Talk:Wheat and chessboard problem

Untitled

Article merged: See old talk-page here -Btyner (talk) 03:38, 30 March 2008 (UTC)

The right sum is $\sum _{i=0}^{63}2^{i}$, and not $\sum _{i=1}^{63}2^{i}$. The rest is ok. Another Wikipedian 04:31, 29 September 2006 (UTC)

I think I got it right now, sorry for the cock-up :) Steevm 04:43, 29 September 2006 (UTC)

Caesar should have used a higher multiplier than 2. Although I'm sure he didn't expend the general to be able to carry 262 kilos!—Preceding unsigned comment added by 207.38.160.124 (talk) 06:29, 10 December 2006

If you write it in python you can see the number is 9223372036854775808:

x = 1 s = 1 print(x) while x < 64:

   s = s * 2
   print(s)
   x += 1  — Preceding unsigned comment added by 189.12.39.240 (talk) 10:58, 8 October 2018 (UTC) 

Total number of grains looks wrong

It's given as "On the entire chessboard there would be 2**64 - 1 = 18,446,744,073,709,551,615 grains". But iinm 2**64 is the number of grains on the last square, not the sum of the grains on all squares. 71.174.160.138 (talk) 20:54, 1 January 2011 (UTC)

No, you're wrong. It's easy to make that mistake by getting goofed up by the numbering system starting at 1, instead of 0 which is correct in this binary progression. The first square is 2^0 not 2^1. So the last square contains 2^63 grains of rice. This makes the total 2^64-1. Look at it this way. If there were only 3 squares, the numbers of rice would be:

1

2

4

or

2^0

2^1

2^2

...which all add up to 7, or 2^3-1.

Tgm1024 (talk) 23:39, 1 April 2011 (UTC)

2022

1 2 4 then at then total will be 9,223,372,036,854,780,000.00 at 64th Square 178.80.157.6 (talk) 15:29, 20 July 2022 (UTC)

A power of 2 can't be divisible by 10,000. I think that your calculator doesn't have enough significant digits... AnonMoos (talk) 15:37, 20 July 2022 (UTC)

proposed merger

The proposed merger does not seem helpful to me. The "Wheat and Chessboard Problem" is well established, as noted in the article/stub by that name, as an example of the power of exponential growth. Its relation to a particular legend about the origin of chess is irrelevant to me for research or reference: any combination of ruler and sage, ruler and dupe, or capitalist and dupe will do; they all illustrate equally well that to undervalue exponential increase is foolish. Best to all, MIchael 08:03, 26 April 2007 (UTC)Douglas Michael Massing

• I see no reason to merge this article, so I will remove the notice.—Preceding unsigned comment added by Voorlandt (talk • contribs) 16:08, 9 June 2007

volume of total amount of grains of rice

There doesn't seem to be a given the volume for the total amount of rice:

I make it about 9 cubic kilometers of rice, assuming that one grain of rice is 2 cubic millimeters

18,446,744,073,709,551,615/(2*(1000,000^3))=9.22(rounded) cubic kilometers

Would someone check this and then add it to the main page? maybe someone knows the average size, when it bags, of a grain of rice....

I think that this is visually more impressive.

Jellyboots (talk) 14:51, 16 August 2008 (UTC)

sorry it was 18446744073709551615*2mm/(1000000^3)=36.8934881 km^3; I put the 2 in the wrong place.

anyway I went ahead and added it. Jellyboots (talk) 22:59, 7 September 2008 (UTC)

1. 1. I took the freedom to fix your equation (changed 18446744073709551615 to 9223372036854775808) —Preceding unsigned comment added by 90.220.114.159 (talk) 16:48, 8 May 2010 (UTC)

Statistics for rice

Based on 54 grains of rice per gram, the whole chessboard comes to 340 billion metric tonnes. The world rice consumption is 432.039 million tonnes (International Rice Research Institute [1]), making the chessboard 787 years worth of the world’s consumption of rice. The value of the rice at US$500 per metric tonne (Index Mundi [2] ) is Trillion US$ 171. That's over 2.3 times the annual GDP of the entire world (Trillion US$ 74, IMF 2010 [3]).

