Mathematician's Sons

Two promenant mathematicians are corresponding by mail.

The first writes: "I have 3 sons and I want you to determine their ages. Once a week you will get a clue. When you know what their ages are let me know and I'll send you a bottle of scotch. The first clue is that the sum of their ages is 13".

No response.

"The second clue is that the product of their ages is your age."

No response.

"The third clue is that my oldest son weights 65 pounds".

The second mathematician then responded with the answer and claimed the scotch.

How old are the first mathematician's three sons?

Originally posted by camilli
Two promenant mathematicians are corresponding by mail.

The first writes: "I have 3 sons and I want you to determine their ages. Once a week you will get a clue. When you know what their ages are let me know and I'll send you a bottle of scotch. The first clue is that the sum of their ages is 13".

No response.

"The second clue is that the produc ...[text shortened]... the answer and claimed the scotch.

How old are the first mathematician's three sons?

Am I missing something here? There are several possible answers. 😕 It's not unheard of kids with these ages with that weight... The oldest father is also much older than the implied age here.

At least:
6 5 2
7 4 2
7 5 1
8 3 2
8 4 1
9 3 1

Nope

You are missing something here. Problem is correctly stated.

Ok, it's 9 2 2. 😏

Good one.

Originally posted by camilli
You are missing something here. Problem is correctly stated.

9,2,2 is correct. I'll leave it to someone else to explain why.

We know from the fact that it took the second mathematician three clues to solve it that his age must be a number expressible in at least two ways as a product of integers summing to 13, so he's 36 (6,6,1 or 9,2,2). The fact that there is an oldest rules out the first possibility.

The answer to this is that the first two clues do not give a unique answer but the third clue eliminates one of the possible answers because it implies that there is an eldest son, i.e. the oldest two children are not twins. Hence a solution like "6, 6, 1" is eliminated.

I've got two problems with this.

Firstly, twins aren't born at exactly the same time (that would be very painful for the mother) and it is normal to refer to an older and younger twin, even though they were born just minutes apart.

Secondly, since the clues are being given at one week intervals, there is a good chance that the age of at least one child could increase during the time period covered. For example, when the first clue was given their ages might have been 8, 4, 1 (summing to 13) and then a week later their ages might be 9, 4, 1 (the product of which is 36) so many solutions might be possible.

Originally posted by camilli
9,2,2 is correct. I'll leave it to someone else to explain why.

Originally posted by Fat Lady
The answer to this is that the first two clues do not give a unique answer but the third clue eliminates one of the possible answers because it implies that there is an eldest son, i.e. the oldest two children are not twins. Hence a solution like "6, 6, 1" is eliminated.

I've got two problems with this.

Firstly, twins aren't born at exactly the same t ...[text shortened]... ood chance that the age of at least one child could increase during the time period covered.

Originally posted by Fat Lady
The answer to this is that the first two clues do not give a unique answer but the third clue eliminates one of the possible answers because it implies that there is an eldest son, i.e. the oldest two children are not twins. Hence a solution like "6, 6, 1" is eliminated.

I've got two problems with this.

Firstly, twins aren't born at exactly the same t ...[text shortened]... heir ages might be 9, 4, 1 (the product of which is 36) so many solutions might be possible.