(a) According to a well-known legend, the game of chess was invented many centur
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Question
(a) According to a well-known legend, the game of chess was invented many centuries ago in northwestern India by a certain sage. When he took his invention to his king, the king liked the game so much that he offered the inventor any reward he wanted. The inventor asked for some grain to be obtained as follows: just a single grain of wheat was to be placed on the first square of the chessboard, two on the second, four on the third, eight on the fourth, and so on, until all 64 squares had been filled. If it took just 1 second to count each grain, how long would it take to count allthe grain due to him? (b) How long would it take if instead of doubling the number of grains for each square of the chessboard, the inventor asked for adding two grains?Explanation / Answer
A)
First square – 20 = 1 grain
Second square – 21 = 2 grains
Third square – 22 = 4 grains
Fourth square – 23 = 8 grains
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.
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64th square – 263 = 9223372036854775808 grains
Therefore, the total grains are = 20+21+22+23+24+25+…….263.
Which is equals to 264-1 grains.
If it will take 1 second to count 1 grain, then it will take 264-1 seconds to count all the grains.
Which is equals to 58,494,24,17,355 years.
B)
If inverter asked to add 2 grains in every square, then
1st square – 2 grains
2nd square – 2 grains
3rd square – 2 grains
.
.
.
64th square – 2 grains
That is 2+2+2+ . . . +2 = 64*2 = 128 grains
If 1 second to count 1 grain, then it will take 128 seconds to count all the grains.
Which is equals to 2 minutes and 8 seconds.
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