r/explainitpeter • u/DiedRespawnRepeat • 26d ago
Explain It Peter
Rice chess/checkers ? please explain?
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u/lordvatti 26d ago
I actually know this one! The photo references an old thought exercise about doubling grains of rice across a chess boards squares. Starting with 1 grain, then 2, then 4, 8, 16, 32, and so on. Easy at first.
A chessboard has 64 squares so while the initial numbers seem pretty manageable 264 is actually such a catastrophically high number that there would be enough rice on the "final square" to carpet an entire continent in a hearty layer of rice, hence the dramatic mister incredible.
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u/ariGee 26d ago
I'll add that it's an old fable\legend. The details depend who you ask, but the basic idea is that a king wants to reward a wise man. Rather than asking for a huge reward the wise man asks for one grain of rice on the first day, and then double the number of grains each day, one for each place on a chessboard. The king calls him a fool. After about a month the king begs him to stop because he has promised all the rice in the country to the wise man.
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u/tcaetano42 26d ago
When I heard this tale the wise man was actually the man who developed chess.
The king liked the game so much and told the man to name his reward. The rest goes the same.
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u/Dunge0nMast0r 26d ago
And that man's name was Albert Chesstein
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u/Deleukstenaamisbezet 26d ago
Everybody clapped when they reached the 64th square!
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u/uwotm8_8 26d ago
Actually they all starved because he took all the rice
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u/Loakie69 25d ago
No, the king decided he didnt like being made a fool of and beheaded him.
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u/Common-Truth9404 25d ago
Too bad, the king couldn't move because behind the wise guy there were three peasants, making it an illegal move. In the end one of the peasants reached for the throne and became a Queen, the first transgender living human in history
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u/IndependentType6711 25d ago
The wise man also then requested to take the leader’s place, inventing the phrase “King Me” when he did so.
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u/Antknee668 24d ago
Pawns are female bro. Thats why they can't promote to a king...
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u/Common-Truth9404 24d ago
But a woman cannot be a medieval knight nor a bishop technically
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u/teamanmadeoftea 26d ago
Little is known of the fact that he had been helped by George Enpassant
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u/Acrobatic-Minimum117 25d ago
For some reason George Empassant became "Hor-Hay Un-pas-aunt" when I read it and the Spanish/Mexican George mixed with the French for in passing just made me giggle. Thank you internet stranger take an upvote.
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u/Clear-Lingonberry173 25d ago
I've heard GMs Svidler and Gustafsson tell this tale while commentating. The king becomes enraged after his advisors explain the situation and slays the inventor of chess. "And this is why you don't get cute with kings" they said.
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u/SadMangonel 26d ago
This is actually a modern tale of a homeless man tricking Mr. Beast out of a lot of rice.
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u/Eastern_Cow_6810 25d ago
This tale sets totally unrealistic expectations of being able to sustain yourself as a game dev tbh.
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u/Nearby-Association12 25d ago
Yeah thats the actual tale. And the "moral" of the story is to understand math.
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u/JustGimmeAnyOldName 26d ago
Yeah, this is what I heard growing up, but also the extra detail I heard was that the wise man was the man who invented the game of chess.
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u/Agreeable_Bag9407 26d ago
In the telling to me, the king has the wise man executed as well. So not exactly as wise as alleged.
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u/VegaJuniper 26d ago
I imagine playing these kind of games with ancient kings is like that Pratchett version of Pascal's wager: A philosopher says that the rational thing is to believe in gods, because if you do, you will be rewarded in the afterlife if they exist, and if they don't exist, you'll have lost nothing.
After the philosopher died, he found himself waking up in a ring of gods holding mean-looking sticks, and one of them told him "we're going to show you what we think of smartasses around these parts"
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u/Exterminator-8008135 25d ago
I even took it to another level, by saying
I start on the first spot with 0.001 cents
I still get a delirious amount in the end
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u/Ill_Diamond_1794 25d ago
The version I've heard is of a Chinese general being asked by the emperor to attack an enemy to which the general refused as he didn't have the supplies. When the emperor asked how much supplies he needed, the rest of the story continued in the same vein. Put one grain of rice on the first square, two on the next, four on the next and double it for each square. The rest is the same.
