math twisters 2? rice and weights....

[smacker124]

Heres another problem that I am working on, any help is appreciated:

 

Once upon a time, Paul invented a board game. The king was so happy with the game that he offered Paul his weight in gold.

 

Paul said he did not want the gold. Instead Paul asked for rice.

 

Paul said to the king:

"Please put 1 grain of rice on the first square of my board game, 2 grains of rice on the 2nd square, 4 grains of rice on the 3rd square, 8 grains on the 4th square, and so on until the 36th square is filled."

 

"Just give me the rice on the 36th square" said Paul.

 

Compare the value of the quantity of rice on the 36th square with the value of Paul's weight in gold.

 

You will need to know that:

-Paul weighs 75 kilograms

-1 kilogram = 1,000 grams

-1 gram of gold is worth $12

-4 grains of rice weigh 1 gram

-1 kilogram of rice costs $1

 

Which quantity was worth more, Paul's weight in gold or the amount of rice on the 36th square? Compare the values, showing how much greater one value is than the other.

 

 

---------

What I got so far, from a few days of thinking and working.

 

36th square = 34,359,738,368 divide by 4 = $858,993,459

Paul's Weight in gold = $900,000

 

I'm not sure that the solution that I came to is correct. Any help is appreciated.

[neo007]

how did u get 36th square = 34,359,738,368?

i've tried to work it out, but i get something complete different. But i'd like to know how you got 34,359,738,368

[JaKiri]

2^35.

 

It's astronomically big.

 

Not quite as big as 2⁶⁴-1, which is the answer to a similar puzzle thing.

 

 

Edit: fixed tags - RadEd

[wolfson]

Scroll down.

[JaKiri]

wolfson said in post # :

Apply the Geometric Progression equation:

 

Sn = a (1 – r^n) / 1 – r

 

Sn = 1 (1-2^36) / 1 – 2 = 6.872e10

 

That's incorrect. The question clearly states ONLY the 36th square is counted, not those that preceed it. Furthermore, it's fairly trivial to demonstrate that the sum of the first 36 squares is 2³⁶-1, and this is merely complicating the matter.

[wolfson]

A bit more lol.

[wolfson]

Hello again,

 

Apply the Geometric Progression equation:

 

tn = ar^n-1

 

a = first term, n = value as a integer and r = common ratio

 

tn = 1*2^(36-1) = 3.436e10

 

3.436e10 / 4 = 8590000000 (into g’s)

 

8590000000 / 1000 = 8,590,000 (into kg’s)

 

8,590,000 x $1 = $8,590,000 (into $).

 

That was for the rice, now for the gold:

 

75 x 1000 = 75000 (into kg)

 

75000 x $12 = $900,000.

 

As you can clearly see the rice is worth more by $7690000, this is the way you set it and answer it, if you need anymore help JUST ASK, gl.

[smacker124]

Not sure how I got to the solutions that I orignally stated. Thanks for wolfson, I'm not sure what the correct solution is but I'll find out in a few week thanks again everyone.

[Mark]

hi i know this question. its related to this theory. the number keeps doubling itself. so i guesse you will have to take a calculater. and keep multiplying your result by 2 till you have done it till you have done it 36 times

[wolfson]

Mark, this question is related to tn = ar^n-1, for a geometric progression, you should not "just jeep doubling it", try and use equations to help minimize time.