1. ## Can someone please check my answers for the following difficult word problems?

How many regions is a sphere divided into by four great circles, where no more than 2 great circles intersect at any single point?

$14$

2. Hello, Macleef!

I'm still trying to visualize the third one . . .

3. The last question seems a bit ambiguous. I get an answer of nine.

4. A census taker came back to a house where a man lived with his three children. The census taker asked, "What is your house number?" The man replied, "The product of my children's ages is 72 and the sum of their ages is my house number." "But that's not enough information," the census taker insisted. "All right," answered the farmer, "the oldest loves cherry pie.

What is the farmer's house number?

Is the answer for this problem 14 or 15?

5. Hello, Macleef!

You've scrambled the statement of the problem.
As you have given it, there is no single solution.

The classic "Census Taker Problem goes like . . .
[
A census taker asked a man, "How old are your three children?"
The man said, "The product of their ages is 72 and the sum is my house number.
The census taker looked at the house number, did some calculations,
then said, "That's not enough information."
The man said, "All right, the oldest loves cherry pie."

How old are his children?

Try it now . . .

6. Originally Posted by Soroban
Hello, Macleef!

You've scrambled the statement of the problem.
As you have given it, there is no single solution.

The classic "Census Taker Problem goes like . . .
[

Try it now . . .

No, it's not about finding the children's ages, it's about finding the house number where the man lives.

7. Originally Posted by Macleef
A census taker came back to a house where a man lived with his three children. The census taker asked, "What is your house number?" The man replied, "The product of my children's ages is 72 and the sum of their ages is my house number." "But that's not enough information," the census taker insisted. "All right," answered the farmer, "the oldest loves cherry pie.

What is the farmer's house number?

Is the answer for this problem 14 or 15?
Hello,

since the farmer didn't mentioned that he has twins I assume that the children are of different age.

Calculate the prime factors of 72:

$72=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$

Now collect these factors in 3 groups:
$72=\left \{ \begin{array}{l}2 \cdot 3 \cdot 12 \\ 2 \cdot 4 \cdot 9 \\2 \cdot 6 \cdot 6\ \longleftarrow\ twins \\2 \cdot 2 \cdot 18\ \longleftarrow\ twins\\4 \cdot 6 \cdot 3\\8 \cdot 3 \cdot 3\ \longleftarrow\ twins\end{array}\right.$

As you see there are only three possible solutions: (2, 3, 12), (2, 4, 9) and (3, 4, 6)

I don't know up to which age it is forbidden for children to eat cherry-pie (I probably never have eaten a cherry-pie) but since the farmer refers to his oldest child my first choice would be the first solution because I know what a mess children of 6 or 9 years can make of their meals.

I would say the house number is 17.

8. ## The Age of Father's Daughters

Hi actually I didn't get how did you solve the question. (The Age of the Father Daughters) because I didn't see enough reason for that, As the people wrote there are three possibilities to answer it.

72= 2.2.2.3.3

2.4.9 sum= 15
2.3.12 sum=17
4.6.3 sum=13