the chessboard tale...please help me...math again...
By lonely_f16
@lonely_f16 (2146)
Philippines
September 18, 2007 11:02pm CST
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!
a. Complete the table up to the 6th square on the board..
No of squares on the board 0 1 2 3 4 ...
No of rice grains 0 1 2 4
b. Complete the equation to describe the number of grains, y, that would be placed on the nth square of the chessboard:
y=________
c. Use the equation to find how many grains go on the 7th, 10th, and 20th squares of the board.
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 for answering if ever...it's too difficult for me...it's a math problem
2 responses
@anshul_datsme (70)
• India
23 Sep 07
for part 'd'
first we find the noof grains in the 7th,10th,20th square.
let it be m for 7th square,n for 10th and o for 20th square.
so total grains are m+n+o
got it!!!
let this total no of rice grains be say 'r'
that means r=m+n+o
now the imp part yet simple part
250 grains = 5 ml
1 grain = (5/25) ml that comes out to be (1/5) ml.
for r no of grains = r*1/5
and thus the answer
hope u get it
1 person likes this
@anshul_datsme (70)
• India
19 Sep 07
here r ur answers.hope they are correct.
a)block no of grains
1 1
2 2
3 4
4 8
5 16
6 32
b)1*2^(n-1)
(one)multiplied by((two)raised to power(n-1))
hope u get it
c)2^6,2^9,2^19
d)20995 ml
give other ans later
do comment if above ans are correct
1 person likes this
@lonely_f16 (2146)
• Philippines
20 Sep 07
thanks...as far as i know your answer in letter a is correct but I'm not sure about the rest...may I ask? how did you get the answer in letter d? is it the volume for all the three asked? is n there the x values in your equation? thanks a lot! and hope you'll not be tired ^_^
