I will collect here my questions. I have now enough to make a thread of them.

Feel free to add your own 6th grader questions.

Are you smarter than a sixth grader? Part I
In a southern town 80% of people speak English, 70% of people speak Spanish, and 60% of people speak Cajun. Everybody speaks at least 2 of these languages. What % of the people in the town speak all 3 languages?


The first correct solution came from tkgprog

Are you smarter than a sixth grader? Part II
A six digit number's first digit is 1. If we move this 1 from the beginning of the number to the end we get a 3 times larger number.
What is the sum of the digits of this number?


The first correct solution came from maven.

Are you smarter than a sixth grader? Part III
What is the greatest common factor of

and
2009?

No correct solutions yet.

Are you smarter than a sixth grader? Part IV

If two prime numbers' difference is 2009, how many divisors does their sum have?

Are you smarter than a 6th grader? Part V
"If nine stoves burn twelve cubic meters of pine in five and a half hours - how long does it take to burn nine cubic meters of pine in twelve stoves?"
-- I teach my child by Karinthy, Frigyes

And more importantly how long will it take Greenpeace to come and tell you not to burn beech anymore but stick with pine?

(I knew a guy who had a farm full of ash trees and did not want to have them cut for any reason. Anytime someone would come and off him lumber money, he would turn them away saying he used it as firewood. Oh the looks he got!)

Also my guess without really trying is 9.75 days.

Guess again.

I fixed the tree issue. It is pine now, and so I had to adjust the time too from days to hours.

5.5

That is closer.

approximately 3.11 hours?

About 3 hours and 5 minutes?

8?

Ok, I think the answer is 2009.

Why? Because 2009 is a factor of 2009. 2009 is a factor of 2009^2. And 2009 is a factor of 2^63. That means that 2009 is also a factor of 2^(63+n) where n is a positive integer. Therefore, 2009 is a factor of 2009, 2009^2, and 2^2009. This also means that 2009 is a factor of (2009^2 + 2^2009). Thus, considering that 2009 is the highest factor of 2009, and it is also a factor of the equation, 2009 must be the Greatest Common Factor of (2009^2 + 2^2009) and 2009.

2009^2 = 7^4*41^2

So the prime factors of 2009^2 are 7 and 41. Obviously the only prime factor of 2^2009 is 2. Since the numbers do not share any prime factors the greatest common factor must be 1.

And guess what? I think that these problems are higher than the average 6th grade curriculum.

Assuming the stoves burn wood at a constant rate we can create a formula quite easily.

Let S=# of stoves, P=Cubic Meters of Pine, T=time in hours and X=Cubic Meters of pine one stove burns in one hour.

then P=S*X*T

Plugging in the first numbers
12 = 9 * X * 5.5
X=8/33

And with the second numbers
9 = 12 * (8/33) * T
T=3.09375hrs

Which translates to about 3 hours and 5 minutes

EDIT: I really have nothing better to do here...god my job is boring

You still fail. The question was how long to burn that much BEECH.

Actually you fail lol ;)

No.

piffle