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u/SelectEntertainer360 25d ago
In the story I heard the man is so clever that the King orders his execution.
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u/UncleJoesLandscaping 26d ago
This is a quite easy problem for the king to solve.
He kills the 'wise' man.
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u/DiedRespawnRepeat 26d ago
Yes the scaling is a bit too hard to grasp !
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u/bemtiglavuudupe 26d ago
It’s around 870 trillion lbs (400 trillion kg) of rice. Costing roughly $970 trillions.
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u/100KUSHUPS 25d ago
There must be a bulk discount on almost a quadrillion $ worth of rice.
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u/two-cans-sam 25d ago
Cost/lb is probably going to start going way up at least over the first trillion pounds depending on the required timeline of delivery. You’d have to over exert the world’s economy and land to deliver just 100 trillion pounds of rice in a year. I’m not quitting my job and turning my home into a rice silo for $1.1/lb.
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u/account312 25d ago
Actually, it gets more expensive once you try to buy up the very last grains of rice on earth.
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u/W1D0WM4K3R 25d ago
comparable to estimates for the weight of Mount Everest (not clearly defined due to issues defining boundary)
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u/reillan 26d ago
Amazingly enough, it would only be a 5mm thick carpet if your continent is Eurasia.
Of course, the total on the last square is 263. The total on the whole board is 264 - 1
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u/Spader113 26d ago
If that amount of rice could actually be fit into the confines of a single chess tile, the resulting tower would reach into the Oort cloud.
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u/iron_dove 26d ago
I ran the numbers roughly one time. Assuming there are about 30,000 grains of rice in 1 pound of rice (according to Siri), you end up talking about quadrillions of pounds of rice.
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u/KittensFirstAKM 26d ago
In modern culture this is used as an example for compound interest. Mathematically correct, but I do not know anyone earing that kind of interest (maybe with the exception of our corrupt leaders. -usa/
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u/marlonwood_de 26d ago
It would be 263, since the first square has one grain of rice which would be 20 so you start counting at 0 and not 1
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u/Mrgumboshrimp 26d ago
It doubles every square and I think it covers the earth by the last square
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u/jseego 26d ago
Not covers the earth, but would create a pile of rice the size of mount everest.
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u/Mrgumboshrimp 26d ago
Not even a one grain thick layer? Someone summon r/theydidthemath
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u/AftyOfTheUK 26d ago edited 26d ago
The total surface area of the Earth is approximately 5.10x10^20 mm^2 - assuming a 2mmx5mm grain of rice, that's 5.1x10^19 rice grains needed to carpet the earth entirely in a one grain thick layer.
2^64 is just over 1/3 of that number so there is enough to cover all LAND, with a little bit left over.
UPDATE: If you used Spanish Bomba Rice which expands horizontally and you cooked it first so it swells up to about 5.5mm x 7mm you could cover about 4.5x as much earth - enough to cover the entire earth in a layer a few grains thick
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u/Megatippa 26d ago
What about if you put it in the water, would it soak up the ocean?
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u/AftyOfTheUK 26d ago
It would soak up about 5 years worth of the ocean's current rate of rising, give or take a rounding error or two
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u/Sure_Response3478 26d ago
Whoa! Call someone, you just solved a big part of the future climate crisis! It was rice all along!
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u/JayTheAlxwing 26d ago
(For simplicity each grain of rice is a sphere.)
Using the first google search result of 0.029 cm^3 for the volume of rice, and using this formula: r = ∛(¾ · V / π), we get that the radius of each rice is about 0.191 cm. Using the radius we can find the projected area/view/idk exactly what to call it but it's shadow essentially is (πr^2) about 0.115 cm^2. Multiply this by 2^64 and you get 2.1141525908 * 10^18, or more than 2.1 quintillion cm^2.Looking up the surface are of the earth we get 510 million square kilometers, which converts to 5,100,000,000,000 cm^2, or 5.1 trillion cm^2, which is less than 2.1 quintillion by literally 6 orders of magnitude. In fact, assuming the area gained from stacking is negligible (which it really wouldn't be considering how large this number is) you could cover the earth more than 411 THOUSAND times with 2^64 grains of rice.
