Talk:Second Half of the Chessboard

Currently this page reads: The term is derived from the fable of an ancient Indian mathematician who according to the fable invented the game of chess. The emperor of India is so pleased with the game that he tells the mathematician he may have anything in his kingdom he wishes. The mathematician replies that he only asks for a meek amount of rice placed on the squares of his chessboard: one grain of rice on the first square, two for the second, et cetera. Each successive square would have grains of rice double the number of the prior square until all 64 squares of the chessboard have had their said amounts.

I feel that it would be better if it read: The term is derived from the fable of an ancient Indian mathematician who, according to the fable, invented the game of chess. The emperor of India was so pleased with the game that he told the mathematician that he could have anything in his kingdom that he wished to have. The mathematician replied that he only asked for a meek amount of rice placed on the squares of his chessboard: one grain of rice on the first square, two for the second, et cetera. Each successive square would have grains of rice double the number of the prior square until all 64 squares of the chessboard had had their said amounts.

This is because of my grammatical prejudices- would anyone feel this to be wrong? Grant McKenna 09:42, 7 November 2006 (UTC)[reply]

2⁶³ -1 is accually the ammount of rice on the last square. In order to add up all the squares one needs to use a sigma notation. $\sum _{x=0}^{63}2^{x}$ . Because of this all the large numbers on this page are incorrect. CheatTheDevil 12:42, 27 December 2006 (UTC)

No, the amount of rice on the last square is 2⁶³. You have to realize that it has to be a power of two, and as such, it cannot be an odd number, which 2⁶³ - 1 is. The total number of rice is, as you correctly claim,

\sum _{x=0}^{63}2^{x}

which happens to be 2⁶⁴ - 1 = 18446744073709551615. rado 09:50, 28 December 2006 (UTC)[reply]

I just changed the page to correct the mass of the grains of rice which were a factor 1000 too high. Measurements yielded a value of 17mg/grain, close enough to the quoted value on the Rice Science web page. I did not control the rice production in India, but just edited it assuming the previous estimate was correct given the calculation at hand. Daccy 10:41, 15 February 2007 (UTC)[reply]

Yes, the amount of rice on the last square is 2⁶³. The amount of rice on the 1st square is 2⁰, on the 2nd it is 2¹ ... and on the 64th it is 2⁶³. But something is wrong: it says that the total number of grains of rice on the second half is 2⁶⁴ grains and the total number of grains on the entire board is 2⁶³ -1 grains of rice. This can't be right. I've changed the text to read that the total number of grains of rice on the second half is 2⁶⁴ - 2³² grains and removed the parentheses.— Preceding unsigned comment added by 85.139.119.41 (talk) 22:21, 9 March 2007

Actually, I've just realized it said that it is APPROXIMATELY 2⁶⁴. My mistake, sorry. But I think that was a bit confusing, albeit correct, and irrelevant given the precise number was given just after that.— Preceding unsigned comment added by 85.139.119.41 (talk) 22:32, 9 March 2007