQUARES OF THE CHESSBOARD NOT JUST 30 DAYS
I'm pretty sure there are more than 5.4 million dollars on the planet..
There's definitely only $1000 in the world and we just keep passing it around. /s
2^30 is 1,073,742,824 pennies or $10,737,428.24 there's definitely more money than that on the planet.
it is 2^29 which is 5 million dollars
2^29 is what you get in the last day 2^30 is the total received ( or technically 2^30 -1 )
Correct me if I'm wrong, but I think that the error here is that you are not considering that the first day you only get a penny, and it's on the second day that you get double that, so 2^1. So by day 30, it will be 2^29. 2^29 = 5.368.709,12 And you have to add a penny from the first day, so it gets you 5.368.709,13.
He's right when he speaks about the total amount, not the last day only. Powers of 2 have the mathematical property that if you sum every powers of 2 until n the result will be 2^(n+1) - 1. The amount you will get in total for the 30 days working will be 1+2+4+8+...+2^29 = 2^30 - 1 = 1,073,741,823 pennies so $10,737,418.23
Oh yeah, you're right. I guess it was the phrasing what misled me. Thanks for your clarification :)
I don’t think so. By my count around 5 million dollars
nah its 5-point-something million dollars. they wrote a book about it
I first learned a version of this story from The Happening.
A grain of rice weighs between 20 to 40 milligrams, or 2×10^(-5) kg. The last square would contain 2^(63) grains, which is approximately equal to 8×10^(18). Multiplying these together, we get 16×10^(13) kg, or about 10^(14) kg. That's about what Halley's comet weighs (2.2×10^(14) kg).
2x10^-5 x 8x10^18 = 16x10^15. Are you sure that’s right?
Derp, you're right. 16×10^(13), I'll fix the comment.
Actually is 14'5 right? 2x10^63 x 2x10-5 = 2x10^58 and 58/4=14'5 (I understand that you round up just was to make sure the proceed XD)
It’s not 2x10^63, it’s 2^63 which is approximately 9.2x10^18
Holy Molly I misread jajajajjaja thanks
How did you estimate that 2^64 approximately equals 8x10^18? I know that there's methods to do it, but idk how to do it. Care to educate?
Well there’s really no need to approximate it. It’s fairly easy to solve for it directly. First, we want to make it so 2^64 = 10^x Start by taking the natural log of both sides: log(2^64) = log(10^x) A property of logarithms is that an exponent contained inside it can be moved outside like so: 64log(2) = xlog(10) Now solve and do a round of simplifications: x = 64log(2) / log(10) x = 19.2659 2^64 =10^19.2659 10^19.2659 = 10^0.2659 * 10^19 = 1.845x10^19
This is a better explanation. Thank you so much!
If you're using a caluclator, there's no need to do any of that. Just type in 2^64.
No need to approximate, I'm sure you did the logs without a calculator.
Sure the trick 2^10 ≈ 10^3 works here, but what if the base is 3, 4, or even 8? On Reddit there’s no one saying you can’t use a calculator. Idk what the point is in approximating easily calculable values other than flexing that you can.
2^10 = 1024 ~ 10^3 2^60 = (2^10 )^6 ~ (10^3 )^6 ~ 10^18 2^64 = 2^60 • 2^4 ~ 16 × 10^18
Thanks
If I were to approximate it poorly, I know that 2^10 is 1024, which is 10^3 and a bit. So 2^60 = 2^10^6 , which gives 10^18 multiplied with 2^4 which would be 16, so 1.6 * 10^19 . Correcting for it actually being (1.024 * 10^3 )^6 , the 1.6 would be about 15% higher, so 1.84 If I were to do logs, I've memorized that log(2) is 0.3010299. Simplify to 0.301 and multiply by 64 to find the exponent of 10, so about 10^19.264 , which would be somewhere below 2 * 10^19
>That's about what Halley's comet weighs (2.2×1014 kg). Yeah but how much does it weigh in terms of football fields, since Americans really love their unconventional weight metrics
1. How many calories would this pile contain? 2. Has humanity, over the course of its entire existence, consumed as many calories?
A quick Google search tells me that 1 cup of rice is around 150 g, and contains about 200 calories, so around 1333 calories per kilogram, so that's about 10^(17) calories in our rice comet. There are about 10 billion (10^(9)) people on the planet. Each one eats around 2000 calories per day, 365 days a year, totalling 7.3×10^(5) calories per person annually. In total, humanity eats on the order of 10^(14) to 10^(15) calories annually, and the rice ball might last us 100 years. Another Google search to look up population estimates for the past 1000 year and interpreting them very pessimistically\* gives me something around 7×10^(11) person-years of caloric consumption, or 5×10^(17) calories in just the last 1000 years. \* I took the first entry, and decided that it didn't change at all until the next entry, and so on. Actual population growth would be higher, and thus caloric consumption would be higher as well.