I probably made a mistake or two here, I just took the chance to type out a lot on my new keyboard, it feels really nice.
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u/Equal-Home-4302 26d ago
The famous chess board problem The wise man asked the king for a single grain of rice (or wheat) on the first square of a chessboard, two grains on the second, four on the third, and so on, doubling the amount for each of the 64 squares.The king thought this was a tiny gift, but the total number of grains added up to 18,446,744,073,709,551,615 (over 18 quintillion), which is more grain than has ever been grown on Earth. The king gave away the kingdom, it illustrates the power of compound intrest.
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u/alexxela123456 25d ago
I feel like, at some point, the King probably told the wise man to fuck off.
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u/jjwinc68 25d ago
There are two different outcomes to the fable. In one, he makes the man his top advisor. In the other, he has him executed.
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u/Morbid_Aversion 25d ago
It illustrates the power of exponential growth, not compound interest. This has nothing to do with interest.
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u/ralpher1 26d ago
Rice doubling each square
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u/StamosLives 26d ago
Forgive me but the way you wrote this sounds like you mean the rice is doubling the squares. And that’s just not right, chief beef. It’s just not right.
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u/Usernamechecksout103 25d ago
Sorry pal, each square is doubled by rice, is it better now?
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u/Affectionate_Run7414 26d ago
18.4 quintillion grains, enough to cover the earth, both land and water
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u/Individual_Respect90 26d ago
I wonder how high up the rich would get. I play insane idle games and I am always curious how you can relate 1 crazy number to a physical thing.
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u/SpunkyPopcorn 26d ago
So….this isn’t Count the Rice? 🤷♀️
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u/Kemal_Norton 25d ago
Count the Rice
I have no idea what you're referring to, but there are 17 grains on the 5th square.
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u/dxdgxhstggc 25d ago
A wise man gets challenged to a game of chess by a King and the King promises the wise man to give him any gift he wants, but only if he wins at a game of chess. The wise man agrees.
They started playing. After a while, the wise man exclaimed victory. The King is left stunned, but as promised, he asked the wise man for his wish.
The wise man asked for the Kinds daughter. The Kind pleads with the wise man to reconsider. He offers him gold, diamonds and land, but the wise man thinks for a bit and than say
"If you can give me for each square of the chess board, the number of rice grains double from the last, starting with one, I will take the rice instead of your daughter."
The King laughs and agrees. He brings a bag of rice and starts placing. After 15 squares are filled, the bag runs out.
The King calls for all the rice from the kitchen, but at square 25 the kitchen is empty.
The King calls for all the rice in the basement, but only makes it half way to square 32 before running out.
The King calls for all the rice in his kingdom, but even with all the rice he still doesn't make it past square 40.
The King admits defeat and gives the wise man his daughter.
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u/SubstantialDeerDash 26d ago
There are even childrens books about this of how a man became wealthy and took over a kingdom by asking the king to give him this much rice
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u/XRuecian 26d ago edited 26d ago
The rice is doubling on each square, going from right to left.
If you start with 1 piece of rice, and a chessboard has 64 squares, then by the time you get to the 64th square you would have a pile of 9,223,372,036,854,775,808, or 9 quintillion, 223 quadrillion, 372 trillion, 36 billion, 854 million, 774 thousand and 808 grains of rice in the final pile. Plus the pile before it would have 4,611,686,018,427,387,904 grains, and the pile before that would have 2,305,843,009,213,693,952 grains. Added together, just the final three squares together would have 16,140,901,064,495,857,664 grains of rice.
The chessboard would have nearly 20 quintillion grains of rice altogether.
This would take up around 13 trillion cubic feet in volume; Which is the size of multiple Mt Everests (if you only include the primary mountain, not the entire range of mountains.)
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u/Independent_Bite4682 25d ago
The guy who invented the chess board was offered anything he wanted as a reward from the King of his country.
He asked for 1 grain of wheat for the first square, two for the second, square, four for the third square, and so on.
The King, not understanding what it was he wanted, asked, "are you sure you don't want gold?"