References: [1] http://beta.irri.org/solutions/index.php?option=com_content&task=view&id=250 [2] http://www.indexmundi.com/commodities/?commodity=rice&months=60 [3] http://en.wikipedia.org/wiki/List_of_countries_by_GDP_(PPP)

Swazi69 (talk) 12:37, 19 February 2011 (UTC)

Computer Program way of solving

I suggest there must be a section that discusses solving the problem through a computer program. I myself wrote a program in Just BASIC for the problem which gave the exact answer. I also tried the problem in Javascript and found that it gives only an approximate answer. Must I start a section and include my findings?? I think it would be most appropriate to do that as this problem is astronomical to be solved by hand or even a calculator. Any ordinary calculator will not have those many digits. jinjanjaa (talk) 10:06, 24 December 2011 (UTC)

It's just a calculation. (So I don't "get" why, even in the article, it's referred to as "problem".) Anyway, can't Javascript to simple mutiplies that gradeschool kids can do?! And why would a computer program that does multiplies, be of any interest and a "must"? I must be missing something. Ihardlythinkso (talk) 12:36, 24 December 2011 (UTC)

I get the "Which would you rather have?" making it a "problem". But the calc isn't difficult or even "math" - it's simple arithmetic! Ihardlythinkso (talk) 21:15, 24 December 2011 (UTC)

Javascript rounds of all the values from 2⁵⁵ onwards, to the nearest multiple of 10. I don't know why but it does that. For eg: 2⁵⁵ is 36028797018963968 but Javascript gives out the value as 36028797018963970. Do you see the last two digits rounded off?? It does that same thing for all the values so the final answer comes to 18446744073709552000 instead of 18446744073709551615 (last 4 digits rounded). And as for why this inclusion is needed, I am not this problem is impossible to solve by hand. It is only difficult to calculate all the values up to 2⁶³ and add up. Instead of, what I reckon would take more than 1½ hours to solve manually, it would take only 5 minutes using a program. Also, if we include the information in Wikipedia, many people who see it can copy the code and try it out themselves. I believe it would be useful for someone out there. — Preceding unsigned comment added by Jinjanjaa (talk • contribs) 12:57, 25 December 2011 (UTC)

It seems to me what you have discovered is a Java s/w bug. The programming complexity of this calc, IMO, would possibly qualify it for a classroom assignment in "Computer Programming 101". (It's just a simple loop!) Ihardlythinkso (talk) 21:45, 25 December 2011 (UTC)

Someone just tell me whether or not its apt to include a section for it. I don't want it to be removed once added. Tell me whether Wikipedia will accept it. jinjanjaa (talk) 12:24, 27 December 2011 (UTC)

My !vote is no, that it adds nothing material. (I "programmed" this in 2 minutes on a 3x5 card. So what?!) Ihardlythinkso (talk) 12:29, 27 December 2011 (UTC)

Anyone else's vote apart from Ihardlythinkso's??? jinjanjaa (talk) 15:12, 27 December 2011 (UTC)

The only reason to add a programming section to a wikipedia article is if it casts new light on the topic of the article itself. (Such sections are very rare, for that reason.) Since there seems to be nothing interesting or worthwhile in programming this very straightforward problem, I do not think it should be added. - DavidWBrooks (talk) 17:33, 27 December 2011 (UTC)

Why am I still not convinced??? jinjanjaa (talk) 06:02, 28 December 2011 (UTC)

Dead link

Removed from article (in reference to India's annual rice output) Sparkie82 (t•c) 13:19, 16 March 2012 (UTC)

References

To do list

1. Rename the "Origin of the problem" section (don't repeat title words in sections).

Done Sparkie82 (t•c) 04:13, 17 March 2012 (UTC)

2. Create a "solutions" section with proofs, or example, a proof for the 2⁶⁴ - 1 solution.

Started -- still needs a proof. Sparkie82 (t•c) 04:13, 17 March 2012 (UTC)

3. Move formulas and nontrivial solutions to "solutions" section. (Although WP has a "no spoiler alerts" guideline, putting them in the solutions section would be courteous. (The guideline actually mentions section titles as intrinsic warnings when explaining support for the guideline.) Also, there is a guideline that says that formulas should not be in the lead whenever possible, especially in an article like this with a lot of beginner readers.

