anybody knows how to answer the rest of the chessboard tale? thanks:p it's
By lonely_f16
@lonely_f16 (2146)
Philippines
September 22, 2007 12:40am CST
difficult
An old tale tells of a Ruler in an ancient Asian country who was tricked into paying for a favor as follows. The ruler was to play by placing one grain of rice on the first square of a chessboard, two on the next square, four on the next square, eight on the next square and keep doubling like this until all 64 squares had been dealt with.
The ruler thought this might take a few kilograms of rice--perhaps even a tonne--but surely not more than that!d. For one brand long-grain rice (uncooked) about 250 grains occupy 5mL. What volume of rice has to be placed on the 7th, 10th and 20th square of the board?e. Imagine that the ruler is still not too worried when he sees that about 10L of rice has to be paid on the 20th square as he thinks this means that about 20L will be paid on the 40th square. Is he correct? Is the Ruler even close? Check with your calculator. How many mega liters of rice will be required on the 40th square?thank you once again...
1 person likes this
1 response
@stvasile (7306)
• Romania
24 Sep 07
The answer to this problem seems to lie in the powers of 2.
The n-th square has on it 2*2*2*...*2 (n times) grains.
This means than on the 7th square there will be 2^7 grains (2^7 means 2*2*2*...*2, 7 times), which is 128 grains, about 2.5 ml.
On the 10th square: 2^10=1024 grains, that occupy 20.48 ml.
On the 20th square: 2^20=1024*1024= 1 048 576 grains, that occupy 20 971.52 ml = 20.97 liters
On the 40th square: 2^40= 1 099 511 627 776 grains, that occupy about 21 990.23 mega liters.
The total to pay for square 40 is not two times that on square 20, it's 2^20*the number of grains from the 20th square.