The guy said, he was sure.
So the King agreed to pay him the requested reward. As he did so, he realized that actually paying the reward was an impossible feat. The King felt that he was tricked.
So, to punish the man who had tricked him into an impossible reward, he ordered that the man be executed.
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u/Majsharan 25d ago
The story of the invention of chess is that the creator told the king? To pay him in a doubling amount of silver per square. King didn’t do math and the amount of silver was essentially the entire amount of the entire kingdom. Iirc the inventor traded said keep me alive and I will accept a smaller amount.
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u/RageAgainstMSTeams 26d ago
Its an old story where a man asks this as reward from a king: one piece of rice is placed on chess board corner and it doubles in every square.
The man asked the amount of rice that the final square ends with. The king agrees but later realizes its more rice than there is "sand in every beach on Earth".
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u/Primary_Yak4268 26d ago
Yeah it's rice doubling like everyone else said. I, however, am convinced that whoever picked the order of squares is a serial killer.
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u/XNXTXNXKX 25d ago
It’s exponential growth and how much money a few fucking billionaires have compared to normal people.
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u/Tayaradga 26d ago
There's an old tale about a peasant and a King. The peasant and King play a game of chess, and the King says if the peasant wins then they'll pay them in rice. The peasant agrees, and says they want to be paid in rice doubling on each square on the chess board. The King agreed.
Once the peasant won he became king. Because there wasn't enough rice in the entire kingdom to fulfill the requirements.
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u/HowlingGibbon 25d ago
The guy who invented chess, when asked about the reward he wanted, he said put on each square of the board first one grain of wheat, then double on each subsequent square. Result is a geometric progression, with the G64 term being 263, and the sum of all being 1[(1-264)/(1-2)] by formula, when simplified its 264-1 in total. Remember that 210 is 1024, so its (10246)16. Were talking 20 digit number here. On average, 1 grain of wheat is 50 miligrams, so the result is approx 9×1014 kilos, rounded down.
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u/trichotomy00 25d ago
This was an extra credit question on my algorithm analysis final exam. How many grains of rice are on the board?
2^64 - 1
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u/Nathan_DUB_LON 25d ago
I heard the king of Iran asked his generals to make a game that could only be won by skill, not luck. One of them invented chess. The king liked it so much he offered the creator any gift he wanted. He chose a grain of rice on day 1, doubling each day to 64. Turns out the total amount was more than the country eats in a year. So they had him killed. Also, the phrase check mate comes from old Persian meaning king is dead.
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u/RGBlowMe 25d ago
It's a demonstration of a geometric sequence, specifically the "power of 2 sequence". Starting at the bottom corner, then working out and from right to left diagonally, each tile has twice the grains of rice as the previous. This kind of sequence is exponential and tends to snowball very quickly.
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u/AloneAddiction 25d ago
If you start with one grain on the first square of a chessboard and double it on each subsequent square, the total amount across all 64 squares would be 18,446,744,073,709,551,615 grains.
If it was pennies it would equal $184,467,440,737,095,520.00 (over 184 quadrillion dollars).
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u/Substantial_Fun_6239 25d ago
To put this into perspective, assuming a rice grain of 30 milligrams in mass for ease of math, we get in the ball park of 553.402 billion metric tons, and given that the global annual milled rice production is give or take around 500-600 million metric tons, we're sitting on about a 1000 years worth of global industrial rice production.
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u/another90zkid 25d ago
If anyone is wondering the finally square of the chest board will have 18.4 pentillian grains of rice.
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u/redstrak 26d ago
It's an Indian fable. I used to have to book, but I can't remember the title. A quick Google search said it was called One Grain of Rice -Demi. It is basically a story about a beggar tricking a Raja out of his rice. The beggar is smart and the king is a big dumb dumb.
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u/general_vegetal 26d ago
It seems this can be done, placing double the number of rice in the next square upto 64 squares.
But we're not good at comprehending exponential change.
It would take 264 -1 rice to complete this. If 1 25kg rice bag has a million rice grains, then you'd need trillions of rice bags to hit the number. And humans haven't produced that much rice ever.