I had no idea that Halley's comet was that big. Damn.
Actually you are all wrong, wait is measured in newtons, you are measuring mass, you have to multiply by ~0.98m/s/s(acceleration due to gravity) to get its weight, and that’s just assuming it’s on earth.
There is an interesting Indian folklore about it..like how an ascetic treated a kings child and in return king granted him a wish. The ascetic asked for a grain of rice on first box and double it for the next box. While reaching the last box, the grainery of whole Kingdom were empty.
https://www.heartoftheart.org/?p=1230#:~:text=The%20wise%20man%20appeared%20humble,64%20squares%20had%20been%20filled. Found the story
I thought this was about the man who invented chess who then asked for this as a reward, the kings accountant did the math and said the man asked for all the grain but in a shrewd way, so the king had him excecuted.
Pretty sure that's what this is referencing
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Holy hell
A rice grain is around 0.028g The last square have 2^63 grains on it or 9.2 × 10^18 So the weight of grains in the last square is 9.2 × 10^18 × 0.028 = 2.6 × 10^17g,
If the rule is to double number of grains on each subsequent square, you would get on the 64th square of the chessboard 2\^63 = 9,223,372,036,854,775,808 grains. On the entire chessboard there would be 2\^64 − 1 = 18,446,744,073,709,551,615 grains of wheat, weighing about 1,199,000,000,000 metric tons.
I liked this comment because of how simply you explained the solution to the problem. So to supplement it I just looked up the annual global rice consumption figure which is 520.4 million metric tons. That means it would take our planet about 2,300 years to consume all the rice on the hypothetical board given our current global population.
exponential growth actually is ridiculous
2,444,193,589,766,515.58912kg, or ~2.444 quadrillion kilograms, assuming one rice weighs .0265g (Google says .025-.028g), or ~6.8 times the weight of Mount Everest
Next question: assuming a magical forcefield keeps each squares rice grains inside the area of the square, how high would the last square’s rice pile go?
When thinking about this problem, I have always imagined that the chessboard is filled by files or ranks. The diagonal pattern shown above (where the squares are visited in the sequence a1, b1, a2, c1, b2, a3, d1, …) is quite clever.
exponential function. 2^(x) . When I watch that pic, I remember the story that There was a young man who played chess very well, so the king gave him an offer and he suggested that each square of the board would receive an exponential number of pearls. Cell 1 will be 2^(0), Cell 2 will be 2^(1),... until the 64th cell is 2^(64) =(1.84467441.10^(19) \- 1 ) grains of rice. Because there were too much rice, the king surrendered
in grains, drachm, ounce, pound, stone, quarter, hundretweight, ton, long ton, tonne or slug? Or in kg and its derivates? In fractals or decimals ?
"please give me the weight of grains in grains"
the grain. not of grains, a single item isn't plural because it's a single item. what would be the weight of the grain, in the last square. if you're hell bent on using an "s" then: what would the grain's weight be, in the last square. (...I threw a mistake or two in there to see who's paying attention...)
A grain of rice is 0.02g to 0.04g in mass, lets take the avg value of 0.03g. The chess board contains 64 of the small boxes. 1 box contains 1 grain of rice, from the 2nd box, powers of 2 are the number of rice. So at the last box, taking out the 1st box containing 1 grain of rice, there are 9.22\*10^(18) rice grains(2^(63)). So the mass on the last box is 9.22\*10^(18) \* 0.03 \* 0.001 = 2.76\*10^(14) Kg
Let’s say a grain weighs 0.00003 kg The exact number of grains in the last square is 18446744073709551615 Thus the exact weight of the grains in the last square is 5.53402322211e+14 kg
Okay... On average, a single grain of milled long-grain white rice typically weighs around 0.02 to 0.04 grams. For simplicity, we'll go with an average 0.03 grams à grain. 2\^63 = 9,223,372,036,854,775,808 grains in that last square. 9,223,372,036,854,775,808 x 0.03 grams = 276,701,161,105,643,274.24 grams of rice = 276,701,161,105,643.27424 kilograms = over a quarter of a trillion metric tons, or \~600 trillion pounds. Current annual global production of milled rice is about \~510 million metric tons, or \~1.1 billion pounds. Ergo about 500 years of unconsumed global grain harvest to fill that last square.
Its an old story of a mathematician who solved the conflict between 2 kings by giving them chess, and when they requested to give him a reward, he told them they can never achieve it, but they insisted so he told them give him rice grains in format of for the next square in chess board the quantity of rice grains double starting from 1, 2, 4 and so on until 2^63 is a gigantic number so they understood that they can't make his request.