Done Sparkie82 (t•c) 04:13, 17 March 2012 (UTC)

4. Add a "derivative problems" section (e.g., how much would it weigh?; how big would the chessboard need to be?, etc.)

I used the word "derivative" in the article to mean problems derived from the original problem, but I think readers will confuse it with calculus derivative, so it needs to be changed. Sparkie82 (t•c) 04:13, 17 March 2012 (UTC)

5. Expand the lead to mention: pedagogical applications, invention of chess story, variations and derivatives, second half of chessboard. Sparkie82 (t•c) 23:22, 16 March 2012 (UTC)

1. mathworld.wolfram.com (at least) mentions Mersenne number :$M_{p}\,$. Also might be added here for $p=64\,$, which is of course not ~ prime. Hm, are there sensible solutions for chessboards for all Mersenne numbers at all? I should better ask - solutions for squared chessboards. Yes there are, and for example number of grains for 1×1, 2×2, 3×3, ... 10×10 chessboards ($0^{2},1^{2},2^{2},3^{2},\cdots 10^{2}\,$) are: 1, 15, 511, 65535, 33554431, 68719476735, 562949953421311, 18446744073709551615, 2417851639229258349412351, 1267650600228229401496703205375. Otherwise chessboards are not squared. --xJaM (talk) 17:37, 6 June 2012 (UTC)

Variations

I have been bold, or perhaps reckless, in editing and have removed the section labelled "variations" - I was going to clean it up, but it had three versions virtually the same as the original problem (gold instead of wheat, days instead of chessboard, etc.) but without any sourcing at all - plus one that was wildly unrelated (paper folding/tearing), and IMHO added nothing to the article. So I killed it. - DavidWBrooks (talk) 17:08, 18 July 2012 (UTC)

Nothing to do with chess

This is a mathematics article, not a chess article. I will take the liberty of removing it from wikiproject chess. MaxBrowne (talk) 01:21, 26 March 2013 (UTC)

Origin

I have removed the following, as a source claims otherwise:

It may also be contained in the Shahnameh, an epic poem written by the Persian poet Ferdowsi between c. 977 and 1010 CE.

If we can find a source that confirms this, it can be restored. HGilbert (talk) 13:03, 4 May 2016 (UTC)

Pedagogical application

I have now reverted this section twice and a fuller explanation is in order. I have mentioned in my edit summary that this material is unsourced. The response to that was a link to WP:BLUE. Well, WP:BLUE is an essay (that I fully agree with) but it is not policy; policy is contained in WP:NOCITE. The section started by claiming that this problem "can" be used to say something about complex questions, however I see nothing in the rest of the section that supports that claim and the section reads like an opinion piece. A citation that showed that someone actually uses this problem in that way would allay my suspicions about this being some editor's OR opinion. What I found unencyclopedic about the section was not its intent but rather its presentation. It was a bit too "folksy" with a definite "engineers have a better understanding of the real world than mathematicians do" POV. And finally, the argument had a glaring error. To say that that amount of rice (or grain) could not fit on a chessboard presupposes something about the size of the chessboard! If this mountain of rice were the size of Mt. Everest, then a chessboard the size of Nepal would probably work. If you're going to be ridiculous, why take half measures? --Bill Cherowitzo (talk) 05:41, 2 March 2017 (UTC)