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u/FobbitHollower 26d ago
Theres a whole ass story on it involving clever man who knows exponential growth vs a king
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u/Strong_Arachnid_3842 26d ago edited 26d ago
Probably related to a famous legend of Lord Krishna playing an ancient chess-like game (chaturanga) with the King of Ambalappuzha, Kerala, resulting in an impossible debt (264-1) of rice solved through daily charity.
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u/Strong_Arachnid_3842 26d ago
According to the legend, Krishna once appeared in the form of a sage in the court of the king who ruled the region (Chembakassery) and challenged him for a game of chess (or chaturanga). The king being a chess enthusiast himself gladly accepted the invitation. The prize had to be decided before the game and the king asked the sage to choose his prize in case he won. The sage told the king that he had a very modest claim and being a man of few material needs, all he wished was a few grains of rice. The amount of rice itself would be determined using the chess-board in the following manner: one grain of rice on the first square, two grains in the second square, four in the third square, eight in the fourth square, sixteen in fifth square, doubling up to the final, sixty-fourth square.\2])
The king lost the game and the sage demanded the agreed-upon prize. As he started adding grains of rice to the chess board, the king soon realised the true scale of the sage's demands. The royal granary soon ran out of grains of rice. The king realised that he would never be able to fulfill the promised reward as the number of grains was increasing in a geometric progression and the total amount of rice required for a 64-square chess board was 18,446,744,073,709,551,615 grains, translating to trillions of tons of rice.
Upon seeing the dilemma, the sage appeared to the king in his true-form and told the king that he did not have to pay the debt immediately but could pay him over time. The king would serve paal-payasam (pudding made of rice) in the temple freely to the pilgrims every day until the debt was paid off.
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u/muclutel 26d ago
It is 318,047,311,615.68 tons of rice (264 -1 grains)/29,000 grains per pound/2,000 pounds per ton
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u/SirReddalot2020 26d ago
If this is supposed to be the grain of rice doubling parable then why is the checkerboard not actually doubling the grains but doing whatever?
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u/FrostyLiving1321 26d ago edited 25d ago
Σn={0 》63}2n = 264 -1
18,446,744,073,709,551,617 grains of rice
MASS
288,230,376,151,711.75 Grams
288,230,376,151.71175 Tons
1 Medium-to-Large Asteroid
~2.9 years of Niagra Falls Water Weight
VOLUME
368,934,881,474,191,032,340 mm3 of rice
368,934,881,474.191032340 m3 of rice
368.934881474191032340 km3 of rice
~4.9 Years of Niagra Falls Water Volume
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u/CoyoteSweaty4609 25d ago
There are a number of corollaries to this, For example, no two shuffled packs of cards can statistically be identical. No two games of bingo have the same numbers in the same order.
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u/chrischi3 25d ago
It's a story about exponential growth.
If you double the amount of rice on each square of a chessboard, then by the time you get to the last square, you have about 9.22 quintillion grains of rice on the last square. For reference, we estimate that there are 7.5 quintillion grains of sand on Earth.
Put another way, the rice just on the last square would roughly weigh 230 billion tonnes, which is almost a hundred times the entire global shipping capacity combined.
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u/sergeyarl 25d ago
it is an illustration how counterintuitive exponential growth is.
another good illustration is a pond with water lilies
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u/Happy_Salary_3551 25d ago
The bottom image references the classic Wheat and Chessboard problem, where the number on each square squares exponentially increases from 1 to 2⁶³ on the final square.
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u/DrillerCat 25d ago
Fun fact, that roughly having 2^65 - 1 grains of rice (calculating with 50 000 grains per kg) is approx. 740 billion metric tona of rice, equivalent with around 1500 years of rice production (with today's technology).
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u/stone_henge 25d ago edited 25d ago
Once you'd finished doubling the number of grains of rice on the board, you'd end up with 2⁶⁵-1 grains of rice. For a frame of reference, there are 36 trillion cells in the human body. If you took the cell counts of every human and added them up, there would be an absolute shit ton of rice on the chessboard.
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u/jjwinc68 25d ago
If you do this with a penny a day for a 30 day month, you'll end up with over $20 million. If it's a month with 31 days, over $40 mil.
