- 01 Apr '09 14:46Two 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? - 01 Apr '09 15:01

ehm .. 10, 2 and 1 years old?*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? - 01 Apr '09 15:51 / 1 editThe 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. - 01 Apr '09 15:54

Just replace "age" with "floor of age in years" in the post, then, if that sort of thing makes you unhappy, and assume none had a birthday between the posing and the answering of the first mathematician's question.*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. - 01 Apr '09 16:55 / 1 edit

Anal retentiveness can ruin a lot of things.*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.