three girls age

there are three girls, the product of their ages is 36 and the sum of their ages is their apartment number. The eldest girl hair is red color, can you guess the ages of the girls ? thank you

The red haired beauty and her two younger sisters live in Apartment 145. the six month old twins and their 'big sis' are renowned in the neighbourhood, but not so much as their parents......

or was there supposed to be a unique solution?

Cheers,

There is additional information given in the original puzzle which enables someone to guess their ages. One person is talking to another. The first person knows the girl's ages and the second is trying to guess their ages. After the first person states that the product of their ages is 36 (or another number, depending on the version of the puzzle), the first person states that they can't determine their ages. At this point, the reader is expected to list all possible ways three ages can have a product of 36 ({1,1,36}, {1,2,18}, (2,2,9}, etc.). Note that the reader must assume that the ages are whole numbers (e.g., a six month old baby isn't allowed), and if two are the same age, neither is older. Then the first person tells the second that the sum of their ages is a certain number, like an apartment number. The apartment number isn't revealed to the reader, but it is to the second person. The second person states that they still can't can't determine their ages. This means that certain combinations can be eliminated. For example, the apartment number couldn't be 38, since the only combination that sums to 38 is {1,1,36}, and the second person *could* determine the girl's ages. Since the second person couldn't determine the ages, the reader knows that the apartment number isn't 38. The first person then tells the second that the eldest has red hair. This is supposed to mean that the two older girl's are not the same age. This allows the second person to know the girl's ages. Using the fact that the second person can now determine the girl's ages, the reader can determine which apartment number (sum) the second person must have seen.

Carl G.

yep it was me who posted the original puzzle and the two guys were in a plane trying to kill time -a

. . . . . . . . . . . . . . . . . . . . and the two combinations are . . . . . . . . . . . . . . . . 1, 6, 6 and 9, 4, 4 since their product is 36 and the sum is 13 so 13 is the apartment number

the next clue is 'oldest' daughter so she has to be 9 -a

I figured that the word 'eldest' was the crucial clue. Of course, you must mean (2,2,9). So this poster must've forgotten to mention that the sum is13, although the puzzle is too easy in that form, anyhow.

Sorry to be tedious, but nobody in the current thread seems to have come up with the standard objection that if the ages were 6,6,1, then one of the 6 year olds could easily be say 11 months older than the other one. That is not even particularly unlikely. In that case, she would be referred to as the oldest or eldest (does anyone know the difference?).

For that reason, I have never found this a very satisfactory puzzle - it seems to me that a good puzzle should not be subject to attack by perfectly reasonable quibbles.

Derek Holt.

No, I agree, I've never liked it either because of the eldest child referrence as being the decisive clue. For the reason you state above and also even twins have an 'eldest' one.