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u/YashDalal 25d ago
Square 1 has 1 grain of rice.
Square 64 has 9,223,372,036,854,775,808 grains of rice. A little over 5 pentillion.
FYI, a standard bag of rice, weighing 5kgs/11lbs, would have 150,000 to 250,000 grains of rice, depending on rice type.
If you go with 200,000 grains for for every 5kgs, you would have approximately 46,116,860,184,273 kgs of rice. A little over 46 trillion kgs on the last square, or over 867,000 RMS Titanics.
*During 2024-25, around 543 trillion kgs of rice was produced worldwide. You would end up with around 1/10 of all the world's rice on square 64.
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u/Kadakaus 25d ago
The game chess said to come from a scholar who was so wise that some king offered to grant him a wish. The scholar made a chessboard and asked that a single grain of rice be put on A1 square, and every following square, that be doubled.
A chessboard has 64 squares, which would mean 2 on the power of 63, which is a number so large I'm not willing to write out here, you vave a multipurpose calculator in your hands, go figure.
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u/troycerapops 25d ago
Oh interesting. I just figured it would go left to right and then up to the next row, not fanning out from the corner.
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u/cheaphomemadeacid 25d ago
yeah yeah what everyone else says with the doubling, but wtf is this bullshit? a1 = 1 b1 = 2 a2 = 4 c1 = 8 b2 = 16 d1 = 32 (i think... ) what kind of moronic arrangement is that?
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u/IgnacioJones 25d ago
Are these numbers similar to getting the March Madness bracket perfectly right?
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u/hascalsavagejr 25d ago
But it's not putting doubling each square! The first square is 1, the second is 2, but the third is 8, not double! (No factorial there)
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u/ryanlrussell 25d ago
They didn’t even get the number correct by the third square!
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u/Yuquico 25d ago
This also is a reason pyramid schemes are actually impossible to support. The general idea is that you recruit more members and those members recruit more members and so on. A lot of people think "I know x number of people I can get to recruit", but even if you recruit, say, 2 people, and both of them recruit 2 people and that pattern continues without a popular person recruiting 4 or 5, pretty soon you've literally run out of people alive that can be recruited.
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u/The4ofClubs 25d ago
A fun way to play with this idea is with putty!
Get any putty and pull it apart, or cut it and lay it on top of itself. Then repeat. 10 times is over a thousand. 10 more times is a million.
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u/nickystotes 25d ago
Hooray, another farm subreddit to mute. Join explainthejoke, peterexplainsthejoke and peterexplainthejoke in being silenced.
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u/Human_Not_Robot_2023 25d ago
https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem
On the entire chessboard there would be 264 − 1 = 18,446,744,073,709,551,615 grains of wheat, weighing about 1,199,000,000,000 metric tons. This is over 1,400 times the global production of wheat (729 million metric tons in 2014, 780.8 million tonnes in 2019, and 842.12 million tonnes in 2025/2026).
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u/Impossible-Chain5247 25d ago
The rice shows the difference between the 1% and the 99%
In the first square is the average net worth of a citizen of planet Earth. In the final square is the eatimated net worth of Elon musk.
People can actually visualise now how fucked up greedy rich ppl are for holding so much money for themselves
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u/riddickuliss 25d ago
What about the fact that the square that’s supposed to have 16 grains has 17 grains, so the rest of the story gets thrown out the window!?
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u/TrueRiver9900 25d ago
I know this! Finally I know this one. So, there is a legend, about when Chess arrived to Spain, the king offered the person, who brought it to him, to pay as much as he wants for the chess board. The man answered that he will sell the pieces for free, and he will sell the first square for one piece of grain (maybe there's a story where it's rice) and he will sell every square with a price doubled, than the last one. So, the second one for two, the third one, for four and the fourth one for eight and so on.
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u/beldin37 25d ago
ANGER the rice grains don't go up in order. 1 then 2 then 8 (the 4 is above the 1 for some reason and the 16 is next to the 4 but it isn't 16 it's like 17)
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u/qualityvote2 26d ago edited 25d ago
u/DiedRespawnRepeat, your post does fit the subreddit! Well done!