No assertion that "engineers have a better understanding of the real world than mathematicians do" was made in the slightest; mathematicians were never mentioned at all. It was not presented as a pissing/ego contest between vocations at all. What it said was that engineering requires common sense as well as mathematics, which is both true and blue. Nothing about the text was ridiculous at all, but I must admit that the introduction of ridiculousness with the point that a chess board the size of Nepal was not ruled out is ridiculously clever, and technically correct, which, as a Futurama joke about bureaucrats had it, is the best kind of correct. What's most ridiculous of all is that the Wikipedia article about fitting an Everest-sized mountain of rice on a chessboard would not say anything anywhere in the article about whether it would even fit, instead conveying a tone throughout that its fitting is assumed. True that fixing that weakness would be a chance to touch on the topic of the size of the chessboard as its own presupposition. That's a good idea. If I take the time to return to this content development, I'll address that. WP:BLUE still applies to the whole theme. Quercus solaris (talk) 06:11, 2 March 2017 (UTC)

Please, no strawman arguments. I did not claim that you said that, all I did was provide a descriptive name for a POV that I inferred from the tone of the passage (note the quotes!) I have no way of knowing whether this was or wasn't intentional, but assuming good faith, I'll assume it wasn't. If I picked this up from reading the passage then others will as well and this is a sign that the passage is not written from a neutral POV. To take a fable, interpret it as a real-world problem and then criticize it for not being realistic is pretty much my definition of ridiculous. If you take the two items in the "usage" section and said that they could be used in that way and left out the references, I would object on exactly the same grounds. In that case, the statements would be super-obviously true and WP:BLUE would still not apply. The reason to include these statements in the first place is that they have been used in the manner indicated and the citations show that this is the case. Without such grounding to the secondary literature, editors would be able write anything that their fertile imaginations could come up with and Wikipedia would be no different than the thousands of blogs running around the internet. --Bill Cherowitzo (talk) 21:30, 2 March 2017 (UTC)

Rice?

It is absurd that an article entitled WHEAT and chessboard problem should give its outputs in terms of rice. How did that happen, and why do editors think that inconsistency is appropriate? Plantsurfer 11:19, 2 March 2017 (UTC)

I assume it happened because the puzzle is often also expressed in terms of rice. No objection to recasting the "India's annual rice output is about 1,200,000 times that amount" stuff in terms of wheat if you want to dig up the numbers. --McGeddon (talk) 11:27, 2 March 2017 (UTC)

Minor inconsistency

In the lead we are told:

"The total number of grains can be shown to be ... over 1.4 trillion metric tons."  ... "which is over 2,000 times the annual world production of wheat, which in the period 2020-21 was an estimated 772.64 million metric tones."

In the section headed: "Second half of the chessboard" we are told:

"On the entire chessboard there would be ... about 1,199,000,000,000 metric tons." ... "This is about 1,645 times the global production of wheat (729,000,000 metric tons in 2014 and 780.8 million tonnes in 2019)" 

Now I can see that the two passages cite different refs, and refer to different years for the annual figures, but it's not a good look.

(Anyway, I can only think of volumes, and then in terms of Olympic swimming pools, so ... meh._{(this bit is a joke)})

Wayne 07:18, 13 October 2021 (UTC)

Doubling Penny Total Wrong and References Broken

2^(30-1) in pennies is $5,368,709.12, not over 10 million dollars. -- Preceding unsigned comment added by 98.21.245.40 (talk) 14:18, 3 April 2022 (UTC)

You used the wrong formula. 2^30-1 = 1073741823. Plantsurfer 14:26, 3 April 2022 (UTC)

Hi, Please correct the Maths

at 32 Square Total Rice will be 2,147,483,648.00 & at 64 Square Total Rice will be 9,223,372,036,854,780,000.00 Because in 1st Square its 1 Rice and Then Double and so on...(Arslan Email: ashoukat1988@gmail.com)

• Correction in 178.80.157.6 (talk) 15:21, 20 July 2022 (UTC)

First off, the ".00" is quite irrelevant, since by the nature of the problem all numbers are integers. Secondly, the cumulative number of grains of rice up to a particular square is one less than a power of 2 (i.e. 1, 3, 7, 15, 63 etc), so the number can't be even... AnonMoos (talk) 15:33, 20 July 2022 (UTC)